# Weeding out the Dealers? The Economics of Cannabis Legalization

Emmanuelle Auriol, Alice Mesnard, Tiffanie Perrault

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Emmanuelle Auriol, Alice Mesnard, Tiffanie Perrault. Weeding out the Dealers? The Economics of Cannabis Legalization. Journal of Economic Behavior and Organization, 2023, 216, pp.62-101. 10.1016/j.jebo.2023.09.027. hal-04234940

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October 2023

# “Weeding out the Dealers?
The Economics of Cannabis Legalization”

Emmanuelle Auriol, Alice Mesnard and Tiffanie Perrault
October 2023

# “Weeding out the Dealers?
The Economics of Cannabis Legalization”

Emmanuelle Auriol, Alice Mesnard and Tiffanie Perrault
Weeding out the Dealers?

The Economics of Cannabis Legalization*

Emmanuelle Auriol†, Alice Mesnard‡, Tiffanie Perrault§

March 30, 2023

Abstract

We model consumer choices for recreational cannabis in a risky environment and its supply under prohibition and legalization. While legalization reduces the profits of illegal providers, it increases cannabis consumption. This trade-off can be overcome by combining legalization with sanctions against the black market, and improvements to the quality of legal products. Numerical calibrations highlight how a policy mix can control the increase in cannabis consumption and throttle the illegal market. In the US, the eviction prices we predict to drive dealers out of business are much lower than the prices of legal cannabis in most of the states that opted for legalization, leaving room for the black market to flourish. Analyzing the compatibility of several policy goals sheds light on the less favorable outcomes of recent legalization reforms and suggests a new way forward.

JEL Classifications : I18, K32, K42, L51

Keywords : recreational cannabis, legalization, crime, policy, regulation

<footnote>*We thank Antonio Estache, Brett Hollenbeck, Pierre-Yves Geoffard, Jeffrey Miron, Sylvaine Poret, Tina Soreide, Jean Tirole and participants at seminars in Paris, Toulouse and Montreal, at the 6th International Meeting in Law and Economics, at the 2019 annual congresses of the Canadian Economics Association and the Société Canadienne de Science Economique, at the 5th DIAL Development conference and at the 13th conference of the International Society for the Study of Drug Policy in Paris for their valuable feedback and constructive comments. We are grateful to the editor, one associate editor of the journal and a referee for their suggestions, which greatly improved the paper. Emmanuelle Auriol acknowledges TSE-IAST funding from the French National Research Agency (ANR) under the Investments for the Future (Investissements d'Avenir) program, grant ANR-17-EURE-0010. All remaining errors are ours.</footnote>

<footnote>†Toulouse School of Economics and CEPR</footnote>

<footnote>‡City, University of London</footnote>

<footnote>§Department of Economics, McGill University</footnote>
# Weeding out the Dealers?
## The Economics of Cannabis Legalization*

Emmanuelle Auriol†, Alice Mesnard‡, Tiffanie Perrault§

March 30, 2023

### Abstract

We model consumer choices for recreational cannabis in a risky environment and its supply under prohibition and legalization. While legalization reduces the profits of illegal providers, it increases cannabis consumption. This trade-off can be overcome by combining legalization with sanctions against the black market, and improvements to the quality of legal products. Numerical calibrations highlight how a policy mix can control the increase in cannabis consumption and throttle the illegal market. In the US, the eviction prices we predict to drive dealers out of business are much lower than the prices of legal cannabis in most of the states that opted for legalization, leaving room for the black market to flourish. Analyzing the compatibility of several policy goals sheds light on the less favorable outcomes of recent legalization reforms and suggests a new way forward.

JEL Classifications: I18, K32, K42, L51

Keywords: recreational cannabis, legalization, crime, policy, regulation

<footnote>*We thank Antonio Estache, Brett Hollenbeck, Pierre-Yves Geoffard, Jeffrey Miron, Sylvaine Poret, Tina Soreide, Jean Tirole and participants at seminars in Paris, Toulouse and Montreal, at the 6th International Meeting in Law and Economics, at the 2019 annual congresses of the Canadian Economics Association and the Société Canadienne de Science Economique, at the 5th DIAL Development conference and at the 13th conference of the International Society for the Study of Drug Policy in Paris for their valuable feedback and constructive comments. We are grateful to the editor, one associate editor of the journal and a referee for their suggestions, which greatly improved the paper. Emmanuelle Auriol acknowledges TSE-IAST funding from the French National Research Agency (ANR) under the Investments for the Future (Investissements d'Avenir) program, grant ANR-17-EURE-0010. All remaining errors are ours.</footnote>

<footnote>†Toulouse School of Economics and CEPR</footnote>

<footnote>‡City, University of London</footnote>

<footnote>§Department of Economics, McGill University</footnote>
# 1 Introduction

Prohibition policies, which target suppliers or consumers of illegal cannabis, are not effective at controlling demand. With 192 million users, cannabis is the most popular illegal recreational drug on earth. It accounts for half of global drug seizures and represents a black market worth 142 billion dollars (UNODC, 2017, 2018). Prohibition has failed to curb consumption and has fueled criminal activities. Drug dealing is the first source of revenue for organized crime and destabilizes the political economy of drug-producing countries while generating criminality in drug-consuming ones. Barro (2003) argues that legalizing and taxing drugs in advanced economies is a more effective way of controlling the drug market than prohibition. Meanwhile, cannabis is less addictive and less deadly than other psychotropic substances.<fnref n="1" /> As a result, governments from advanced and developing countries have decided to legalize the recreational use of cannabis. Reforms vary widely from one country/state to the next and reflect different priorities, such as protecting the youth, improving the quality of the products consumed by adults, creating new legal jobs, or raising taxes. However, all reforms share the common goal of reducing criminal activity.

This article investigates theoretically the different ways legalization can be implemented to reach this objective. We explore a legalization policy aimed at strangling the illegal cannabis market through predatory pricing. We examine its impact on several key aspects affecting drug use, including product quality and price, and analyze how defeating crime may conflict with other objectives, such as raising taxes or decreasing consumption. Our analysis highlights a policy trade-off: although a smart legalization reform at predatory pricing may undermine the profits from illegal providers, it also increases cannabis use, which is a sensitive issue politically. In contrast, prohibition decreases cannabis consumption but strengthens the illegal market and fuels criminality. By illuminating this trade-off, our analysis warns policy makers against the unintended consequences of legalization reforms if they neglect the black market responses or if they pursue incompatible objectives.

One simple idea advocated by several politicians, notably in Canada, is to sell legal cannabis at a price that competes with the price on the black market *pre-legalization*. The analysis shows that this will not be sufficient to eliminate the black market. Prohibition creates barriers to entry, which foster the concentration of the market in the hands of criminal organizations. These networks are able to respond to the legal competition by lowering their price and still make a profit. In this case, cannabis legalization increases consumption of “low-cost” illegal cannabis, with all the negative externalities this entails for society. Furthermore, policy makers have often in the past underestimated consumers’

<footnote n="1">¹According to a 2017 meta analysis study of more than 10,000 articles, there are no proven serious adverse effects of moderate cannabis use on the health of adults. It is almost impossible to overdose with cannabis (see Nat. Ac. of Sc., 2017).</footnote>
# 1 Introduction

Prohibition policies, which target suppliers or consumers of illegal cannabis, are not effective at controlling demand. With 192 million users, cannabis is the most popular illegal recreational drug on earth. It accounts for half of global drug seizures and represents a black market worth 142 billion dollars (UNODC, 2017, 2018). Prohibition has failed to curb consumption and has fueled criminal activities. Drug dealing is the first source of revenue for organized crime and destabilizes the political economy of drug-producing countries while generating criminality in drug-consuming ones. Barro (2003) argues that legalizing and taxing drugs in advanced economies is a more effective way of controlling the drug market than prohibition. Meanwhile, cannabis is less addictive and less deadly than other psychotropic substances.<fnref n="1" /> As a result, governments from advanced and developing countries have decided to legalize the recreational use of cannabis. Reforms vary widely from one country/state to the next and reflect different priorities, such as protecting the youth, improving the quality of the products consumed by adults, creating new legal jobs, or raising taxes. However, all reforms share the common goal of reducing criminal activity.

This article investigates theoretically the different ways legalization can be implemented to reach this objective. We explore a legalization policy aimed at strangling the illegal cannabis market through predatory pricing. We examine its impact on several key aspects affecting drug use, including product quality and price, and analyze how defeating crime may conflict with other objectives, such as raising taxes or decreasing consumption. Our analysis highlights a policy trade-off: although a smart legalization reform at predatory pricing may undermine the profits from illegal providers, it also increases cannabis use, which is a sensitive issue politically. In contrast, prohibition decreases cannabis consumption but strengthens the illegal market and fuels criminality. By illuminating this trade-off, our analysis warns policy makers against the unintended consequences of legalization reforms if they neglect the black market responses or if they pursue incompatible objectives.

One simple idea advocated by several politicians, notably in Canada, is to sell legal cannabis at a price that competes with the price on the black market *pre-legalization*. The analysis shows that this will not be sufficient to eliminate the black market. Prohibition creates barriers to entry, which foster the concentration of the market in the hands of criminal organizations. These networks are able to respond to the legal competition by lowering their price and still make a profit. In this case, cannabis legalization increases consumption of “low-cost” illegal cannabis, with all the negative externalities this entails for society. Furthermore, policy makers have often in the past underestimated consumers’

<footnote n="1">¹According to a 2017 meta analysis study of more than 10,000 articles, there are no proven serious adverse effects of moderate cannabis use on the health of adults. It is almost impossible to overdose with cannabis (see Nat. Ac. of Sc., 2017).</footnote>
needs and choices. Examples include shortage and low quality of products sold on the legal market following the reforms in Uruguay and Canada, as well as new requirements for getting a medical card and high taxes on recreational products in California. This turned users of cannabis to the illegal market, in contradiction with the initial objectives of the reforms.<fnref n="2" />

After exploring case-studies of recent legalization reforms, we embed their several objec-
tives in a unified framework and analyze their compatibility. Our findings complement the
flourishing literature on cannabis legalization. As reviewed in section 2, this literature is
mainly empirical and focuses on the impacts of legalization on specific areas, such as crime,
drug use among the young/adult, public finance. Our paper contributes to the literature by
providing a theoretical framework to analyze the highlighted pitfalls, as well as a strategy
to avoid them when designing future cannabis legalization policies, which include choosing
the price and quality of cannabis sold on the legal market.

We model the demand for cannabis from risk averse individuals in a general framework encompassing both Tversky and Kahneman (1992)'s cumulative prospect theory (CPT) and expected utility theory (EUT), which establishes the robustness of our results. Our use of CPT is consistent with agents' behavior considering risky gambles (for a literature review see Barberis and Thaler, 2003; DellaVigna, 2009; Barberis, 2013).<fnref n="3" /> If the sale of cannabis is illegal, consumers weigh the benefits of consumption against the risk and costs of participating in an illegal trade where the price is determined by illegal providers who maximize their profits. To crowd out illegal suppliers, we show that a government must set a low enough price for legal cannabis such that dealers reach their marginal cost if they attempt to keep some customers. They are therefore forced out of the market at this "eviction price". The consequence of this predatory pricing strategy is a sharp increase in cannabis consumption: the demand for cannabis post-legalization is equal to the demand of cannabis that would prevail if the dealers were behaving competitively. This increase in consumption of psychoactive substances resulting from legalization is opposed by a large portion of society and hence problematic politically. To overcome this issue, we examine a policy mix that combines pricing regulation – to limit consumption post-legalization – with sanctions against illegal trade – to push criminals out of the market through the sale of legal cannabis. We show that the eviction price for legal cannabis can be adjusted by penalties and marketing tools. In particular, our analysis shows that investment in quality of legal cannabis is an effective instrument for controlling the demand following legalization

<footnote n="2">²See: Fueller, Thomas. 2019. "Getting Worse, Not Better: Illegal Pot Market Booming in California Despite Legalization". *New-York Times*. April 17. https://www.nytimes.com/2019/04/27/us/marijuana-california-legalization.html</footnote>

<footnote n="3">³This theory is the most prominent among non-expected utility theories and provides realistic predictions for individual behavior when confronted to risky choices, both inside (Glöckner and Betsch, 2008; Baltussen et al., 2016) and outside (Barberis et al., 2016; Post et al., 2008) the lab.</footnote>
needs and choices. Examples include shortage and low quality of products sold on the legal market following the reforms in Uruguay and Canada, as well as new requirements for getting a medical card and high taxes on recreational products in California. This turned users of cannabis to the illegal market, in contradiction with the initial objectives of the reforms.<fnref n="2" />

After exploring case-studies of recent legalization reforms, we embed their several objec-
tives in a unified framework and analyze their compatibility. Our findings complement the
flourishing literature on cannabis legalization. As reviewed in section 2, this literature is
mainly empirical and focuses on the impacts of legalization on specific areas, such as crime,
drug use among the young/adult, public finance. Our paper contributes to the literature by
providing a theoretical framework to analyze the highlighted pitfalls, as well as a strategy
to avoid them when designing future cannabis legalization policies, which include choosing
the price and quality of cannabis sold on the legal market.

We model the demand for cannabis from risk averse individuals in a general framework encompassing both Tversky and Kahneman (1992)'s cumulative prospect theory (CPT) and expected utility theory (EUT), which establishes the robustness of our results. Our use of CPT is consistent with agents' behavior considering risky gambles (for a literature review see Barberis and Thaler, 2003; DellaVigna, 2009; Barberis, 2013).<fnref n="3" /> If the sale of cannabis is illegal, consumers weigh the benefits of consumption against the risk and costs of participating in an illegal trade where the price is determined by illegal providers who maximize their profits. To crowd out illegal suppliers, we show that a government must set a low enough price for legal cannabis such that dealers reach their marginal cost if they attempt to keep some customers. They are therefore forced out of the market at this "eviction price". The consequence of this predatory pricing strategy is a sharp increase in cannabis consumption: the demand for cannabis post-legalization is equal to the demand of cannabis that would prevail if the dealers were behaving competitively. This increase in consumption of psychoactive substances resulting from legalization is opposed by a large portion of society and hence problematic politically. To overcome this issue, we examine a policy mix that combines pricing regulation – to limit consumption post-legalization – with sanctions against illegal trade – to push criminals out of the market through the sale of legal cannabis. We show that the eviction price for legal cannabis can be adjusted by penalties and marketing tools. In particular, our analysis shows that investment in quality of legal cannabis is an effective instrument for controlling the demand following legalization

<footnote n="2">²See: Fueller, Thomas. 2019. "Getting Worse, Not Better: Illegal Pot Market Booming in California Despite Legalization". *New-York Times*. April 17. https://www.nytimes.com/2019/04/27/us/marijuana-california-legalization.html</footnote>

<footnote n="3">³This theory is the most prominent among non-expected utility theories and provides realistic predictions for individual behavior when confronted to risky choices, both inside (Glöckner and Betsch, 2008; Baltussen et al., 2016) and outside (Barberis et al., 2016; Post et al., 2008) the lab.</footnote>
reforms.

Since legalization reforms have generally multiple objectives, we then embed in our theo-
retical framework a larger set of policy objectives than drying up the illegal market. We show
that prohibition policies are optimal only if a government seeks to minimize total consump-
tion of cannabis and neglects other objectives, such as minimizing the enforcement costs
of prohibition. We also show that reducing crime through a regulated market of cannabis
sold at the eviction price is compatible with the maximization of consumers’ surplus, the
minimization of enforcement costs of repression measures, and with the minimization of
negative externalities from illegal cannabis consumption. In contrast, the maximization of
tax revenues generally leads to the co-existence of legal and illegal markets.

Based on evidence from cannabis markets in the U.S., we next calibrate our model
to show its relevance and its usefulness in designing effective legalization policies through
counter-factual analysis. Our policy simulations compute eviction prices and the subsequent
increases in cannabis use for the US market. In our baseline scenario with a 0.1% probability
of arrest and a USD 1,000 fine for illegal purchase, a legal price around USD 98 per ounce
would evict illegal suppliers and increase consumption by 53% to 91%, depending on the
elasticity of demand. This is in line with the legalization experiences of Colorado and
Oregon, where relatively low prices for legal cannabis – around USD 135 per ounce – diverted
consumers from the black market but increased consumption by almost 60%. The policy
simulations also highlight the complementarities between the different instruments. For
example, not enforcing repression against illegal providers would allow them to compete
fiercely and push the eviction price of cannabis down to USD 42, increasing consumption
*post-legalization* by 64% to 111%. Interestingly, if a government’s objective is to limit the
increase in consumption *post-legalization*, the eviction price can be adjusted by improving
the quality of legal cannabis relative to illegal products. Doubling consumers’ relative
valuation of legal products as compared to illegal ones (for example through information
campaigns about the dangers of using illegal products, R&D and marketing investments
in legal products) would push the eviction price of cannabis up to USD 186, limiting the
increase in consumption to range between 37% and 63%. This “quality” channel has been
neglected by most authorities, including in Canada and Uruguay. Yet, our simulations
show that it is effective to modulate the eviction price and, thereby, to control consumption
*post-legalization*.

The rest of the paper is organized as follows. In section 2 we describe the evolution
of the regulation of recreational cannabis markets and review the empirical literature on
the impact of legalization measures. In section 3 we present the set-up of the model, which
explains the illegal market structure under status quo (prohibition). In section 4 we analyze
how to combine a legal market with measures targeting consumers and suppliers to drive
reforms.

Since legalization reforms have generally multiple objectives, we then embed in our theo-
retical framework a larger set of policy objectives than drying up the illegal market. We show
that prohibition policies are optimal only if a government seeks to minimize total consump-
tion of cannabis and neglects other objectives, such as minimizing the enforcement costs
of prohibition. We also show that reducing crime through a regulated market of cannabis
sold at the eviction price is compatible with the maximization of consumers’ surplus, the
minimization of enforcement costs of repression measures, and with the minimization of
negative externalities from illegal cannabis consumption. In contrast, the maximization of
tax revenues generally leads to the co-existence of legal and illegal markets.

Based on evidence from cannabis markets in the U.S., we next calibrate our model
to show its relevance and its usefulness in designing effective legalization policies through
counter-factual analysis. Our policy simulations compute eviction prices and the subsequent
increases in cannabis use for the US market. In our baseline scenario with a 0.1% probability
of arrest and a USD 1,000 fine for illegal purchase, a legal price around USD 98 per ounce
would evict illegal suppliers and increase consumption by 53% to 91%, depending on the
elasticity of demand. This is in line with the legalization experiences of Colorado and
Oregon, where relatively low prices for legal cannabis – around USD 135 per ounce – diverted
consumers from the black market but increased consumption by almost 60%. The policy
simulations also highlight the complementarities between the different instruments. For
example, not enforcing repression against illegal providers would allow them to compete
fiercely and push the eviction price of cannabis down to USD 42, increasing consumption
*post-legalization* by 64% to 111%. Interestingly, if a government’s objective is to limit the
increase in consumption *post-legalization*, the eviction price can be adjusted by improving
the quality of legal cannabis relative to illegal products. Doubling consumers’ relative
valuation of legal products as compared to illegal ones (for example through information
campaigns about the dangers of using illegal products, R&D and marketing investments
in legal products) would push the eviction price of cannabis up to USD 186, limiting the
increase in consumption to range between 37% and 63%. This “quality” channel has been
neglected by most authorities, including in Canada and Uruguay. Yet, our simulations
show that it is effective to modulate the eviction price and, thereby, to control consumption
*post-legalization*.

The rest of the paper is organized as follows. In section 2 we describe the evolution
of the regulation of recreational cannabis markets and review the empirical literature on
the impact of legalization measures. In section 3 we present the set-up of the model, which
explains the illegal market structure under *status quo* (prohibition). In section 4 we analyze
how to combine a legal market with measures targeting consumers and suppliers to drive
smugglers out of business and regulate cannabis consumption. In section 5 we enlarge the set of policy objectives to shed more light on current policies. In section 6 we calibrate the model based on evidence from the U.S. cannabis market and study its policy implications before concluding in section 7.

## 2 Legalization of recreational cannabis: an overview of policy impacts

In response to an increase in cannabis use, the seventies were characterized by a wave of decriminalization measures. In the United-States, possessing small amounts (usually up to 1 ounce) of cannabis was declassified to a misdemeanor in eleven states and Alaska declared possession of small amounts of cannabis to be protected under the state constitutional right to privacy (see appendix A for a chronology of cannabis laws across states in the US). Across the Atlantic, the Netherlands took a bold step by making cannabis available for recreational use in coffee shops. However, the attempts to legalize cannabis more generally stalled with the *War on Drugs* launched by Ronald Reagan in the eighties. Rising concerns about the legitimacy and efficacy of this war led to a second wave of decriminalization and the first laws in favor of medical use in the U.S. at the end of the nineties. This liberalization movement accelerated in the last decade.

In 2012, Uruguay was the first country to legalize recreational cannabis with the aim to counter drug-related crime. The same year, Colorado and Washington states passed bills legalizing recreational use of cannabis, following popular referendums. From 2014 onward, seventeen other states and the District of Columbia followed in the US (see appendix A), and in 2018, Canada, South Africa and Georgia also changed their legislation in favor of legalizing recreational cannabis. Legalization policies implemented so far are diverse.

In Uruguay, a state monopoly was created. It delegated the production of cannabis to strictly regulated private companies, which led to a sluggish implementation and penury. To eradicate the black market, Uruguay had initially set the price of legal cannabis at the same level as the black market. However, the government's attempt to control consumption led to a severe underestimation of the size of the market and rationing.<fnref n="4" /> Thus, several years after legalization, a majority of consumers continue to turn to the black market for their consumption, defeating the initial objective of the reform.

<footnote n="4">⁴By the end of 2017, only two producers were approved for an annual volume of one ton each, while the market has been estimated at between 35 and 40 tons. In addition, the hostility of pharmacists, charged by the state to sell cannabis, has made it more difficult and unpleasant for users to obtain supplies. The authorization of self-cultivation or small producers' clubs, also tightly limited and regulated, has not compensated for the inadequacy of the public supply. See: González, Eric. 2018. "Uruguay loses momentum in the marijuana legalization stakes". *El País*. October 17. https://english.elpais.com/elpais/2018/10/16/inenglish/1539687522_144922.html</footnote>
smugglers out of business and regulate cannabis consumption. In section 5 we enlarge the set of policy objectives to shed more light on current policies. In section 6 we calibrate the model based on evidence from the U.S. cannabis market and study its policy implications before concluding in section 7.

## 2 Legalization of recreational cannabis: an overview of policy impacts

In response to an increase in cannabis use, the seventies were characterized by a wave of decriminalization measures. In the United-States, possessing small amounts (usually up to 1 ounce) of cannabis was declassified to a misdemeanor in eleven states and Alaska declared possession of small amounts of cannabis to be protected under the state constitutional right to privacy (see appendix A for a chronology of cannabis laws across states in the US). Across the Atlantic, the Netherlands took a bold step by making cannabis available for recreational use in coffee shops. However, the attempts to legalize cannabis more generally stalled with the *War on Drugs* launched by Ronald Reagan in the eighties. Rising concerns about the legitimacy and efficacy of this war led to a second wave of decriminalization and the first laws in favor of medical use in the U.S. at the end of the nineties. This liberalization movement accelerated in the last decade.

In 2012, Uruguay was the first country to legalize recreational cannabis with the aim to counter drug-related crime. The same year, Colorado and Washington states passed bills legalizing recreational use of cannabis, following popular referendums. From 2014 onward, seventeen other states and the District of Columbia followed in the US (see appendix A), and in 2018, Canada, South Africa and Georgia also changed their legislation in favor of legalizing recreational cannabis. Legalization policies implemented so far are diverse.

In Uruguay, a state monopoly was created. It delegated the production of cannabis to strictly regulated private companies, which led to a sluggish implementation and penury. To eradicate the black market, Uruguay had initially set the price of legal cannabis at the same level as the black market. However, the government's attempt to control consumption led to a severe underestimation of the size of the market and rationing.<fnref n="4" /> Thus, several years after legalization, a majority of consumers continue to turn to the black market for their consumption, defeating the initial objective of the reform.

<footnote n="4">⁴By the end of 2017, only two producers were approved for an annual volume of one ton each, while the market has been estimated at between 35 and 40 tons. In addition, the hostility of pharmacists, charged by the state to sell cannabis, has made it more difficult and unpleasant for users to obtain supplies. The authorization of self-cultivation or small producers' clubs, also tightly limited and regulated, has not compensated for the inadequacy of the public supply. See: González, Eric. 2018. "Uruguay loses momentum in the marijuana legalization stakes". *El País*. October 17. https://english.elpais.com/elpais/2018/10/16/inenglish/1539687522_144922.html</footnote>
In Colorado and Washington states, the reforms have been market oriented, with a clear focus on consumers’ needs and taxation. Ten years after legalization, both states are pleased with these reforms: public finances are thriving and cannabis users have access to abundant and diverse products of quality. In Canada, retail sale of cannabis is legal although the policies vary across provinces, from Québec’s government monopoly to Alberta’s privately run stores, with mixed results. Section 6 discusses the effects of legalization reforms in North America and their pitfalls in light of our theory.

Based on these examples, the flourishing empirical literature we review below examines
the impact of legalization policies on a variety of outcomes.

**2.1 Impacts of legalization on crime and violence**

The first strand of the literature highlights the costs of drug prohibition, in terms of criminal activities and violence. Resignato (2000) shows that most drug-related violent crimes are the consequence of systemic factors linked to the War on Drugs rather than of psycho-pharmacological effects of drug use on crime. Indeed, prohibition increases incentives to engage in criminal behavior (MacCoun and Reuter, 2001). It promotes violence as almost the only way to resolve conflicts and secure market power, encouraging market strategies based on violence (Miron, 1999, 2003). This strengthens the concentration of the market and leads Miron and Zwiebel (1995) to conclude that a free market for drugs would probably outperform prohibition in terms of social costs. The social costs linked to prohibition are exacerbated by “zero-tolerance” policies, which may encourage users to hold higher quantities (Caulkins, 1993).

In line with these arguments, Dills et al. (2017) show that liberalizing cannabis across
US states did not lead to a rise in crime. Other evidence by Brinkman and Mok-Lamme
(2019) shows that overall crime in Colorado decreased in areas where cannabis dispensaries
were added. In particular, cannabis legalization could be responsible for a drop in local
rapes and property crimes (Dragone et al., 2019).

The benefits of legalization policies extend to organized crime. In the states bordering Mexico, legalization of cannabis for medical purposes has decreased drug-trafficking related crime (Morris et al., 2014; Gavrilova et al., 2019; Chang and Jacobson, 2017). Furthermore legalization policies have shrunk criminals’ profits, weakening their power. In Italy, a legislative loophole leading to an unintended liberalization of cannabis decreased revenues from cannabis sales on the black market by 90-170 million euros (Carrieri et al., 2019).
In Colorado and Washington states, the reforms have been market oriented, with a clear focus on consumers’ needs and taxation. Ten years after legalization, both states are pleased with these reforms: public finances are thriving and cannabis users have access to abundant and diverse products of quality. In Canada, retail sale of cannabis is legal although the policies vary across provinces, from Québec’s government monopoly to Alberta’s privately run stores, with mixed results. Section 6 discusses the effects of legalization reforms in North America and their pitfalls in light of our theory.

Based on these examples, the flourishing empirical literature we review below examines
the impact of legalization policies on a variety of outcomes.

**2.1 Impacts of legalization on crime and violence**

The first strand of the literature highlights the costs of drug prohibition, in terms of criminal activities and violence. Resignato (2000) shows that most drug-related violent crimes are the consequence of systemic factors linked to the War on Drugs rather than of psycho-pharmacological effects of drug use on crime. Indeed, prohibition increases incentives to engage in criminal behavior (MacCoun and Reuter, 2001). It promotes violence as almost the only way to resolve conflicts and secure market power, encouraging market strategies based on violence (Miron, 1999, 2003). This strengthens the concentration of the market and leads Miron and Zwiebel (1995) to conclude that a free market for drugs would probably outperform prohibition in terms of social costs. The social costs linked to prohibition are exacerbated by “zero-tolerance” policies, which may encourage users to hold higher quantities (Caulkins, 1993).

In line with these arguments, Dills et al. (2017) show that liberalizing cannabis across
US states did not lead to a rise in crime. Other evidence by Brinkman and Mok-Lamme
(2019) shows that overall crime in Colorado decreased in areas where cannabis dispensaries
were added. In particular, cannabis legalization could be responsible for a drop in local
rapes and property crimes (Dragone et al., 2019).

The benefits of legalization policies extend to organized crime. In the states bordering Mexico, legalization of cannabis for medical purposes has decreased drug-trafficking related crime (Morris et al., 2014; Gavrilova et al., 2019; Chang and Jacobson, 2017). Furthermore legalization policies have shrunk criminals’ profits, weakening their power. In Italy, a legislative loophole leading to an unintended liberalization of cannabis decreased revenues from cannabis sales on the black market by 90-170 million euros (Carrieri et al., 2019).
## 2.2 Impacts of legalization on drug consumption

Due to their prohibited nature, illicit drugs are difficult to access and of uncertain quality, adding substantial search costs for consumers (Galenianos et al., 2012). Using a structural approach, Jacobi and Sovinsky (2016) explore the idea that cannabis legalization reduces this cost and removes the stigma attached to illicit consumption. They find that legalizing recreational cannabis would increase its use by around 48%. This is supported by Miller et al. (2017), who use survey data on undergraduate students at Washington State University to show that cannabis legalization induced a rise in consumption early after being implemented. Moreover, the ease of access to licit drugs encourages individuals to start consuming cannabis earlier, as shown in the Netherlands by Palali and van Ours (2015).

Consumers react to the risk of being caught while buying cannabis illegally. Jacobson (2004) shows that lower probabilities to be arrested for cannabis possession increases consumption. So do policy changes involving lower sanctions (as suggested by Pacula et al., 2010), although the size and significance of such effects may vary across different population groups (Williams, 2004). Moreover, experiences of medical and recreational cannabis legalization in the US are correlated with rises in cannabis use. For example, Hunt et al. (2018) find that Marijuana Dispensary Laws in California are associated with a significant increase in driving under influence arrests. In this, cannabis is a normal good, with consumers sensitive to risk and costs variations.

In contrast to adult consumption, legalizing cannabis seems to decrease consumption among the young, provided legal retailers refuse to sell it to underage consumers. DiNardo and Lemieux (2001) do not find any effect of cannabis decriminalization on consumption among high school students, a result confirmed by a recent study in Oregon (Kerr et al., 2017). Furthermore, consumption of cannabis by teenagers is estimated to have decreased by 12% following legalization in the states of Washington and Colorado (SAMHSA, 2014). Finally, legalization does not seem to lead to the feared gateway effect on the use of other psychotropic substance (Dills et al., 2017). On the contrary, cannabis seems to act as a substitute for more powerful and addictive opioids (Powell et al., 2018).

## 2.3 Legalization and taxation

From a public policy viewpoint, legalization creates a new source of revenue through taxation (Caputo and Ostrom, 1994, 1996). For instance, the state of Colorado collected USD 325.1 million of tax and fee revenue in 2022 and the state of Washington collected USD 515.2 million in the same fiscal year.<fnref n="5" /> In the state of Washington, this tax revenue is

<footnote n="5">⁵See Washington State Treasurer at https://www.tre.wa.gov/portfolio-item/washington-state-marijuana-revenues-and-health/ and Colorado Department of Revenue at https://cdor.colorado.gov/data-and-reports/marijuana-data/marijuana-tax-reports, retrieved online on March 3, 2022.</footnote>
## 2.2 Impacts of legalization on drug consumption

Due to their prohibited nature, illicit drugs are difficult to access and of uncertain quality, adding substantial search costs for consumers (Galenianos et al., 2012). Using a structural approach, Jacobi and Sovinsky (2016) explore the idea that cannabis legalization reduces this cost and removes the stigma attached to illicit consumption. They find that legalizing recreational cannabis would increase its use by around 48%. This is supported by Miller et al. (2017), who use survey data on undergraduate students at Washington State University to show that cannabis legalization induced a rise in consumption early after being implemented. Moreover, the ease of access to licit drugs encourages individuals to start consuming cannabis earlier, as shown in the Netherlands by Palali and van Ours (2015).

Consumers react to the risk of being caught while buying cannabis illegally. Jacobson (2004) shows that lower probabilities to be arrested for cannabis possession increases consumption. So do policy changes involving lower sanctions (as suggested by Pacula et al., 2010), although the size and significance of such effects may vary across different population groups (Williams, 2004). Moreover, experiences of medical and recreational cannabis legalization in the US are correlated with rises in cannabis use. For example, Hunt et al. (2018) find that Marijuana Dispensary Laws in California are associated with a significant increase in driving under influence arrests. In this, cannabis is a normal good, with consumers sensitive to risk and costs variations.

In contrast to adult consumption, legalizing cannabis seems to decrease consumption among the young, provided legal retailers refuse to sell it to underage consumers. DiNardo and Lemieux (2001) do not find any effect of cannabis decriminalization on consumption among high school students, a result confirmed by a recent study in Oregon (Kerr et al., 2017). Furthermore, consumption of cannabis by teenagers is estimated to have decreased by 12% following legalization in the states of Washington and Colorado (SAMHSA, 2014). Finally, legalization does not seem to lead to the feared gateway effect on the use of other psychotropic substance (Dills et al., 2017). On the contrary, cannabis seems to act as a substitute for more powerful and addictive opioids (Powell et al., 2018).

## 2.3 Legalization and taxation

From a public policy viewpoint, legalization creates a new source of revenue through taxation (Caputo and Ostrom, 1994, 1996). For instance, the state of Colorado collected USD 325.1 million of tax and fee revenue in 2022 and the state of Washington collected USD 515.2 million in the same fiscal year.<fnref n="5" /> In the state of Washington, this tax revenue is

<footnote n="5">⁵See Washington State Treasurer at https://www.tre.wa.gov/portfolio-item/washington-state-marijuana-revenues-and-health/ and Colorado Department of Revenue at https://cdor.colorado.gov/data-and-reports/marijuana-data/marijuana-tax-reports, retrieved online on March 3, 2022.</footnote>
secured by a substantial degree of market concentration, which results itself from the high
taxes set by the authorities (Hollenbeck and Uetake, 2021). Jacobi and Sovinsky (2016)
estimate at around USD 12 billion the tax revenue, which could be raised from country-wide
cannabis legalization in the US.

Moreover, since consumers are price sensitive – with price elasticities of demand between
-0.5 and -0.79 (Davis et al., 2016; van Ours and Williams, 2007) –, a government may use
taxes to regulate the increase in cannabis use following legalization. Becker et al. (2006)
shows that policies controlling drug use by taxes are more efficient than quantity reduc-
tions through prohibition. Taxing cannabis consumption may discourage early initiation
into cannabis use by younger users, who are very responsive to low prices (van Ours and
Williams, 2007).

This literature review shows that prohibition fuels crime and violence, while stretching
law enforcement resources. In contrast, legalization leads to a decrease in overall criminality
and generates tax revenue but at the cost of increasing cannabis consumption. By their
empirical focus the papers reviewed cannot explain these results in a comprehensive way.
They are limited by data availability and focus on specific geographic areas and topics (e.g.
violence, youth consumption, public finance). They miss some aspects of the market. For
instance, none of the papers address consumer welfare and quality issues. Having a more
comprehensive view of the implications of legalizing recreational cannabis is important
for policymakers before embarking on such a controversial reform. We complement this
literature by studying the theory behind the policy trade-offs.

3 Prohibition equilibrium

We start our analysis by studying the illegal market under prohibition. In the absence of
a legal option, consumers can only purchase illegal cannabis from dealers. We describe the
demand and supply sides of the illegal market, which determine the price in equilibrium.

3.1 Demand under prohibition

Potential customers for illegal cannabis are heterogeneous. They have different “tastes” for
the commodity, $\theta$, which are drawn from the distribution $G(\theta)$, twice differentiable, with
support $\mathbb{R}$ and density function $g$.

Individuals who like cannabis are characterized by a positive $\theta$, and those who dislike it, by a negative one. When the illegal cannabis is of quality $v > 0$, its value for individual $\theta$ is given by $\theta v$. In other words, cannabis is vertically differentiated (i.e., a higher $v$ corresponds to a better quality cannabis). This assumption is an improvement over the existing literature, in which cannabis is generally modeled as a uniform product.
secured by a substantial degree of market concentration, which results itself from the high
taxes set by the authorities (Hollenbeck and Uetake, 2021). Jacobi and Sovinsky (2016)
estimate at around USD 12 billion the tax revenue, which could be raised from country-wide
cannabis legalization in the US.

Moreover, since consumers are price sensitive – with price elasticities of demand between
-0.5 and -0.79 (Davis et al., 2016; van Ours and Williams, 2007) –, a government may use
taxes to regulate the increase in cannabis use following legalization. Becker et al. (2006)
shows that policies controlling drug use by taxes are more efficient than quantity reduc-
tions through prohibition. Taxing cannabis consumption may discourage early initiation
into cannabis use by younger users, who are very responsive to low prices (van Ours and
Williams, 2007).

This literature review shows that prohibition fuels crime and violence, while stretching
law enforcement resources. In contrast, legalization leads to a decrease in overall criminality
and generates tax revenue but at the cost of increasing cannabis consumption. By their
empirical focus the papers reviewed cannot explain these results in a comprehensive way.
They are limited by data availability and focus on specific geographic areas and topics (e.g.
violence, youth consumption, public finance). They miss some aspects of the market. For
instance, none of the papers address consumer welfare and quality issues. Having a more
comprehensive view of the implications of legalizing recreational cannabis is important
for policymakers before embarking on such a controversial reform. We complement this
literature by studying the theory behind the policy trade-offs.

3 Prohibition equilibrium

We start our analysis by studying the illegal market under prohibition. In the absence of
a legal option, consumers can only purchase illegal cannabis from dealers. We describe the
demand and supply sides of the illegal market, which determine the price in equilibrium.

**3.1 Demand under prohibition**

Potential customers for illegal cannabis are heterogeneous. They have different “tastes” for
the commodity, $\theta$, which are drawn from the distribution $G(\theta)$, twice differentiable, with
support $\mathbb{R}$ and density function $g$.

Individuals who like cannabis are characterized by a positive $\theta$, and those who dislike
it, by a negative one. When the illegal cannabis is of quality $v > 0$, its value for individual
$\theta$ is given by $\theta v$. In other words, cannabis is vertically differentiated (i.e., a higher $v$
corresponds to a better quality cannabis). This assumption is an improvement over the
existing literature, in which cannabis is generally modeled as a uniform product.
Under prohibition, a consumer who purchases black market cannabis at the unit price $p$ is subject to a probability $q \in [0, 1]$ of being caught by the police. If caught, he/she loses the benefit of the commodity, the price paid for it, $p$, and faces a legal punishment $F \ge 0$ (e.g. fine, prison term). The net payoff of a consumer caught by the police while purchasing illegally is: $-p - F$; while the net payoff for an individual who is not caught is $\theta v - p$. Accordingly, we model the decision to consume cannabis illegally as a lottery $\mathcal{L}_{illegal} = [-p - F, \theta v - p; q, 1 - q]$. For an individual of taste $\theta \in \mathbb{R}$, the lottery has an expected value of

$$w^{+}(1-q)u(\theta v - p) + w^{-}(q)u(-p - F), \quad (1)$$

where the utility function $u$ is continuous, strictly increasing in $x \in \mathbb{R}$ and such that $u(0) = 0$,<fnref n="6" /> while the probability weighting functions $w^+$ and $w^-$ are increasing in $x \in [0, 1]$, so that $w^+(0) = w^-(0) = 0$ and $w^+(1) = w^-(1) = 1$.

This framework is general. It encompasses the standard expected utility approach by setting $w^+(1-q) = 1-q$ and $w^-(q) = q$ and considering an increasing, concave utility function (e.g., CARA). It also encompasses Tversky and Kahneman (1992)'s cumulative prospect theory (CPT), where attitudes towards risk are reference-dependent, probability weighting functions are not linear and the value function $u$ is S-shaped, with an inflection point at zero.<fnref n="7" />

The consumer, who is indifferent between illegal consumption and no consumption, is characterized by the taste $\theta^I$, solution to the following equation:

$$w^{+}(1-q)u(\theta^{I}v - p) + w^{-}(q)u(-p - F) = 0 \quad (2)$$

Any consumer of type $\theta \ge \theta^I$ purchases illegal cannabis, while consumer of type $\theta < \theta^I$ does not. We show in appendix B that, under our assumptions, $\theta^I > 0$ exists and is unique.

The demand for the illegal commodity can thus be written as:

$$D^I(p) = \int_{\theta^I}^{+\infty} g(\theta)d\theta = 1 - G(\theta^I) \quad (3)$$

The following comparative statics results regarding the marginal consumer and the price elasticity of demand for illegal cannabis are derived in appendix B.

First, $\theta^I$ increases with $p$ so that a higher price reduces the demand, illustrating that cannabis is a normal good. However, this is not a policy instrument under prohibition, since

<footnote n="6">⁶This normalization reflects that losses lead to a negative value and gains lead to a positive value.</footnote>

<footnote n="7">⁷While expected utility theories focus on final wealth, CPT models variations in outcome from a given status quo. The S-shaped value function allows for diminishing sensitivity and loss aversion. In other words, it accounts for the facts that “perceptions are a concave function of the magnitudes of change” and that “people dislike losses significantly more than they like gains” (Rabin, 1998).</footnote>
Under prohibition, a consumer who purchases black market cannabis at the unit price $p$ is subject to a probability $q \in [0, 1]$ of being caught by the police. If caught, he/she loses the benefit of the commodity, the price paid for it, $p$, and faces a legal punishment $F \ge 0$ (e.g. fine, prison term). The net payoff of a consumer caught by the police while purchasing illegally is: $-p - F$; while the net payoff for an individual who is not caught is $\theta v - p$. Accordingly, we model the decision to consume cannabis illegally as a lottery $\mathcal{L}_{illegal} = [-p - F, \theta v - p; q, 1 - q]$. For an individual of taste $\theta \in \mathbb{R}$, the lottery has an expected value of

$$w^{+}(1-q)u(\theta v - p) + w^{-}(q)u(-p - F), \qquad (1)$$

where the utility function $u$ is continuous, strictly increasing in $x \in \mathbb{R}$ and such that $u(0) = 0$,<fnref n="6" /> while the probability weighting functions $w^+$ and $w^-$ are increasing in $x \in [0, 1]$, so that $w^+(0) = w^-(0) = 0$ and $w^+(1) = w^-(1) = 1$.

This framework is general. It encompasses the standard expected utility approach by setting $w^+(1-q) = 1-q$ and $w^-(q) = q$ and considering an increasing, concave utility function (e.g., CARA). It also encompasses Tversky and Kahneman (1992)'s cumulative prospect theory (CPT), where attitudes towards risk are reference-dependent, probability weighting functions are not linear and the value function $u$ is S-shaped, with an inflection point at zero.<fnref n="7" />

The consumer, who is indifferent between illegal consumption and no consumption, is characterized by the taste $\theta^I$, solution to the following equation:

$$w^{+}(1-q)u(\theta^{I}v - p) + w^{-}(q)u(-p - F) = 0 \qquad (2)$$

Any consumer of type $\theta \ge \theta^I$ purchases illegal cannabis, while consumer of type $\theta < \theta^I$ does not. We show in appendix B that, under our assumptions, $\theta^I > 0$ exists and is unique.

The demand for the illegal commodity can thus be written as:

$$D^{I}(p) = \int_{\theta^{I}}^{+\infty} g(\theta)d\theta = 1 - G(\theta^{I}) \qquad (3)$$

The following comparative statics results regarding the marginal consumer and the price elasticity of demand for illegal cannabis are derived in appendix B.

First, $\theta^I$ increases with $p$ so that a higher price reduces the demand, illustrating that cannabis is a normal good. However, this is not a policy instrument under prohibition, since

<footnote n="6">⁶This normalization reflects that losses lead to a negative value and gains lead to a positive value.</footnote>

<footnote n="7">⁷While expected utility theories focus on final wealth, CPT models variations in outcome from a given status quo. The S-shaped value function allows for diminishing sensitivity and loss aversion. In other words, it accounts for the facts that “perceptions are a concave function of the magnitudes of change” and that “people dislike losses significantly more than they like gains” (Rabin, 1998).</footnote>
the equilibrium price on the illegal market results from interactions between unregulated (and untaxed) criminals. Second, $\theta^I$ increases with $q$: the demand for the illegal commodity decreases with the probability of arrest, which is the desired effect of prohibition policies. It discourages individuals from purchasing illegally, which leads to a more positive selection of consumers (i.e. a larger $\theta^I$).

Finally, our framework establishes that, for taste distributions $G(\theta)$ satisfying the monotone hazard rate (MHR) property,<fnref n="8" /> the (absolute value of the) price elasticity of demand,

$$ \epsilon_{D^I, p} = \frac{-D^{I'}(p)p}{D^I(p)} = \frac{d\theta^I}{dp} \frac{g(\theta^I)}{1 - G(\theta^I)} p, \quad (4) $$

increases with the risk of being caught $q \in [0, 1]$.

## 3.2 Cannabis supply under prohibition

We model the oligopolistic market for the illegal supply of cannabis as a generalized Cournot competition, with initially a fixed number $N \ge 1$ of criminal networks operating. This model allows us to incorporate some market power and to circumvent the Bertrand paradox without burdening the model with features such as capacity constraints, first mover advantage or horizontal product differentiation (in addition to the vertical product differentiation already present). Since the paper does not rely on any implication of a Cournot competition other than the oligopoly-induced market power, this assumption is innocuous.

We focus on the retail market for cannabis. We assume that black-market suppliers are subject to symmetrical cost functions: $C(q_i) = cq_i + K$ where $K \ge 0$ is the sunk fixed cost to set up the illegal network and $c \ge 0$ is the constant marginal cost of supplying the commodity. Each of the $N$ suppliers competes by simultaneously determining the quantities $q_i$ they offer. The market price $p^N$ is determined by the inverse demand function $p(Q)$, where $Q = \sum_{i=1}^N q_i$. Each supplier $i = 1, ..., N$ chooses the quantity $q_i \ge 0$ maximizing their profit, $q_i p(q_i + q_{-i}) - C(q_i)$, where $q_{-i} \equiv Q - q_i$. The first order condition of this problem determines their reaction function:

$$ q_i = - \frac{p(q_i + q_{-i}) - c}{p'(q_i + q_{-i})} \quad (5) $$

Since, at equilibrium, each of the $N$ suppliers best-responds to the others, and since their cost functions are symmetrical, the right-hand side of equation (5) is the same for all $i = 1, ..., N$. Each dealer supplies the same quantity $q_i = \frac{Q}{N}$ and the generalized Cournot price $p^N$ with $N \ge 1$ smugglers is implicitly defined by the following equation (see Carlton

<footnote n="8">⁸The monotone hazard rate (MHR) property is satisfied by most usual distributions.</footnote>
the equilibrium price on the illegal market results from interactions between unregulated (and untaxed) criminals. Second, $\theta^I$ increases with $q$: the demand for the illegal commodity decreases with the probability of arrest, which is the desired effect of prohibition policies. It discourages individuals from purchasing illegally, which leads to a more positive selection of consumers (i.e. a larger $\theta^I$).

Finally, our framework establishes that, for taste distributions $G(\theta)$ satisfying the monotone hazard rate (MHR) property,<fnref n="8" /> the (absolute value of the) price elasticity of demand,

$$ \epsilon_{D^I, p} = \frac{-D^{I'}(p)p}{D^I(p)} = \frac{d\theta^I}{dp} \frac{g(\theta^I)}{1 - G(\theta^I)} p, \quad (4) $$

increases with the risk of being caught $q \in [0, 1]$.

## 3.2 Cannabis supply under prohibition

We model the oligopolistic market for the illegal supply of cannabis as a generalized Cournot competition, with initially a fixed number $N \ge 1$ of criminal networks operating. This model allows us to incorporate some market power and to circumvent the Bertrand paradox without burdening the model with features such as capacity constraints, first mover advantage or horizontal product differentiation (in addition to the vertical product differentiation already present). Since the paper does not rely on any implication of a Cournot competition other than the oligopoly-induced market power, this assumption is innocuous.

We focus on the retail market for cannabis. We assume that black-market suppliers are subject to symmetrical cost functions: $C(q_i) = cq_i + K$ where $K \ge 0$ is the sunk fixed cost to set up the illegal network and $c \ge 0$ is the constant marginal cost of supplying the commodity. Each of the $N$ suppliers competes by simultaneously determining the quantities $q_i$ they offer. The market price $p^N$ is determined by the inverse demand function $p(Q)$, where $Q = \sum_{i=1}^N q_i$. Each supplier $i = 1, ..., N$ chooses the quantity $q_i \ge 0$ maximizing their profit, $q_i p(q_i + q_{-i}) - C(q_i)$, where $q_{-i} \equiv Q - q_i$. The first order condition of this problem determines their reaction function:

$$ q_i = - \frac{p(q_i + q_{-i}) - c}{p'(q_i + q_{-i})} \quad (5) $$

Since, at equilibrium, each of the $N$ suppliers best-responds to the others, and since their cost functions are symmetrical, the right-hand side of equation (5) is the same for all $i = 1, ..., N$. Each dealer supplies the same quantity $q_i = \frac{Q}{N}$ and the generalized Cournot price $p^N$ with $N \ge 1$ smugglers is implicitly defined by the following equation (see Carlton

<footnote n="8">⁸The monotone hazard rate (MHR) property is satisfied by most usual distributions.</footnote>
and Perloff, 2015 chapter 6):<fnref n="9" />

$$ \frac{p^N - c}{p^N} = \frac{1}{N} \frac{1}{\epsilon_{D^I, p}} \qquad (6) $$

where $\epsilon_{D^I, p}$ is the price elasticity of demand defined in (4). It is easy to check that, all else being equal, the price in (6) is increasing in the marginal cost of production, c, an intuitive result, and decreasing in N: the higher the number of competing providers the lower their mark-up. The generalized Cournot competition price is between two extreme cases: $c \le p^N \le p^m$ for all $N \ge 1$ where $p^m \equiv p^1$ in the monopoly case and $p^\infty = c$ in the competitive case when $N \to \infty$.

We have established in appendix B that the price elasticity of demand, $\epsilon_{D^I, p}$, increases with q. Using (6) we deduce that the oligopolistic price is lower when the risk q increases. Risk-aversion implies that the price charged by smugglers is lower than the price they would impose on risk-neutral individuals with the same expected payoff from consumption.<fnref n="10" /> Dealers must compensate risk-averse consumers for the risk involved in purchasing illegal cannabis.

Finally, for ease of exposition, we assume that N is initially fixed, as it is in the short run. However, in a more dynamic setting when the government opens the market to legal substitutes, we can endogenize N. We focus on a free entry equilibrium where dealers enter the market when their expected profit is positive and exit the market when their variable profit is negative. The asymmetry between entry and exit decisions reflects the fact that the fixed cost of setting up an illegal cannabis production and distribution network, K, is sunk. Once the drug dealers have paid it, there is no way to recoup K by exiting the market. The decision to exit the market is therefore based on the variable profit, $\pi(N) = (p^N - c)\frac{D^I(p^N)}{N}$. When $\pi(N) < 0$, we assume that some dealers exit the market until their number $N' \in \{0...N\}$ is such that $\pi(N') \ge 0$. By contrast, there is entry of a new dealer when $\pi(N+1) > K$. The maximal number of criminal organizations N that can operate profitably is the integer part of n such that $\pi(n) = K$, where $\pi(n) = (p^n - c)\frac{D^I(p^n)}{n}$ is the firm variable rent. Therefore, any repressive measure increasing c or K reduces the number of criminal networks active on the market and increases the price they charge (see equation 6).

<footnote n="9">⁹Since $q_i = \frac{Q}{N}$ equation (5) becomes $\frac{Q}{N} = -\frac{p(Q)-c}{p'(Q)}$, equivalent to $\frac{p(Q)-c}{p(Q)} = -\frac{1}{N}\frac{Qp'(Q)}{p(Q)}$ which yields (6).</footnote>

<footnote n="10">¹⁰Dealers face different types of consumers. If they can identify them, they may apply different prices. As is standard with third degree price discrimination, groups with the largest price elasticity get the smallest price. In contrast, captive consumers (i.e., groups with low price elasticity) are charged higher prices.</footnote>
and Perloff, 2015 chapter 6):<fnref n="9" />

$$ \frac{p^N - c}{p^N} = \frac{1}{N} \frac{1}{\epsilon_{D^I, p}} \qquad (6) $$

where $\epsilon_{D^I, p}$ is the price elasticity of demand defined in (4). It is easy to check that, all else being equal, the price in (6) is increasing in the marginal cost of production, c, an intuitive result, and decreasing in N: the higher the number of competing providers the lower their mark-up. The generalized Cournot competition price is between two extreme cases: $c \le p^N \le p^m$ for all $N \ge 1$ where $p^m \equiv p^1$ in the monopoly case and $p^\infty = c$ in the competitive case when $N \to \infty$.

We have established in appendix B that the price elasticity of demand, $\epsilon_{D^I, p}$, increases with q. Using (6) we deduce that the oligopolistic price is lower when the risk q increases. Risk-aversion implies that the price charged by smugglers is lower than the price they would impose on risk-neutral individuals with the same expected payoff from consumption.<fnref n="10" /> Dealers must compensate risk-averse consumers for the risk involved in purchasing illegal cannabis.

Finally, for ease of exposition, we assume that N is initially fixed, as it is in the short run. However, in a more dynamic setting when the government opens the market to legal substitutes, we can endogenize N. We focus on a free entry equilibrium where dealers enter the market when their expected profit is positive and exit the market when their variable profit is negative. The asymmetry between entry and exit decisions reflects the fact that the fixed cost of setting up an illegal cannabis production and distribution network, K, is sunk. Once the drug dealers have paid it, there is no way to recoup K by exiting the market. The decision to exit the market is therefore based on the variable profit, $\pi(N) = (p^N - c)\frac{D^I(p^N)}{N}$. When $\pi(N) < 0$, we assume that some dealers exit the market until their number $N' \in \{0...N\}$ is such that $\pi(N') \ge 0$. By contrast, there is entry of a new dealer when $\pi(N+1) > K$. The maximal number of criminal organizations N that can operate profitably is the integer part of n such that $\pi(n) = K$, where $\pi(n) = (p^n - c)\frac{D^I(p^n)}{n}$ is the firm variable rent. Therefore, any repressive measure increasing c or K reduces the number of criminal networks active on the market and increases the price they charge (see equation 6).

<footnote n="9">⁹Since $q_i = \frac{Q}{N}$ equation (5) becomes $\frac{Q}{N} = -\frac{p(Q)-c}{p'(Q)}$, equivalent to $\frac{p(Q)-c}{p(Q)} = -\frac{1}{N}\frac{Qp'(Q)}{p(Q)}$ which yields (6).</footnote>

<footnote n="10">¹⁰Dealers face different types of consumers. If they can identify them, they may apply different prices. As is standard with third degree price discrimination, groups with the largest price elasticity get the smallest price. In contrast, captive consumers (i.e., groups with low price elasticity) are charged higher prices.</footnote>
# 4 Legalization policies

This section studies the effect of legalization policies on the cannabis market equilibrium. We model legalization as a game led by the government which is a Stackelberg leader. The black-market retailers react to the actions of the government. Their payoffs are determined in the final stage by consumers’ decisions who choose between legal and illegal products when both are supplied on the market. The timing of the game, solved by backward induction, is described below.

## 4.1 Timing of the legalization game

1. The government sets up the legal retail market for cannabis and the level of repression on the black market to maximize its objective function, which is eradicating the drug-dealers in section 4.4 and a compound of several policy objectives (consumer surplus, revenue from excise taxes, negative externalities generated by the legal and illegal sectors, policy enforcement costs) in section 5.

(a) It determines the price of the legal cannabis $p^L = (1 + \tau)c^L$, where $c^L$ is the marginal cost of producing the commodity legally, by setting the level of excise tax $\tau$.<fnref n="11" />

(b) It chooses whether to boost the “quality differential” $b \ge 1$ between legal and illegal products, of quality $bv$ and $v$ respectively. The parameter $b$ captures the fact that, unlike illegal products, legal products are certified and their potency and composition, including pesticide and other chemicals, are known to consumers at the time of purchase.<fnref n="12" /> Moreover, purchasing legally alleviates search costs and personal cost in terms of ethics and social stigma. Finally, the purchase experience is usually better in a shop than on the street.

(c) It sets the level of enforcement of repression against consumers and producers of illegal cannabis, $e = (q, \delta)$. It influences on the demand side the probability of arrest $q$, and on the supply side, the increase in marginal cost to produce illegally

<footnote n="11">¹¹The government chooses the final price $p^L$ paid by consumers through the tax rate. Cannabis is an easy to grow agricultural product, highly adaptable to various climatic conditions. When the government encourages competition among the growers and the retailers, they do not make any rent. It can then modulate the final price by imposing an excise tax $\tau$ (e.g. as is widely done for the retail of tobacco). More generally, the government may influence the concentration of the legal market by artificially raising its cost of entry (e.g. limiting the number of licenses). Our results extend easily to an oligopoly setting, in which the Cournot price when legal retailers compete among themselves, net of taxes, is proportional to the marginal cost and the share of the sector rent captured by the government is simply smaller.</footnote>

<footnote n="12">¹²Quality certification under legalization usually involves regulating cropping techniques; in particular the use of pesticides, which are shown to be harmful for health (Subritzky et al., 2017). So, in general, for the same type of product (e.g., loose cannabis of a given strain), quality is better in the legal sector.</footnote>
# 4 Legalization policies

This section studies the effect of legalization policies on the cannabis market equilibrium. We model legalization as a game led by the government which is a Stackelberg leader. The black-market retailers react to the actions of the government. Their payoffs are determined in the final stage by consumers’ decisions who choose between legal and illegal products when both are supplied on the market. The timing of the game, solved by backward induction, is described below.

## 4.1 Timing of the legalization game

1. The government sets up the legal retail market for cannabis and the level of repression on the black market to maximize its objective function, which is eradicating the drug-dealers in section 4.4 and a compound of several policy objectives (consumer surplus, revenue from excise taxes, negative externalities generated by the legal and illegal sectors, policy enforcement costs) in section 5.

(a) It determines the price of the legal cannabis $p^L = (1 + \tau)c^L$, where $c^L$ is the marginal cost of producing the commodity legally, by setting the level of excise tax $\tau$.<fnref n="11" />

(b) It chooses whether to boost the “quality differential” $b \ge 1$ between legal and illegal products, of quality $bv$ and $v$ respectively. The parameter $b$ captures the fact that, unlike illegal products, legal products are certified and their potency and composition, including pesticide and other chemicals, are known to consumers at the time of purchase.<fnref n="12" /> Moreover, purchasing legally alleviates search costs and personal cost in terms of ethics and social stigma. Finally, the purchase experience is usually better in a shop than on the street.

(c) It sets the level of enforcement of repression against consumers and producers of illegal cannabis, $e = (q, \delta)$. It influences on the demand side the probability of arrest $q$, and on the supply side, the increase in marginal cost to produce illegally

<footnote n="11">¹¹The government chooses the final price $p^L$ paid by consumers through the tax rate. Cannabis is an easy to grow agricultural product, highly adaptable to various climatic conditions. When the government encourages competition among the growers and the retailers, they do not make any rent. It can then modulate the final price by imposing an excise tax $\tau$ (e.g. as is widely done for the retail of tobacco). More generally, the government may influence the concentration of the legal market by artificially raising its cost of entry (e.g. limiting the number of licenses). Our results extend easily to an oligopoly setting, in which the Cournot price when legal retailers compete among themselves, net of taxes, is proportional to the marginal cost and the share of the sector rent captured by the government is simply smaller.</footnote>

<footnote n="12">¹²Quality certification under legalization usually involves regulating cropping techniques; in particular the use of pesticides, which are shown to be harmful for health (Subritzky et al., 2017). So, in general, for the same type of product (e.g., loose cannabis of a given strain), quality is better in the legal sector.</footnote>
due to repression, $\delta \ge 0$, such that $c = (1 + \delta)c^L$. In addition, it could, at least in theory, influence the level of fine $F$. In practice, fines are very constrained by the legal framework, determined more by the “punishment proportionality” principle than by any other consideration such as cost-effectiveness. Overinflated fines may also be too costly to enforce and congest the judiciary system. This is why we take the maximum possible fine, $F$, as given in our analysis.

2. The dealers respond to the government's legalization policy. In the absence of certification norms on the black market, dealers have no way to credibly signal quality to consumers.<fnref n="13" /> Hence, they cannot adjust the quality of their product. They can only adjust their prices to maximize the profit

$$ \Pi(p, p^L|b) = (p-c) D^I(p, p^L|b) $$

where $D^I(p, p^L|b)$ denotes the residual demand for black-market cannabis. If this variable profit is negative, dealers exit the market, until either the variable profit with the new number of drug-dealers $N'$ is positive or there is none left to serve the illegal market. Should the illegal retailers exit the market, their payoff is zero. They share equally the variable profit otherwise.

3. The final payoffs of both parties are determined by the market outcomes, as consumers decide whether to consume or not, and on which market. Depending on the relative prices of legal and illegal products and the quality differential, the black market survives or is eradicated.

## 4.2 The demand for legal and illegal cannabis

Turning to the final stage of the game, this section studies consumption decisions following the implementation of a market for legal cannabis of quality $b$, sold at price $p^L$, given that dealers sell illegal products at price $p$.

We present in the main text the analysis under the assumption that consumers behave according to prospect theory. However all our results hold whether we model consumers' behavior under expected utility theory or prospect theory, as shown in appendices C through D. Only the way the marginal consumer is derived under legalization differs slightly. In prospect theory, the marginal type, $\theta^L(p, p^L)$, indifferent between legal and illegal consumers

<footnote n="13">¹³Besides, illegal retailers are likely to be subject to sticky contracts upstream, since most transactions on the black market happen between individuals who are already acquainted (Caulkins and Pacula, 2006).</footnote>
due to repression, $\delta \ge 0$, such that $c = (1 + \delta)c^L$. In addition, it could, at least in theory, influence the level of fine $F$. In practice, fines are very constrained by the legal framework, determined more by the “punishment proportionality” principle than by any other consideration such as cost-effectiveness. Overinflated fines may also be too costly to enforce and congest the judiciary system. This is why we take the maximum possible fine, $F$, as given in our analysis.

2. The dealers respond to the government's legalization policy. In the absence of certification norms on the black market, dealers have no way to credibly signal quality to consumers.<fnref n="13" /> Hence, they cannot adjust the quality of their product. They can only adjust their prices to maximize the profit

$$ \Pi(p, p^L|b) = (p-c) D^I(p, p^L|b) $$

where $D^I(p, p^L|b)$ denotes the residual demand for black-market cannabis. If this variable profit is negative, dealers exit the market, until either the variable profit with the new number of drug-dealers $N'$ is positive or there is none left to serve the illegal market. Should the illegal retailers exit the market, their payoff is zero. They share equally the variable profit otherwise.

3. The final payoffs of both parties are determined by the market outcomes, as consumers decide whether to consume or not, and on which market. Depending on the relative prices of legal and illegal products and the quality differential, the black market survives or is eradicated.

## 4.2 The demand for legal and illegal cannabis

Turning to the final stage of the game, this section studies consumption decisions following the implementation of a market for legal cannabis of quality $b$, sold at price $p^L$, given that dealers sell illegal products at price $p$.

We present in the main text the analysis under the assumption that consumers behave according to prospect theory. However all our results hold whether we model consumers' behavior under expected utility theory or prospect theory, as shown in appendices C through D. Only the way the marginal consumer is derived under legalization differs slightly. In prospect theory, the marginal type, $\theta^L(p, p^L)$, indifferent between legal and illegal con-

<footnote n="13">¹³Besides, illegal retailers are likely to be subject to sticky contracts upstream, since most transactions on the black market happen between individuals who are already acquainted (Caulkins and Pacula, 2006).</footnote>
sumption, is the solution of :<fnref n="14" />

$$w^+(1-q)u(p^L - p - \theta v(b-1)) + w^-(q)u(p^L - p - \theta bv - F) = 0, \quad (7)$$

while, if individuals are expected utility maximizers, the marginal consumer is the solution of: $(1-q)u(\theta v - p) + qu(-p-F) = u(\theta bv - p^L)$. For example, with a CARA utility function $\theta^L(p, p^L)$ is such that $(1-q)u(p^L - p - \theta v(b-1)) + qu(p^L - p - \theta bv - F) = 1$, which is similar to (7) but not equal. Appendix C shows that in both cases (EUT and CPT) there is a range of legal prices such that $\theta^L(p, p^L)$, increasing in $p^L$ and decreasing in $p$, exists and is unique. Any individual above this threshold prefers to purchase legally rather than illegally, and symmetrically for those below the threshold.

Finally to determine the demand for legal cannabis we also need to consider the threshold $\theta^0$, above which consumers prefer to consume legal cannabis at price $p^L$ rather than not consuming at all:<fnref n="15" />

$$\theta^0(p^L) = \frac{p^L}{bv} \qquad (8)$$

Following the implementation of a legal market for cannabis sold at price $p^L$, when the price on the illegal market is $p$, two cases may occur (as formally shown in appendix D.1).

* The legal price is set low enough: $p^L \le \tilde{p}^L(p) = \theta^Ibv$. The legalization has the intended effect of drying up the illegal cannabis market: $\theta^L \le \theta^0 \le \theta^I$.<fnref n="16" /> In this case, illustrated in figure 1, $\int_{\theta^0}^{\theta^I} g(\theta)d\theta$ new cannabis consumers appear.

<figure><img src="image_1.png" /><figcaption>Figure 1: Change in consumer choices post-legalization when $p^L \le \tilde{p}^L(p)$</figcaption></figure>

* The legal price is too high to totally undermine the dealers: $p^L > \tilde{p}^L(p) = \theta^Ibv$. The illegal cannabis market survives: $\theta^I < \theta^0 < \theta^L$. In this case, if the illegal providers

<footnote n="14">¹⁴In prospect theory individuals deciding between legal and illegal consumption take the certain payoff associated with the legal option, $\theta bv - p^L$, as reference. Concretely they make their decision by subtracting the certain payoff from their payoffs when they purchase illegally. Engaging in illegal consumption is then modeled as a lottery $[p^L - p - \theta bv - F, p^L - p - \theta(b-1)v; q, 1-q]$ which yields (7).</footnote>

<footnote n="15">¹⁵That is, it is such that $u(\theta bv - p^L) = 0$.</footnote>

<footnote n="16">¹⁶Recall that $\theta^I$ defined in (2) is the threshold above which an individual prefers to make an illegal purchase rather than no purchase at all. When $p^L \le \tilde{p}^L(p)$, $\theta^I$ becomes higher than $\theta^L$, the threshold above which an individual prefers to buy legally rather than illegally: the illegal market disappears.</footnote>
sumption, is the solution of :<fnref n="14" />

$$w^+(1-q)u(p^L - p - \theta v(b-1)) + w^-(q)u(p^L - p - \theta bv - F) = 0, \quad (7)$$

while, if individuals are expected utility maximizers, the marginal consumer is the solution of: $(1-q)u(\theta v - p) + qu(-p-F) = u(\theta bv - p^L)$. For example, with a CARA utility function $\theta^L(p, p^L)$ is such that $(1-q)u(p^L - p - \theta v(b-1)) + qu(p^L - p - \theta bv - F) = 1$, which is similar to (7) but not equal. Appendix C shows that in both cases (EUT and CPT) there is a range of legal prices such that $\theta^L(p, p^L)$, increasing in $p^L$ and decreasing in $p$, exists and is unique. Any individual above this threshold prefers to purchase legally rather than illegally, and symmetrically for those below the threshold.

Finally to determine the demand for legal cannabis we also need to consider the threshold $\theta^0$, above which consumers prefer to consume legal cannabis at price $p^L$ rather than not consuming at all:<fnref n="15" />

$$\theta^0(p^L) = \frac{p^L}{bv} \qquad (8)$$

Following the implementation of a legal market for cannabis sold at price $p^L$, when the price on the illegal market is $p$, two cases may occur (as formally shown in appendix D.1).

* The legal price is set low enough: $p^L \le \tilde{p}^L(p) = \theta^Ibv$. The legalization has the intended effect of drying up the illegal cannabis market: $\theta^L \le \theta^0 \le \theta^I$.<fnref n="16" /> In this case, illustrated in figure 1, $\int_{\theta^0}^{\theta^I} g(\theta)d\theta$ new cannabis consumers appear.

<figure><img src="image_2.png" /><figcaption>Figure 1: Change in consumer choices post-legalization when $p^L \le \tilde{p}^L(p)$</figcaption></figure>

* The legal price is too high to totally undermine the dealers: $p^L > \tilde{p}^L(p) = \theta^Ibv$. The illegal cannabis market survives: $\theta^I < \theta^0 < \theta^L$. In this case, if the illegal providers

<footnote n="14">¹⁴In prospect theory individuals deciding between legal and illegal consumption take the certain payoff associated with the legal option, $\theta bv - p^L$, as reference. Concretely they make their decision by subtracting the certain payoff from their payoffs when they purchase illegally. Engaging in illegal consumption is then modeled as a lottery $[p^L - p - \theta bv - F, p^L - p - \theta(b-1)v; q, 1-q]$ which yields (7).</footnote>

<footnote n="15">¹⁵That is, it is such that $u(\theta bv - p^L) = 0$.</footnote>

<footnote n="16">¹⁶Recall that $\theta^I$ defined in (2) is the threshold above which an individual prefers to make an illegal purchase rather than no purchase at all. When $p^L \le \tilde{p}^L(p)$, $\theta^I$ becomes higher than $\theta^L$, the threshold above which an individual prefers to buy legally rather than illegally: the illegal market disappears.</footnote>
maintained the same price as under prohibition, the overall demand for cannabis would not change. The high-type segment of the former black market, consumers with valuation above $\theta^L$, would switch to the legal market as shown in figure 2. Under legalization, individuals with a high valuation for cannabis turn to the legal market and pay attention to quality, while they neglect it under prohibition where products are not certified. The residual demand for illegal cannabis would become:

$$D^I(p, p^L) = \int_{\theta^I(p)}^{\theta^L(p, p^L)} g(\theta) d\theta. \qquad (9)$$

<figure><img src="image_2.png" /><figcaption>Figure 2: Change in consumer choices post-legalization when $p^L > \tilde{p}^L(p)$</figcaption></figure>

## 4.3 Response of illegal providers

To keep some consumers and maximize their profits, illegal providers adjust their price in stage 2. The price $p^N(p^L)$ – of illegal cannabis following legalization – is the result of the Stackelberg competition between the legal and the illegal providers on one hand, as well as the competition within the illegal market on the other hand. Formally, the price reaction function of the smugglers is the solution of the following equation:

$$p(p^L) = \begin{cases} p^N(p^L) & \text{if } c \le p^N(p^L) < \frac{p^L}{b} \\ \emptyset & \text{otherwise} \end{cases} \qquad (10)$$

where $p^N(p^L)$ is the solution of (6) computed with $\epsilon_{D^I,p} = -\frac{\partial D^I(p, p^L)}{\partial p} \frac{p}{D^I(p, p^L)}$, the direct price elasticity of the demand $D^I(p, p^L)$ defined in (9).

Rewriting (6) as $p^N = c \left(1 + \frac{1}{N\epsilon_{D^I,p}-1}\right)$ shows that the reaction price is increasing in $c$ and decreasing in $N$. Besides, as shown in appendix C.3, $\epsilon_{D^I,p}$ decreases with $p^L$ and hence $p^N$ increases with $p^L$. This allows us to establish the following lemma.

**Lemma** As long as the illegal providers are active, i.e. have positive margins, their reaction price is increasing in their marginal operating costs, $c$, and in the price on the legal market, $p^L$; and is decreasing in the number of active criminal networks in the market, $N$.

Facing competition from the legal market on the high bound of the consumer distribution, illegal providers push down their prices. However, they need to make a positive margin
maintained the same price as under prohibition, the overall demand for cannabis would not change. The high-type segment of the former black market, consumers with valuation above $\theta^L$, would switch to the legal market as shown in figure 2. Under legalization, individuals with a high valuation for cannabis turn to the legal market and pay attention to quality, while they neglect it under prohibition where products are not certified. The residual demand for illegal cannabis would become:

$$D^I(p, p^L) = \int_{\theta^I(p)}^{\theta^L(p, p^L)} g(\theta) d\theta. \qquad (9)$$

<figure><img src="image_3.png" /><figcaption>Figure 2: Change in consumer choices post-legalization when $p^L > \tilde{p}^L(p)$</figcaption></figure>

## 4.3 Response of illegal providers

To keep some consumers and maximize their profits, illegal providers adjust their price in stage 2. The price $p^N(p^L)$ – of illegal cannabis following legalization – is the result of the Stackelberg competition between the legal and the illegal providers on one hand, as well as the competition within the illegal market on the other hand. Formally, the price reaction function of the smugglers is the solution of the following equation:

$$p(p^L) = \begin{cases} p^N(p^L) & \text{if } c \le p^N(p^L) < \frac{p^L}{b} \\ \emptyset & \text{otherwise} \end{cases} \qquad (10)$$

where $p^N(p^L)$ is the solution of (6) computed with $\varepsilon_{D^I,p} = -\frac{\partial D^I(p, p^L)}{\partial p} \frac{p}{D^I(p, p^L)}$, the direct price elasticity of the demand $D^I(p, p^L)$ defined in (9).

Rewriting (6) as $p^N = c \left(1 + \frac{1}{N\varepsilon_{D^I,p}-1}\right)$ shows that the reaction price is increasing in $c$ and decreasing in $N$. Besides, as shown in appendix C.3, $\varepsilon_{D^I,p}$ decreases with $p^L$ and hence $p^N$ increases with $p^L$. This allows us to establish the following lemma.

**Lemma** As long as the illegal providers are active, i.e. have positive margins, their reaction price is increasing in their marginal operating costs, $c$, and in the price on the legal market, $p^L$; and is decreasing in the number of active criminal networks in the market, $N$.

Facing competition from the legal market on the high bound of the consumer distribution, illegal providers push down their prices. However, they need to make a positive margin
to continue their operations. If the value for money of black-market cannabis is sufficiently attractive relative to legal cannabis, the black market survives: $\theta^I(p^N(p^L)) < \theta^L$. The illegal providers have the ability to compete with the provision of legal cannabis and attract consumers in the middle bound of the taste distribution by pushing down their price $p^N(p^L)$ – and still make a profit. The resulting demand for legal and illegal cannabis is illustrated in figure 3. Because the price-response of the black market pushes down $\theta^I(p^N(p^L))$, the total number of consumers of (legal and illegal) cannabis increases *post-legalization*.

<figure><img src="image_3.png" /></figure>

Note: *p* is the price of cannabis on the black market under prohibition and $p^N(p^L)$ its price following legalization.

<caption>Figure 3: Change in consumers choice *post-legalization* when $p^L > \tilde{p}^L(p)$ and illegal providers push down their price in response to legalization.</caption>

Otherwise, if the price of legal cannabis, $p^L$, is set at a sufficiently low level, the drug-dealers exit the cannabis market, some consumers of illegal cannabis switch to legal cannabis and, in addition, new users appear. Two situations may typically lead to this configuration: (i) the dealers' marginal cost of operations, *c*, is too high relative to the price they need to charge to retain some customers, pushing them out of the market; or (ii) the price value for legal cannabis is high – i.e. its quality *b* is high compared to its price $p^L$ – so that consumers switch to legal cannabis, drying up the demand for illegal products.<fnref n="17" />

We deduce the next proposition.

**Proposition 1** *Once a legal market is implemented, if the costs of operating on the black market and the repression against illegal purchases are held constant, for any level of quality differential, $b \ge 1$, the overall demand for cannabis increases.*

**Proof.** See appendix D.2. ■

In other words, cannabis consumption increases post-legalization. This has been observed everywhere that cannabis has been legalized so far. Proposition 1 thus highlights a policy trade-off: policy makers have to choose between controlling cannabis consumption with the help of dealers regulating the illegal market (the *status-quo* in many countries), or implementing a legal market, which necessarily increases consumption.

<footnote n="17">¹⁷When *c* and/or *b* are high it becomes more difficult for criminals to push down their price and meet the constraint $c \le p^N(p^L) < \frac{p^L}{b}$.</footnote>
to continue their operations. If the value for money of black-market cannabis is sufficiently attractive relative to legal cannabis, the black market survives: $\theta^I(p^N(p^L)) < \theta^L$. The illegal providers have the ability to compete with the provision of legal cannabis and attract consumers in the middle bound of the taste distribution by pushing down their price $p^N(p^L)$ – and still make a profit. The resulting demand for legal and illegal cannabis is illustrated in figure 3. Because the price-response of the black market pushes down $\theta^I(p^N(p^L))$, the total number of consumers of (legal and illegal) cannabis increases *post-legalization*.

<figure><img src="image_4.png" /></figure>

Note: *p* is the price of cannabis on the black market under prohibition and $p^N(p^L)$ its price following legalization.

<caption>Figure 3: Change in consumers choice *post-legalization* when $p^L > \tilde{p}^L(p)$ and illegal providers push down their price in response to legalization.</caption>

Otherwise, if the price of legal cannabis, $p^L$, is set at a sufficiently low level, the drug-dealers exit the cannabis market, some consumers of illegal cannabis switch to legal cannabis and, in addition, new users appear. Two situations may typically lead to this configuration: (i) the dealers' marginal cost of operations, *c*, is too high relative to the price they need to charge to retain some customers, pushing them out of the market; or (ii) the price value for legal cannabis is high – i.e. its quality *b* is high compared to its price $p^L$ – so that consumers switch to legal cannabis, drying up the demand for illegal products.<fnref n="17" />

We deduce the next proposition.

**Proposition 1** *Once a legal market is implemented, if the costs of operating on the black market and the repression against illegal purchases are held constant, for any level of quality differential, $b \ge 1$, the overall demand for cannabis increases.*

**Proof.** See appendix D.2. ■

In other words, cannabis consumption increases post-legalization. This has been observed everywhere that cannabis has been legalized so far. Proposition 1 thus highlights a policy trade-off: policy makers have to choose between controlling cannabis consumption with the help of dealers regulating the illegal market (the *status-quo* in many countries), or implementing a legal market, which necessarily increases consumption.

<footnote n="17">¹⁷When *c* and/or *b* are high it becomes more difficult for criminals to push down their price and meet the constraint $c \le p^N(p^L) < \frac{p^L}{b}$.</footnote>
In the past, several policy makers with the goal of eradicating the illegal market have used the intuitive approach of matching the price of legal cannabis to the black-market price: $p^L = p$. Our analysis explains why this policy leads to significant increases in consumption. For a given price, the value of consuming legal cannabis is higher ($b > 1$) and there is no risk of being sanctioned ($q = 0$), such that the demand for cannabis increases: $\theta^0(p) < \theta^I(p) \quad \forall p > 0$.<fnref n="18" /> Further, such price setting strategy ignores the fact that dealers may lower their price to keep some customers, as analyzed above: in addition to increasing consumption, this policy does not necessarily eradicate crime.

This is illustrated by the legalization experience in Québec, where the *Société Québécoise du Cannabis (SQDC)*, a subsidiary of the provincial society for alcohols, provides cannabis both in shops and online. Dried flower products were initially priced between CAD 8 and 10 per gram by the SQDC, depending on potency and strain type, which was close to the *pre-legalization* black-market price.<fnref n="19" /> This pricing policy promoted by the Minister of Public Health at the time, Lucie Charlebois, to annihilate illegal consumption did not anticipate the response of dealers. The black market survived by lowering prices. In mid March 2019, the crowd-sourced website www.priceofweed.com reported the average black-market price in Québec having fallen below CAD 6 per gram. As a result, cannabis consumption increased among adults.<fnref n="20" />

## 4.4 Eradicating the illegal market through eviction pricing

Since legalization reforms all share the goal to eradicate crime, we now consider a price setting strategy for the legal supply which destroys economic incentives for dealers to operate. The strategy is such that the price of dealers is pushed below their marginal costs after they respond to the policy. Let $\theta^I(p)$ be defined in (2). We deduce the next proposition.

**Proposition 2** *To drive illegal suppliers out of business, the legal price of cannabis should be set below the eviction price $\underline{p}^L = bv\theta^I(c)$, which, without additional measures, yields the same level of consumption as under perfect competition among illegal suppliers: $D^L(\underline{p}^L) = D^I(c)$.*

**Proof.** See appendix E.1. ■

This result is general. Irrespective of the way we model consumers’ behavior (i.e. expected utility or prospect theory) and the initial market conditions (i.e. monopolist,

<footnote n="18">¹⁸Since $\theta^I$ increases with the risk $q$, we deduce that: $\theta^I(p) > \theta^I_{q=0}(p) = \frac{p}{v} \ge \theta^0(p) = \frac{p}{bv}$, $\forall b \ge 1$ and $q > 0$.</footnote>

<footnote n="19">¹⁹See “Environ ‘7-8 dollars le gramme’ pour du pot légal” by Martin Croteau in *La Presse*, Sep. 21 2017.</footnote>

<footnote n="20">²⁰The statistical bureau of Quebec (*Institut de la Statistique du Québec*) reported that the proportion of cannabis users aged 15 and over increased from 14% to nearly 20% between 2018 and 2021 in Québec. In particular, 26% of the 25- to 34-year-old reported to have consumed cannabis in the year prior to 2018; while they were 36% in 2021. See: *Institut de la Statistique du Québec*. Oct. 15 2021. https://statistique.quebec.ca/en/communique/augmentation-consommation-cannabis-plus-25-ans-mais-diminution-15-17-ans-en</footnote>
In the past, several policy makers with the goal of eradicating the illegal market have used the intuitive approach of matching the price of legal cannabis to the black-market price: $p^L = p$. Our analysis explains why this policy leads to significant increases in consumption. For a given price, the value of consuming legal cannabis is higher ($b > 1$) and there is no risk of being sanctioned ($q = 0$), such that the demand for cannabis increases: $\theta^0(p) < \theta^I(p) \quad \forall p > 0$.<fnref n="18" /> Further, such price setting strategy ignores the fact that dealers may lower their price to keep some customers, as analyzed above: in addition to increasing consumption, this policy does not necessarily eradicate crime.

This is illustrated by the legalization experience in Québec, where the *Société Québécoise du Cannabis (SQDC)*, a subsidiary of the provincial society for alcohols, provides cannabis both in shops and online. Dried flower products were initially priced between CAD 8 and 10 per gram by the SQDC, depending on potency and strain type, which was close to the *pre-legalization* black-market price.<fnref n="19" /> This pricing policy promoted by the Minister of Public Health at the time, Lucie Charlebois, to annihilate illegal consumption did not anticipate the response of dealers. The black market survived by lowering prices. In mid March 2019, the crowd-sourced website www.priceofweed.com reported the average black-market price in Québec having fallen below CAD 6 per gram. As a result, cannabis consumption increased among adults.<fnref n="20" />

## 4.4 Eradicating the illegal market through eviction pricing

Since legalization reforms all share the goal to eradicate crime, we now consider a price setting strategy for the legal supply which destroys economic incentives for dealers to operate. The strategy is such that the price of dealers is pushed below their marginal costs after they respond to the policy. Let $\theta^I(p)$ be defined in (2). We deduce the next proposition.

**Proposition 2** *To drive illegal suppliers out of business, the legal price of cannabis should be set below the eviction price $\underline{p}^L = bv\theta^I(c)$, which, without additional measures, yields the same level of consumption as under perfect competition among illegal suppliers: $D^L(\underline{p}^L) = D^I(c)$.*

**Proof.** See appendix E.1. ■

This result is general. Irrespective of the way we model consumers’ behavior (i.e. expected utility or prospect theory) and the initial market conditions (i.e. monopolist,

<footnote n="18">¹⁸Since $\theta^I$ increases with the risk $q$, we deduce that: $\theta^I(p) > \theta^I_{q=0}(p) = \frac{p}{v} \ge \theta^0(p) = \frac{p}{bv}$, $\forall b \ge 1$ and $q > 0$.</footnote>

<footnote n="19">¹⁹See “Environ ‘7-8 dollars le gramme’ pour du pot légal” by Martin Croteau in *La Presse*, Sep. 21 2017.</footnote>

<footnote n="20">²⁰The statistical bureau of Quebec (*Institut de la Statistique du Québec*) reported that the proportion of cannabis users aged 15 and over increased from 14% to nearly 20% between 2018 and 2021 in Québec. In particular, 26% of the 25- to 34-year-old reported to have consumed cannabis in the year prior to 2018; while they were 36% in 2021. See: *Institut de la Statistique du Québec*. Oct. 15 2021. https://statistique.quebec.ca/en/communique/augmentation-consommation-cannabis-plus-25-ans-mais-diminution-15-17-ans-en</footnote>
oligopolistic or competitive), if the government wants to drive out illegal providers, it has
to apply a price lower than the threshold price $p^L = bv\theta^I(c)$, which is such that their mark-
up vanishes after they respond to the policy. We refer to the price $p^L$ as the *eviction price*.
Since $\theta^I(c)v - c > 0$ it follows that $p^L > c$: the eviction price of legal cannabis is higher
than illegal providers' marginal cost, $c$. Nevertheless, since legal cannabis is of better qual-
ity and its purchase involves no risk, the demand at this eviction price, which is now legal,
is at the same level as if illegal suppliers were pricing their products on the illegal market
at marginal cost.

As compared to the status-quo situation of an oligopolistic illegal market, such an in-
crease in drug consumption following legalization may not be desirable for the society, nor
politically sustainable. In fact, to date, not a single politician proponent of legalization
has disputed this. They highlight the benefits of legalization in eradicating crime but seem
to assume that consumption will remain the same after legalization. This assumption has
led in the past to a serious underestimation of demand after legalization, as for example
in Canada and Uruguay, and thus to the rationing of cannabis users who have turned to
the black market. On the other hand, if the increase in cannabis consumption is antic-
ipated, this will prompt opposition to legalization by many citizens, health workers and
anti-drug associations. Policy makers need more sophisticated tools to regulate the demand
for cannabis *post-legalization*. Our theoretical framework shows that the price that drives
criminals out of business can be adjusted.

**Corollary** *The eviction price* $p^L$ *increases with the marginal costs of illegal providers c, the probability of arrest of their consumers q, the associated fine amount F, and the quality differential between legal and illegal cannabis b.*

**Proof.** See appendix E.2.

Intuitively, additional measures affecting *c*, *q*, *F* and *b* make competing with the legal
provision of cannabis more difficult for illegal providers. Combining these four instruments
helps contain the increase in cannabis consumption following legalization: their economic
activities can be throttled more easily such that the eviction price can be set higher. This
is either because consumers have higher relative expected payoffs if they consume legally,
or because illegal providers operate with increased costs. This dampens the increase in
demand following legalization. The optimal combination of these instruments is discussed
with the policy objectives in the next section.

**5 Enlarging the set of policy objectives**

So far we have focused on policies that try to eliminate the black market through eviction
pricing. Yet governments pursue a larger set of objectives when they implement legalization
oligopolistic or competitive), if the government wants to drive out illegal providers, it has
to apply a price lower than the threshold price $p^L = bv\theta^I(c)$, which is such that their mark-
up vanishes after they respond to the policy. We refer to the price $p^L$ as the *eviction price*.
Since $\theta^I(c)v - c > 0$ it follows that $p^L > c$: the eviction price of legal cannabis is higher
than illegal providers' marginal cost, $c$. Nevertheless, since legal cannabis is of better qual-
ity and its purchase involves no risk, the demand at this eviction price, which is now legal,
is at the same level as if illegal suppliers were pricing their products on the illegal market
at marginal cost.

As compared to the status-quo situation of an oligopolistic illegal market, such an in-
crease in drug consumption following legalization may not be desirable for the society, nor
politically sustainable. In fact, to date, not a single politician proponent of legalization
has disputed this. They highlight the benefits of legalization in eradicating crime but seem
to assume that consumption will remain the same after legalization. This assumption has
led in the past to a serious underestimation of demand after legalization, as for example
in Canada and Uruguay, and thus to the rationing of cannabis users who have turned to
the black market. On the other hand, if the increase in cannabis consumption is antic-
ipated, this will prompt opposition to legalization by many citizens, health workers and
anti-drug associations. Policy makers need more sophisticated tools to regulate the demand
for cannabis *post-legalization*. Our theoretical framework shows that the price that drives
criminals out of business can be adjusted.

**Corollary** *The eviction price* $p^L$ *increases with the marginal costs of illegal providers c, the probability of arrest of their consumers q, the associated fine amount F, and the quality differential between legal and illegal cannabis b.*

**Proof.** See appendix E.2.

Intuitively, additional measures affecting *c*, *q*, *F* and *b* make competing with the legal
provision of cannabis more difficult for illegal providers. Combining these four instruments
helps contain the increase in cannabis consumption following legalization: their economic
activities can be throttled more easily such that the eviction price can be set higher. This
is either because consumers have higher relative expected payoffs if they consume legally,
or because illegal providers operate with increased costs. This dampens the increase in
demand following legalization. The optimal combination of these instruments is discussed
with the policy objectives in the next section.

**5 Enlarging the set of policy objectives**

So far we have focused on policies that try to eliminate the black market through eviction
pricing. Yet governments pursue a larger set of objectives when they implement legalization
policies. These include reducing the negative externalities for health – especially large for the youngest users (i.e. teenagers) – and for societies generated by the consumption of psychoactive substances, redeploying police forces and relieving congestion in courts and prisons to reduce enforcement costs, increasing consumer surplus while controlling the quality of products and developing a sector that generates legal activities and new tax revenues. Although current reforms share most of these objectives, they may have different priorities. In this section we model a (utilitarian) government’s objective function as a linear combination of these objectives and study their interactions with the crime eradication objective.

Recall that $e = (\delta, q)$. The government maximizes its objectives as follows:

$$ \max W^G (e, b, \tau) = \alpha_T T (e, b, \tau) - \alpha_C C (e, b, \tau) + \alpha_S S^c (e, b, \tau) - \alpha_\xi \xi (e, b, \tau) \quad (11) $$

where $\alpha_T \ge 0$, $\alpha_C \ge 0$, $\alpha_S \ge 0$, $\alpha_\xi \ge 0$ are the weights attached to each objective in the utilitarian welfare function and where

* $T(e, b, \tau) = \tau c^L D^L (p, (1+\tau)c^L|b)$ is the revenue from excise taxes on legal cannabis.

* $C(e, b, \tau) = E(\delta, q) - qD^I(p, (1+\tau)c^L|b) F$ is the enforcement cost $E(\delta, q)$, increasing and convex in $\delta$ and $q$, net of the fines.

* $S^c(e, b, \tau) = S^L(p, (1+\tau)c^L|b) + S^I(p, (1+\tau)c^L|b) - \Psi(b)$ is the sum of the consumer surpluses on the legal and illegal markets, net of $\Psi(b)$, the cost of legal cannabis quality improvement, which is strictly increasing and convex.

- $S^L(p, (1+\tau)c^L|b) = \int_{(1+\tau)c^L}^{\infty} D^L(p, t|b)dt$ is the net consumer surplus on the legal market.

- $S^I(p, (1+\tau)c^L|b) = (1-q) \int_p^{\bar{p}^I} D^I(t, (1+\tau)c^L|b) dt - qD^I(p, (1+\tau)c^L|b) F$ is the net consumer surplus on the illegal market, with $\bar{p}^I$ being the choke-off price on the illegal market.

* $\xi(e, b, \tau) = \xi_I D^I(p, (1+\tau)c^L|b) + \xi_L D^L(p, (1+\tau)c^L|b)$, with $\xi_I \ge 0$ and $\xi_L \ge 0$, is the negative externalities generated by the illegal and legal sectors, which are increasing in their respective demands.

We consider in turn four different objectives that can be decentralized through the choice of enforcement of sanctions against the illegal sector, $e = (q, \delta)$, and regulation of the legal sector $(b, \tau)$, and study whether they are compatible with the goal of deflating organized crime by setting an eviction price for legal cannabis. We show that the objectives sometimes
policies. These include reducing the negative externalities for health – especially large for the youngest users (i.e. teenagers) – and for societies generated by the consumption of psychoactive substances, redeploying police forces and relieving congestion in courts and prisons to reduce enforcement costs, increasing consumer surplus while controlling the quality of products and developing a sector that generates legal activities and new tax revenues. Although current reforms share most of these objectives, they may have different priorities. In this section we model a (utilitarian) government's objective function as a linear combination of these objectives and study their interactions with the crime eradication objective.

Recall that $e = (\delta, q)$. The government maximizes its objectives as follows:

$$ \max W^G (e, b, \tau) = \alpha_T T (e, b, \tau) - \alpha_C C (e, b, \tau) + \alpha_S S^c (e, b, \tau) - \alpha_\xi \xi (e, b, \tau) \quad (11) $$

where $\alpha_T \ge 0$, $\alpha_C \ge 0$, $\alpha_S \ge 0$, $\alpha_\xi \ge 0$ are the weights attached to each objective in the utilitarian welfare function and where

* $T(e, b, \tau) = \tau c^L D^L (p, (1+\tau)c^L|b)$ is the revenue from excise taxes on legal cannabis.

* $C(e, b, \tau) = E(\delta, q) - qD^I(p, (1+\tau)c^L|b)F$ is the enforcement cost $E(\delta, q)$, increasing and convex in $\delta$ and $q$, net of the fines.

* $S^c(e, b, \tau) = S^L(p, (1+\tau)c^L|b) + S^I(p, (1+\tau)c^L|b) - \Psi(b)$ is the sum of the consumer surpluses on the legal and illegal markets, net of $\Psi(b)$, the cost of legal cannabis quality improvement, which is strictly increasing and convex.

- $S^L(p, (1+\tau)c^L|b) = \int_{(1+\tau)c^L}^{\infty} D^L(p, t|b)dt$ is the net consumer surplus on the legal market.

- $S^I(p, (1+\tau)c^L|b) = (1-q) \int_p^{\bar{p}^I} D^I(t, (1+\tau)c^L|b) dt - qD^I(p, (1+\tau)c^L|b)F$ is the net consumer surplus on the illegal market, with $\bar{p}^I$ being the choke-off price on the illegal market.

* $\xi(e, b, \tau) = \xi_I D^I(p, (1+\tau)c^L|b) + \xi_L D^L(p, (1+\tau)c^L|b)$, with $\xi_I \ge 0$ and $\xi_L \ge 0$, is the negative externalities generated by the illegal and legal sectors, which are increasing in their respective demands.

We consider in turn four different objectives that can be decentralized through the choice of enforcement of sanctions against the illegal sector, $e = (q, \delta)$, and regulation of the legal sector $(b, \tau)$, and study whether they are compatible with the goal of deflating organized crime by setting an eviction price for legal cannabis. We show that the objectives sometimes
reinforce each other, while in other cases they are conflicting. This offers an explanation as to why some reforms have been disappointing in the past.

**Minimizing negative externalities:** $\alpha_T = \alpha_S = \alpha_C = 0$ and $\alpha_\xi > 0$

Because both legal and illegal consumption of psychotropic substances entail health hazards, a government focusing on such externalities minimizes $\xi(e, b, \tau) = \xi_I D^I (p, (1+\tau)c^L|b) + \xi_L D^L (p, (1+\tau)c^L|b)$. We need to distinguish two cases.

* $\xi_I \le \xi_L$: when legal use of cannabis is perceived as having larger negative externalities than illegal use then the government will choose prohibition. Only in this case does the government minimize total consumption. All else being equal (i.e. for the same investment level in repression) legalization inevitably leads to an increase in demand as shown in section 4. Therefore, for a given repression budget, prohibition is the policy that minimizes total consumption of cannabis. To limit the demand for (illegal) cannabis, the government should invest in repression. It should increase the repression against users (i.e. $q$) to decrease the number of people willing to purchase the illegal substance (i.e. to increase $\theta^I$ in (3)). Similarly, increasing the sunk costs and the marginal cost of producing illegally pushes the number of illegal providers $N$ down and their prices up, as shown in section 3. The highest price and lowest demand is achieved by a criminal monopolist.

* $\xi_I > \xi_L$: in contrast, a government may consider that illegal cannabis is more harmful than legal cannabis for several reasons. The quality of legal products can be certified and health damages reduced. Illegal cannabis can be sold to minors or vulnerable groups, who are at risk of developing psychosis. The ban of sale to the under-aged cannot be enforced on the black market: criminals do not mind who is buying their products, as long as they get paid. Finally, it generates a whole range of criminal activities, including violence, corruption and money laundering (see section 2).

Clearly if $\xi_L = 0$, the legalization below eviction price $p^L = bv\theta^I(c)$ derived in proposition 2 is optimal. Indeed if consumers derive utility from cannabis consumption without incurring, nor generating, any negative externality, then reducing its use is a cost, not a benefit. Certain practices, such as driving or working under the influence, should still clearly be prohibited but should be targeted through a different kind of selective policies.<fnref n="21" /> Now if $\xi_L > 0$, the government seeks to annihilate illegal consumption while controlling legal demand, which is achieved through a policy mix described in the corollary to proposition 2.

<footnote n="21">²¹We are grateful to Jeffrey Miron for suggesting this discussion.</footnote>
reinforce each other, while in other cases they are conflicting. This offers an explanation as to why some reforms have been disappointing in the past.

**Minimizing negative externalities:** $\alpha_T = \alpha_S = \alpha_C = 0$ and $\alpha_\xi > 0$

Because both legal and illegal consumption of psychotropic substances entail health hazards, a government focusing on such externalities minimizes $\xi(e, b, \tau) = \xi_I D^I (p, (1+\tau)c^L|b) + \xi_L D^L (p, (1+\tau)c^L|b)$. We need to distinguish two cases.

* $\xi_I \le \xi_L$: when legal use of cannabis is perceived as having larger negative externalities than illegal use then the government will choose prohibition. Only in this case does the government minimize total consumption. All else being equal (i.e. for the same investment level in repression) legalization inevitably leads to an increase in demand as shown in section 4. Therefore, for a given repression budget, prohibition is the policy that minimizes total consumption of cannabis. To limit the demand for (illegal) cannabis, the government should invest in repression. It should increase the repression against users (i.e. $q$) to decrease the number of people willing to purchase the illegal substance (i.e. to increase $\theta^I$ in (3)). Similarly, increasing the sunk costs and the marginal cost of producing illegally pushes the number of illegal providers $N$ down and their prices up, as shown in section 3. The highest price and lowest demand is achieved by a criminal monopolist.

* $\xi_I > \xi_L$: in contrast, a government may consider that illegal cannabis is more harmful than legal cannabis for several reasons. The quality of legal products can be certified and health damages reduced. Illegal cannabis can be sold to minors or vulnerable groups, who are at risk of developing psychosis. The ban of sale to the under-aged cannot be enforced on the black market: criminals do not mind who is buying their products, as long as they get paid. Finally, it generates a whole range of criminal activities, including violence, corruption and money laundering (see section 2).

Clearly if $\xi_L = 0$, the legalization below eviction price $p^L = bv\theta^I(c)$ derived in proposition 2 is optimal. Indeed if consumers derive utility from cannabis consumption without incurring, nor generating, any negative externality, then reducing its use is a cost, not a benefit. Certain practices, such as driving or working under the influence, should still clearly be prohibited but should be targeted through a different kind of selective policies.<fnref n="21" /> Now if $\xi_L > 0$, the government seeks to annihilate illegal consumption while controlling legal demand, which is achieved through a policy mix described in the corollary to proposition 2.

<footnote n="21">²¹We are grateful to Jeffrey Miron for suggesting this discussion.</footnote>
This leaves open the question of how much the government should invest in the repression
against the dealers and their customers. We study this question next.

Optimizing net enforcement cost: $\alpha_C > 0$

The net enforcement cost of repression, $C(e, b, \tau) = E(\delta, q) - qD^I(p, (1+\tau)c^L|b)F$ is strictly positive because, in practice, $qD^I(p, (1+\tau)c^L|b)F$, the revenue from arrests, is always lower than the gross cost of enforcement, $E(\delta, q)$. A government concerned about the cost of the war on drugs might try to optimize the use of law enforcement instruments. We consider two cases.

• Minimizing net enforcement cost: $\alpha_T = \alpha_S = \alpha_\xi = 0$ or $\alpha_\xi > 0$ and $\xi_I > \xi_L = 0$.

In these two cases the government wants to minimize the burden for tax payers of
the net enforcement cost of repression, $C(e, b, \tau) = E(\delta, q) - qD^I(p, (1+\tau)c^L|b)F$,
without restricting consumption. The solution consists in implementing the eviction
price $\underline{p}^L = bv\theta^I(c)$. The government avoids investing too much in repression ($q$ and $\delta$
should be minimal) as it is costly. It implies that $\theta^I(c)$ in (3) will be low in equilibrium.
It also implies that the level of taxes will have to be relatively low at $\tau^{\alpha_C} = \frac{bv\theta^I(c)}{c^L} - 1 > 0$
since $v\theta^I(c) > c \ge c^L$.<fnref n="22" /> In other words, minimizing the cost of enforcement in a
regulated cannabis market is best achieved by implementing a relatively low eviction
price, which means that the subsequent increase in demand for cannabis is large.

• Implementing the eviction price under a demand target: $\bar{D}$

A government concerned by the increase in consumption following the legalization
at the eviction price, as would typically be the case when $\xi_I > \xi_L > 0$, may try to
minimize the net enforcement cost, while containing consumption. It then aims to
minimize $C(e) = E(\delta, q)$ subject to $D^L(\underline{p}^L) \le \bar{D}$ with $\underline{p}^L = bv\theta^I((1+\delta)c^L)$ being
the eviction price defined in proposition 2. This case yields the following proposi-
tion describing the cost-effective combination of instruments required to limit the
consumption of legal cannabis post-legalization.

**Proposition 3** *To eradicate the illegal market while containing the (legal) use of cannabis to a level *D*, the cost-effective combination of policy instruments is such that the consump-*

<footnote n="22">²²Applying the eviction price $\underline{p}^L$, the corresponding level of taxes $\tau^{\alpha_C}$ is simply given by: $bv\theta^I(c) = (1+\tau^{\alpha_C})c^L \Leftrightarrow \tau^{\alpha_C} = \frac{bv\theta^I(c)}{c^L} - 1$. Note that $\tau^{\alpha_C} > 0$. Indeed, $c = (1+\delta)c^L$ and, by definition, $\theta^I(c)$ satisfies $w^+(1-q)u(\theta^I(c)v-c) + w^-(q)u(-c-F) = 0$, such that $v\theta^I(c) > c \ge c^L$.</footnote>
This leaves open the question of how much the government should invest in the repression
against the dealers and their customers. We study this question next.

Optimizing net enforcement cost: $\alpha_C > 0$

The net enforcement cost of repression, $C(e, b, \tau) = E(\delta, q) - qD^I(p, (1+\tau)c^L|b)F$ is strictly positive because, in practice, $qD^I(p, (1+\tau)c^L|b)F$, the revenue from arrests, is always lower than the gross cost of enforcement, $E(\delta, q)$. A government concerned about the cost of the war on drugs might try to optimize the use of law enforcement instruments. We consider two cases.

• Minimizing net enforcement cost: $\alpha_T = \alpha_S = \alpha_\xi = 0$ or $\alpha_\xi > 0$ and $\xi_I > \xi_L = 0$.

In these two cases the government wants to minimize the burden for tax payers of
the net enforcement cost of repression, $C(e, b, \tau) = E(\delta, q) - qD^I(p, (1+\tau)c^L|b)F$,
without restricting consumption. The solution consists in implementing the eviction
price $\underline{p}^L = bv\theta^I(c)$. The government avoids investing too much in repression ($q$ and $\delta$
should be minimal) as it is costly. It implies that $\theta^I(c)$ in (3) will be low in equilibrium.
It also implies that the level of taxes will have to be relatively low at $\tau^{\alpha_C} = \frac{bv\theta^I(c)}{c^L} - 1 > 0$
since $v\theta^I(c) > c \ge c^L$.<fnref n="22" /> In other words, minimizing the cost of enforcement in a
regulated cannabis market is best achieved by implementing a relatively low eviction
price, which means that the subsequent increase in demand for cannabis is large.

• Implementing the eviction price under a demand target: $\bar{D}$

A government concerned by the increase in consumption following the legalization
at the eviction price, as would typically be the case when $\xi_I > \xi_L > 0$, may try to
minimize the net enforcement cost, while containing consumption. It then aims to
minimize $C(e) = E(\delta, q)$ subject to $D^L(\underline{p}^L) \le \bar{D}$ with $\underline{p}^L = bv\theta^I((1+\delta)c^L)$ being
the eviction price defined in proposition 2. This case yields the following proposi-
tion describing the cost-effective combination of instruments required to limit the
consumption of legal cannabis post-legalization.

**Proposition 3** *To eradicate the illegal market while containing the (legal) use of cannabis to a level *D*, the cost-effective combination of policy instruments is such that the consump-*

<footnote n="22">²²Applying the eviction price $\underline{p}^L$, the corresponding level of taxes $\tau^{\alpha_C}$ is simply given by: $bv\theta^I(c) = (1+\tau^{\alpha_C})c^L \Leftrightarrow \tau^{\alpha_C} = \frac{bv\theta^I(c)}{c^L} - 1$. Note that $\tau^{\alpha_C} > 0$. Indeed, $c = (1+\delta)c^L$ and, by definition, $\theta^I(c)$ satisfies $w^+(1-q)u(\theta^I(c)v-c) + w^-(q)u(-c-F) = 0$, such that $v\theta^I(c) > c \ge c^L$.</footnote>
tion constraint is binding, $D^L(p^L) = \bar{D}$, and:

$$ \frac{\frac{\partial D^L(p^L)}{\partial q}}{\frac{\partial D^L(p^L)}{\partial \delta}} = \frac{\frac{\partial E(\delta, q)}{\partial q}}{\frac{\partial E(\delta, q)}{\partial \delta}} \qquad (12) $$

**Proof.** See appendix F.1. ■

This is a standard result: to optimize the utilization of inputs (here law enforcement resources) the marginal rate of transformation between $q$ and $\delta$ in terms of reduction of demand should be equal to their relative marginal cost.

* Minimizing net enforcement cost under a demand target $\bar{D}$: $\alpha_C > 0$ and $\alpha_\xi > 0$

If $\xi_I \le \xi_L$, then the government objective is to minimize the net enforcement cost of repression $C(e, b, \tau) = E(\delta, q) - qD^I(p, (1+\tau)c^L|b)F$ subject to $D^I(p, (1+\tau)c^L|b) \le \bar{D}$. This is typically the objective of most prohibitionist governments. Since reducing the illegal demand is only made possible by further – costly – investments, for a given level of fine $F$, the constraint is binding: $D^I(p, (1+\tau)c^L|b) = \bar{D}$ and the optimal levels of $q$ and $\delta$ then satisfy:

$$ \frac{\frac{\partial D^I(p,(1+\tau)c^L|b)}{\partial q}}{\frac{\partial D^I(p,(1+\tau)c^L|b)}{\partial \delta}} = \frac{\frac{\partial E(\delta,q)}{\partial q} - F\bar{D}}{\frac{\partial E(\delta,q)}{\partial \delta}} \qquad (13) $$

Compared to equation (12), the demand in the left-hand side of (13) is the demand under prohibition and on the right-hand side there is the additional term $-F\bar{D}$. It disappears in (12) because when the regulator chooses legalization at eviction price the black market does not survive and there is no fine collected. Interestingly, under prohibition, everything else being equal, increasing $q$ is more cost effective than increasing $\delta$ as the government collects fines when users are arrested. In theory, fixing a very large value for $F$ is a cheap way to control demand. Yet, very high fines are not feasible in practice. First they would violate the proportionality requirement of punishment (buying cannabis is not a serious crime). Second, as most individuals caught would not be able to pay them, this would result in – costly – congestion of the judicial system. This is why we consider it as given and fixed at its maximum level $F$, as discussed in section 4.1.

Finally the way repression is targeted and enforced matters too. For the sake of simplicity, we abstract from the fine tuning of repression policies by focusing on vertically integrated drug dealers. Yet, unpacking the vertical relationship between traffickers and retailers yields interesting and subtle insights (Poret, 2002, 2009). The effects of stricter
tion constraint is binding, $D^L(p^L) = \bar{D}$, and:

$$ \frac{\frac{\partial D^L(p^L)}{\partial q}}{\frac{\partial D^L(p^L)}{\partial \delta}} = \frac{\frac{\partial E(\delta, q)}{\partial q}}{\frac{\partial E(\delta, q)}{\partial \delta}} \qquad (12) $$

**Proof.** See appendix F.1. ■

This is a standard result: to optimize the utilization of inputs (here law enforcement resources) the marginal rate of transformation between $q$ and $\delta$ in terms of reduction of demand should be equal to their relative marginal cost.

* Minimizing net enforcement cost under a demand target $\bar{D}$: $\alpha_C > 0$ and $\alpha_\xi > 0$

If $\xi_I \le \xi_L$, then the government objective is to minimize the net enforcement cost of repression $C(e, b, \tau) = E(\delta, q) - qD^I(p, (1+\tau)c^L|b)F$ subject to $D^I(p, (1+\tau)c^L|b) \le \bar{D}$. This is typically the objective of most prohibitionist governments. Since reducing the illegal demand is only made possible by further – costly – investments, for a given level of fine $F$, the constraint is binding: $D^I(p, (1+\tau)c^L|b) = \bar{D}$ and the optimal levels of $q$ and $\delta$ then satisfy:

$$ \frac{\frac{\partial D^I(p,(1+\tau)c^L|b)}{\partial q}}{\frac{\partial D^I(p,(1+\tau)c^L|b)}{\partial \delta}} = \frac{\frac{\partial E(\delta,q)}{\partial q} - F\bar{D}}{\frac{\partial E(\delta,q)}{\partial \delta}} \qquad (13) $$

Compared to equation (12), the demand in the left-hand side of (13) is the demand under prohibition and on the right-hand side there is the additional term $-F\bar{D}$. It disappears in (12) because when the regulator chooses legalization at eviction price the black market does not survive and there is no fine collected. Interestingly, under prohibition, everything else being equal, increasing $q$ is more cost effective than increasing $\delta$ as the government collects fines when users are arrested. In theory, fixing a very large value for $F$ is a cheap way to control demand. Yet, very high fines are not feasible in practice. First they would violate the proportionality requirement of punishment (buying cannabis is not a serious crime). Second, as most individuals caught would not be able to pay them, this would result in – costly – congestion of the judicial system. This is why we consider it as given and fixed at its maximum level $F$, as discussed in section 4.1.

Finally the way repression is targeted and enforced matters too. For the sake of simplicity, we abstract from the fine tuning of repression policies by focusing on vertically integrated drug dealers. Yet, unpacking the vertical relationship between traffickers and retailers yields interesting and subtle insights (Poret, 2002, 2009). The effects of stricter
drug law enforcement policies, depending on whether they target retailers or traffickers, have different effects on wholesale and retail prices of drugs. Poret (2002) hence shows that ill targeted efforts to increase repression can, by disrupting well organized drug cartels, decrease final users' prices and increase consumption.

**Maximizing consumer surplus:** $\alpha_T = \alpha_\xi = \alpha_C = 0$ and $\alpha_S > 0$

We consider the case of a government aiming at maximizing consumer surplus $S^c(e, b, \tau) = S^L(p, (1+\tau)c^L|b) + S^I(p, (1+\tau)c^L|b) - \Psi(b)$. Legal cannabis is a superior good compared to illegal cannabis. First, the quality of legal cannabis is better, and second, the purchase experience involves no risk. It implies that when they are sold at the same price all consumers prefer legal cannabis to illegal cannabis. The consumer willingness to pay for legal cannabis is higher than the consumer willingness to pay for illegal cannabis. Moreover, costs of supplying legal cannabis are lower than costs of illegal cannabis. Hence, for a given quantity, the consumer surplus is the highest when only legal cannabis is exchanged. A government prioritizing consumer surplus will therefore choose a legalization policy such that the illegal market does not survive (see these conditions in case 1, appendix F.2). In other words, a government focusing on consumer surplus should choose a price lower than the eviction price. If the government has the sole objective of maximizing the consumer surplus, it should set the price of legal cannabis as low as feasible, and not tax legal cannabis, i.e. set $\tau = 0$ and $p^L = c^L$. The government should also aim to improve the quality of cannabis products (notably in terms of variety, availability, marketing and packaging) to increase $S^L(p, (1+\tau)c^L|b)$ while taking into account the costs of this investment, $\Psi(b)$. That is, the government maximizes with respect to $b$ the function $\int_{(1+\tau)c^L}^{\infty} D^L(t|b) dt - \Psi(b)$. The next proposition derives the optimal investment level.

**Proposition 4** To maximize consumer surplus a government should invest in quality $b^*$ such that:

$$ \int_{(1+\tau)c^L}^{\infty} \frac{\partial D^L(t|b)}{\partial b} dt = \Psi'(b). \quad (14) $$

The quality investment, $b^*$, that maximizes consumer surplus equalizes the marginal surplus of consumers with the marginal cost of quality improvement. This aspect of legalization reforms is generally neglected by policy makers. It is rarely discussed in public debates or by the media. Because cannabis is perceived as a sinful product, it is not treated like other consumption goods, for which quality is a central issue for consumers, producers and regulators. This is unfortunate because selling legal products of better quality facilitates the eviction of the illegal cannabis market, while increasing the surplus of consumers of legal products.
drug law enforcement policies, depending on whether they target retailers or traffickers, have different effects on wholesale and retail prices of drugs. Poret (2002) hence shows that ill targeted efforts to increase repression can, by disrupting well organized drug cartels, decrease final users' prices and increase consumption.

**Maximizing consumer surplus:** $\alpha_T = \alpha_\xi = \alpha_C = 0$ and $\alpha_S > 0$

We consider the case of a government aiming at maximizing consumer surplus $S^c(e, b, \tau) = S^L(p, (1+\tau)c^L|b) + S^I(p, (1+\tau)c^L|b) - \Psi(b)$. Legal cannabis is a superior good compared to illegal cannabis. First, the quality of legal cannabis is better, and second, the purchase experience involves no risk. It implies that when they are sold at the same price all consumers prefer legal cannabis to illegal cannabis. The consumer willingness to pay for legal cannabis is higher than the consumer willingness to pay for illegal cannabis. Moreover, costs of supplying legal cannabis are lower than costs of illegal cannabis. Hence, for a given quantity, the consumer surplus is the highest when only legal cannabis is exchanged. A government prioritizing consumer surplus will therefore choose a legalization policy such that the illegal market does not survive (see these conditions in case 1, appendix F.2). In other words, a government focusing on consumer surplus should choose a price lower than the eviction price. If the government has the sole objective of maximizing the consumer surplus, it should set the price of legal cannabis as low as feasible, and not tax legal cannabis, i.e. set $\tau = 0$ and $p^L = c^L$. The government should also aim to improve the quality of cannabis products (notably in terms of variety, availability, marketing and packaging) to increase $S^L(p, (1+\tau)c^L|b)$ while taking into account the costs of this investment, $\Psi(b)$. That is, the government maximizes with respect to $b$ the function $\int_{(1+\tau)c^L}^{\infty} D^L(t|b) dt - \Psi(b)$. The next proposition derives the optimal investment level.

**Proposition 4** To maximize consumer surplus a government should invest in quality $b^*$ such that:

$$ \int_{(1+\tau)c^L}^{\infty} \frac{\partial D^L(t|b)}{\partial b} dt = \Psi'(b). \quad (14) $$

The quality investment, $b^*$, that maximizes consumer surplus equalizes the marginal surplus of consumers with the marginal cost of quality improvement. This aspect of legalization reforms is generally neglected by policy makers. It is rarely discussed in public debates or by the media. Because cannabis is perceived as a sinful product, it is not treated like other consumption goods, for which quality is a central issue for consumers, producers and regulators. This is unfortunate because selling legal products of better quality facilitates the eviction of the illegal cannabis market, while increasing the surplus of consumers of legal products.
**Maximizing tax revenue: $\alpha_S = \alpha_\xi = \alpha_C = 0$ and $\alpha_T > 0$**

Some governments have the objective to substantially increase their tax revenue when they legalize recreational cannabis. This objective is for instance at the heart of the legalization reforms in California. When focusing on tax revenue, the government will choose $\tau^{\alpha_T} > 0$ such that $\frac{\partial T}{\partial \tau} = 0$, assuming an interior solution exists. We deduce the next proposition.

**Proposition 5** To maximize tax revenues a government should choose the excise tax level $\tau^{\alpha_T} > 0$ such that:

$$1 - G(\theta^l) = \tau c^L g(\theta^l) \frac{\partial \theta^l}{\partial p^L}, \qquad (15)$$

with $\theta^l = \theta^0 = \frac{p^L}{b\nu}$ if the black market has been eliminated, and $\theta^l = \theta^L$ defined in (7) if not.

**Proof.** See appendix F.2 ■

Note that the black market may survive or not depending on the level of tax, the level of repression on both the demand and supply sides of the cannabis market and the quality differential. In appendix F.2, we develop an example where $\theta$ follows an exponential distribution on the positive real line so that we can derive closed form solutions. This simple example highlights that the unconstrained solution (i.e., in the absence of competition by the black market) leads to a larger excise tax than the constrained solution: $\tau_0^{\alpha_T} \ge \tau^{\alpha_T}$,<fnref n="23" /> which is intuitive. When the government does not have to deal with competition it can impose higher taxes, as the consumers are captive. Unsurprisingly, the price resulting from the tax optimization problem is generally higher than the eviction price $\underline{p}^L = b\nu\theta^I((1+\delta)c^L)$. There is a trade-off between maximizing tax revenue and crime eradication.

The flourishing opium market at the beginning of the 19th century illustrates this trade-off. To control the opium market in the East-Indies, the Dutch government imposed a state monopoly and provided licences to consumers in what was called *opium regie*. Although the aim was to regulate the market and tax it better, it had to compromise between imposing low prices (getting lower revenues) and having fewer smugglers on the market, or getting higher revenues with a high regulated price, which allowed smugglers to enter the market and compete on price (van Ours, 1995).

A way to limit the problem of black-market resurgence is to encourage investment by legal producers and distributors in quality of their products. A higher quality gap $b$ between the legal and illegal market increases the eviction price and implies a lower increase in post-legalization demand or the possibility to implement higher tax rates, without fueling the illegal market. For instance, if the goal is to maximize tax revenue, investment in quality, $b_\tau$, should be set so that: $\tau c^L \frac{\partial D^L(p, (1+\tau)c^L/b)}{\partial b} = \Psi'(b)$. At the optimum, the marginal benefit in terms of tax collection of the quality improvement is equal to its marginal cost. Nevertheless,

<footnote n="23">²³They are equal only when $q = 1$.</footnote>
**Maximizing tax revenue: $\alpha_S = \alpha_\xi = \alpha_C = 0$ and $\alpha_T > 0$**

Some governments have the objective to substantially increase their tax revenue when they legalize recreational cannabis. This objective is for instance at the heart of the legalization reforms in California. When focusing on tax revenue, the government will choose $\tau^{\alpha_T} > 0$ such that $\frac{\partial T}{\partial \tau} = 0$, assuming an interior solution exists. We deduce the next proposition.

**Proposition 5** To maximize tax revenues a government should choose the excise tax level $\tau^{\alpha_T} > 0$ such that:

$$1 - G(\theta^l) = \tau c^L g(\theta^l) \frac{\partial \theta^l}{\partial p^L}, \qquad (15)$$

with $\theta^l = \theta^0 = \frac{p^L}{b\nu}$ if the black market has been eliminated, and $\theta^l = \theta^L$ defined in (7) if not.

**Proof.** See appendix F.2 ■

Note that the black market may survive or not depending on the level of tax, the level of repression on both the demand and supply sides of the cannabis market and the quality differential. In appendix F.2, we develop an example where $\theta$ follows an exponential distribution on the positive real line so that we can derive closed form solutions. This simple example highlights that the unconstrained solution (i.e., in the absence of competition by the black market) leads to a larger excise tax than the constrained solution: $\tau_0^{\alpha_T} \ge \tau^{\alpha_T}$,<fnref n="23" /> which is intuitive. When the government does not have to deal with competition it can impose higher taxes, as the consumers are captive. Unsurprisingly, the price resulting from the tax optimization problem is generally higher than the eviction price $\underline{p}^L = b\nu\theta^I((1+\delta)c^L)$. There is a trade-off between maximizing tax revenue and crime eradication.

The flourishing opium market at the beginning of the 19th century illustrates this trade-off. To control the opium market in the East-Indies, the Dutch government imposed a state monopoly and provided licences to consumers in what was called *opium regie*. Although the aim was to regulate the market and tax it better, it had to compromise between imposing low prices (getting lower revenues) and having fewer smugglers on the market, or getting higher revenues with a high regulated price, which allowed smugglers to enter the market and compete on price (van Ours, 1995).

A way to limit the problem of black-market resurgence is to encourage investment by legal producers and distributors in quality of their products. A higher quality gap $b$ between the legal and illegal market increases the eviction price and implies a lower increase in *post-legalization* demand or the possibility to implement higher tax rates, without fueling the illegal market. For instance, if the goal is to maximize tax revenue, investment in quality, $b_\tau$, should be set so that: $\tau c^L \frac{\partial D^L(p, (1+\tau)c^L/b)}{\partial b} = \Psi'(b)$. At the optimum, the marginal benefit in terms of tax collection of the quality improvement is equal to its marginal cost. Nevertheless,

<footnote n="23">²³They are equal only when $q = 1$.</footnote>
when the government aims at maximizing tax revenues, and neglects to encourage R&D investments to improve quality, or to substantially increase sanctions against dealers, part of the black market will survive. We explore whether this is indeed likely to be the case in practice in section 6.

## Discussion of the compatibility of reforms' objectives

This review of legalization objectives shows that deflating crime through an eviction price is compatible with the maximization of consumer surplus, the minimization of enforcement cost related to the regulation of cannabis market, and the minimization of negative externalities entailed by illegal cannabis use. Interestingly enough, justifying prohibition based on our general economic framework requires that public authorities consider health hazards and other negative externalities entailed by legal cannabis consumption equal or worse than those entailed by illegal cannabis. The current dominant policies of prohibition are only optimal when the government wishes to minimize the total consumption of cannabis regardless of its source.

Moreover, we have shown that for legalization reforms to succeed at eradicating crime, the quantity and quality of legal cannabis, as well as the relative value of the purchasing experience for legal versus illegal products must be high. An important and generally overlooked tool the government can use to regulate the cannabis market post-legalization is to improve the quality of legal cannabis relative to illegal cannabis. To fight the black market, an abundant provision of products of good quality is key. This effort should be increased as governments put more weight on health externalities, consumer surplus, enforcement cost or tax revenue.

Finally, the analysis suggests that the maximization of tax revenue may conflict with the eradication of the black market. For many values of the model parameters, without substantial reinforcement of repression against illegal activities or quality improvements of legal products, the objective of maximizing tax revenue leads to higher final prices of legal cannabis than eviction prices. This leaves room for illegal providers to operate. Whether this is likely to happen in practice, following legalization reforms, is explored in the following section.

# 6 Policy implications

In this section we calibrate eviction prices based on data from the US market and explore corresponding variations in cannabis consumption *post-legalization* depending on how policy instruments – investments in repression of illegal activities and in quality of legal cannabis – are combined. We then use these calibrations to examine whether maximizing tax revenue
when the government aims at maximizing tax revenues, and neglects to encourage R&D investments to improve quality, or to substantially increase sanctions against dealers, part of the black market will survive. We explore whether this is indeed likely to be the case in practice in section 6.

## Discussion of the compatibility of reforms' objectives

This review of legalization objectives shows that deflating crime through an eviction price is compatible with the maximization of consumer surplus, the minimization of enforcement cost related to the regulation of cannabis market, and the minimization of negative externalities entailed by illegal cannabis use. Interestingly enough, justifying prohibition based on our general economic framework requires that public authorities consider health hazards and other negative externalities entailed by legal cannabis consumption equal or worse than those entailed by illegal cannabis. The current dominant policies of prohibition are only optimal when the government wishes to minimize the total consumption of cannabis regardless of its source.

Moreover, we have shown that for legalization reforms to succeed at eradicating crime, the quantity and quality of legal cannabis, as well as the relative value of the purchasing experience for legal versus illegal products must be high. An important and generally overlooked tool the government can use to regulate the cannabis market post-legalization is to improve the quality of legal cannabis relative to illegal cannabis. To fight the black market, an abundant provision of products of good quality is key. This effort should be increased as governments put more weight on health externalities, consumer surplus, enforcement cost or tax revenue.

Finally, the analysis suggests that the maximization of tax revenue may conflict with the eradication of the black market. For many values of the model parameters, without substantial reinforcement of repression against illegal activities or quality improvements of legal products, the objective of maximizing tax revenue leads to higher final prices of legal cannabis than eviction prices. This leaves room for illegal providers to operate. Whether this is likely to happen in practice, following legalization reforms, is explored in the following section.

# 6 Policy implications

In this section we calibrate eviction prices based on data from the US market and explore corresponding variations in cannabis consumption *post-legalization* depending on how policy instruments – investments in repression of illegal activities and in quality of legal cannabis – are combined. We then use these calibrations to examine whether maximizing tax revenue
may lead policy makers to set retail prices of legal cannabis higher than eviction prices, which by itself explains the survival of black market. Finally, comparing our model’s predictions to case-studies, we offer explanations for why past legalization reforms in some states of the U.S. have been disappointing.

The calibration exercise uses the CPT functional forms derived by Tversky and Kahneman (1992) detailed in appendix G. In particular, they assume that individuals are risk-averse for gains, risk-seeking for losses and that “losses loom larger than gains” (Kahneman and Tversky, 1979). These features of consumers’ attitude towards risk are modeled using the following value function:

$$u(x) = \begin{cases} x^{\alpha}, & \text{if } x > 0 \\ -\lambda(-x)^{\alpha}, & \text{if } x \le 0 \end{cases} \qquad (16)$$

with $\alpha \in (0, 1)$ and $\lambda \ge 1$ measuring the degree of loss aversion. Further, they allow for individuals to have a poor ability to assess probabilities, by overestimating the odds of rare salient events, and underestimating the odds of more common events. These distortions reflect cognitive biases in criminal behavior as individuals commonly overestimate the typically low risk of being arrested (Chalfin and McCrary, 2017). Individuals’ distorted perceptions of positive (respectively negative) outcomes are modeled by the probability weights $w^+$ (respectively $w^-$), where:

$$w^x(q) = \frac{q^{\gamma^x}}{(q^{\gamma^x} + (1-q)^{\gamma^x})^{\frac{1}{\gamma^x}}} \quad \text{with } x = +, -. \qquad (17)$$

Using these specifications and our model, the eviction price $\underline{p}^L = bv\theta^I(c)$ takes the following closed-form expression shown in appendix G:

$$\underline{p}^L = b \left[ \left( \lambda \frac{w^-(q)}{w^+(1-q)} \right)^{\frac{1}{\alpha}} (F+c) + c \right], \qquad (18)$$

## 6.1 Benchmark parameters

The exogenous parameters calibrated by Tversky and Kahneman (1992) are $\lambda = 2.25$, $\alpha = 0.88$, $\gamma^+ = 0.61$ and $\gamma^- = 0.69$.<fnref n="24" /> We benchmark the policy parameters $F$, $q$, $c$, and $b$ based on studies of the US market.

We use the maximum fine of the federal law, set at USD 1,000 for cannabis possession

<footnote n="24">²⁴The (weak) sensitivity of the distribution parameters and of the predictions of the models to the behavioral parameters $\gamma^+$, $\gamma^-$, $\alpha$ and $\lambda$ is discussed in appendix H.2.</footnote>
may lead policy makers to set retail prices of legal cannabis higher than eviction prices, which by itself explains the survival of black market. Finally, comparing our model’s predictions to case-studies, we offer explanations for why past legalization reforms in some states of the U.S. have been disappointing.

The calibration exercise uses the CPT functional forms derived by Tversky and Kahneman (1992) detailed in appendix G. In particular, they assume that individuals are risk-averse for gains, risk-seeking for losses and that “losses loom larger than gains” (Kahneman and Tversky, 1979). These features of consumers’ attitude towards risk are modeled using the following value function:

$$u(x) = \begin{cases} x^{\alpha}, & \text{if } x > 0 \\ -\lambda(-x)^{\alpha}, & \text{if } x \le 0 \end{cases} \qquad (16)$$

with $\alpha \in (0, 1)$ and $\lambda \ge 1$ measuring the degree of loss aversion. Further, they allow for individuals to have a poor ability to assess probabilities, by overestimating the odds of rare salient events, and underestimating the odds of more common events. These distortions reflect cognitive biases in criminal behavior as individuals commonly overestimate the typically low risk of being arrested (Chalfin and McCrary, 2017). Individuals’ distorted perceptions of positive (respectively negative) outcomes are modeled by the probability weights $w^+$ (respectively $w^-$), where:

$$w^x(q) = \frac{q^{\gamma^x}}{(q^{\gamma^x} + (1-q)^{\gamma^x})^{\frac{1}{\gamma^x}}} \quad \text{with } x = +, -. \qquad (17)$$

Using these specifications and our model, the eviction price $\underline{p}^L = bv\theta^I(c)$ takes the following closed-form expression shown in appendix G:

$$\underline{p}^L = b \left[ \left( \lambda \frac{w^-(q)}{w^+(1-q)} \right)^{\frac{1}{\alpha}} (F+c) + c \right], \qquad (18)$$

## 6.1 Benchmark parameters

The exogenous parameters calibrated by Tversky and Kahneman (1992) are $\lambda = 2.25$, $\alpha = 0.88$, $\gamma^+ = 0.61$ and $\gamma^- = 0.69$.<fnref n="24" /> We benchmark the policy parameters $F$, $q$, $c$, and $b$ based on studies of the US market.

We use the maximum fine of the federal law, set at USD 1,000 for cannabis possession

<footnote n="24">²⁴The (weak) sensitivity of the distribution parameters and of the predictions of the models to the behavioral parameters $\gamma^+$, $\gamma^-$, $\alpha$ and $\lambda$ is discussed in appendix H.2.</footnote>
on a first offense, as a benchmark, given it is applied in a non-negligible number of states.<fnref n="25" />
Since fines vary across states, we perform a sensitivity analysis on a range of realistic values.

Nguyen and Reuter (2012) highlight that the average probability of being arrested in possession of cannabis where it is prohibited is around 1% although sex, age, and ethnicity strongly influence the probability of being stopped by the police. Following the legalization of recreational cannabis, illegal users are more difficult to detect, which is why we set the benchmark value for the probability of arrest at $q = 0.1\%$ post-legalization and perform a sensitivity analysis using a large range of values for this policy parameter. This includes a 0 probability of being arrested to reflect lax enforcement against the consumers of illegal cannabis.

Although production costs of operation by illegal providers are hard to estimate precisely, we choose USD 50 per ounce as our benchmark value.<fnref n="26" /> This cost increases strongly with sanctions against black market suppliers, who may incur large losses and have to constantly adapt their activities. This motivates our sensitivity analysis using a large range of values.

The extent to which individuals value more highly the use of legal cannabis relatively to illegal one, $b$, is also difficult to measure. It reflects not only some product attributes in terms of chemical composition (e.g. potency, taste), but also in their quality standards, both at upstream (cropping and processing) and retail (shopping experience) levels. We set the benchmark measure of $b$ using the relative THC potency of legal and illegal cannabis. Taking the potency or purity as a measure of quality is relatively standard in the literature on markets for illicit drugs (see for instance Galenianos et al., 2012; Galenianos and Gavazza, 2017). According to ElSohly et al. (2016), the average THC potency of cannabis seized in the US in 2014 was 11.84%, while around the same time, the THC potency on Colorado's legal market was 18.7%, yielding $b = \frac{18.7}{11.84} \approx 1.58$ as a benchmark.<fnref n="27" /> The fact that consumers consider legal cannabis superior to illegal cannabis is also in line with experimental findings on the substitutability of legal and illegal cannabis in catchment areas where the two types of products are available (Amlung et al., 2019). Our sensitivity analysis uses a large range of values for the parameter $b$, which strongly depends on public policies as well. It includes values below 1, reflecting poor quality of products as initially experienced by consumers in Canada following the legalization reform.

<footnote n="25">²⁵Fines for any amount seized, on a first offense, are described at: https://norml.org/laws/federal-penalties-2/</footnote>

<footnote n="26">²⁶The LSE Expert Group on the Economics of Drug Policy (Quah et al., 2014) estimates the wholesale price of a pound of illegal cannabis under prohibition to be around USD 3,500, and about 10 times smaller under legalization – which is consistent with Caulkins (2010). The LSE Expert Group also reports the typical farmgate price quoted in the media to be around USD 2,000 per pound (i.e. USD 125 per ounce). Accordingly, the marginal cost for an ounce of illegal cannabis *post-legalization* ranges between USD 25 and USD 125.</footnote>

<footnote n="27">²⁷Briggs, Bill. 2015 “Colorado Marijuana Study Finds Legal Weed Contains Potent THC Levels”. *CNBC News*, March 23.</footnote>
on a first offense, as a benchmark, given it is applied in a non-negligible number of states.<fnref n="25" />
Since fines vary across states, we perform a sensitivity analysis on a range of realistic values.

Nguyen and Reuter (2012) highlight that the average probability of being arrested in possession of cannabis where it is prohibited is around 1% although sex, age, and ethnicity strongly influence the probability of being stopped by the police. Following the legalization of recreational cannabis, illegal users are more difficult to detect, which is why we set the benchmark value for the probability of arrest at $q = 0.1\%$ post-legalization and perform a sensitivity analysis using a large range of values for this policy parameter. This includes a 0 probability of being arrested to reflect lax enforcement against the consumers of illegal cannabis.

Although production costs of operation by illegal providers are hard to estimate precisely, we choose USD 50 per ounce as our benchmark value.<fnref n="26" /> This cost increases strongly with sanctions against black market suppliers, who may incur large losses and have to constantly adapt their activities. This motivates our sensitivity analysis using a large range of values.

The extent to which individuals value more highly the use of legal cannabis relatively to illegal one, $b$, is also difficult to measure. It reflects not only some product attributes in terms of chemical composition (e.g. potency, taste), but also in their quality standards, both at upstream (cropping and processing) and retail (shopping experience) levels. We set the benchmark measure of $b$ using the relative THC potency of legal and illegal cannabis. Taking the potency or purity as a measure of quality is relatively standard in the literature on markets for illicit drugs (see for instance Galenianos et al., 2012; Galenianos and Gavazza, 2017). According to ElSohly et al. (2016), the average THC potency of cannabis seized in the US in 2014 was 11.84%, while around the same time, the THC potency on Colorado's legal market was 18.7%, yielding $b = \frac{18.7}{11.84} \approx 1.58$ as a benchmark.<fnref n="27" /> The fact that consumers consider legal cannabis superior to illegal cannabis is also in line with experimental findings on the substitutability of legal and illegal cannabis in catchment areas where the two types of products are available (Amlung et al., 2019). Our sensitivity analysis uses a large range of values for the parameter $b$, which strongly depends on public policies as well. It includes values below 1, reflecting poor quality of products as initially experienced by consumers in Canada following the legalization reform.

<footnote n="25">²⁵Fines for any amount seized, on a first offense, are described at: https://norml.org/laws/federal-penalties-2/</footnote>

<footnote n="26">²⁶The LSE Expert Group on the Economics of Drug Policy (Quah et al., 2014) estimates the wholesale price of a pound of illegal cannabis under prohibition to be around USD 3,500, and about 10 times smaller under legalization – which is consistent with Caulkins (2010). The LSE Expert Group also reports the typical farmgate price quoted in the media to be around USD 2,000 per pound (i.e. USD 125 per ounce). Accordingly, the marginal cost for an ounce of illegal cannabis *post-legalization* ranges between USD 25 and USD 125.</footnote>

<footnote n="27">²⁷Briggs, Bill. 2015 “Colorado Marijuana Study Finds Legal Weed Contains Potent THC Levels”. *CNBC News*, March 23.</footnote>
## 6.2 Eviction price of cannabis and demand increase following legalization

We first use the benchmark values and specifications discussed above to calibrate the eviction price on the U.S. cannabis market given in (18). We obtain a price for legal cannabis at around USD 97.79 per ounce. Then we compute the increase in demand following the legalization at eviction price. This requires an estimate of the price elasticity of demand of cannabis. Based on the estimates of van Ours and Williams (2007) between -0.50 and -0.70 and of Davis et al. (2016) between -0.67 and -0.79, our calibrations allow for a range of price elasticities of demand between -0.5 and -0.8. Assuming that the taste for cannabis $\theta$ is normally distributed, we calibrate in appendix H.1 the parameters of the Gaussian distribution using our model and the literature on cannabis demand.<fnref n="28" /> We find predicted increases in demand in the range of 53% to 92%, depending on the price elasticity of demand adopted.

For comparison, we present in table 1 the illegal and legal prices, $p$ and $p^L$ respectively, observed in 7 states of the U.S. in 2018. We also report the number of licensed recreational retailers, and, for comparison, the number of McDonald's restaurants, as well as each state's share of the U.S. legal market for cannabis. These figures give an idea of the degree of liberalization of the market for recreational cannabis in each state, which we discuss with the legalization reforms below.

In most states, the predicted eviction price for legal cannabis is much lower than the observed legal prices, which helps explaining why the black market is thriving, especially in California. But in the case of Colorado and Oregon prices of legal cannabis are closer to the eviction price, which explains why, in these two states, cannabis consumers have massively shifted toward the legal market.<fnref n="29" /> The research firm New Frontier Data (NFD) estimates Oregon's legal market share at 86% in 2020, just behind its share in Colorado, at 87% (New Frontier Data, 2020). In the same report, NFD forecasts that by 2025, 93% of cannabis demand in Oregon will be met with legal products.

This shift toward legal cannabis was accompanied by a bump in overall demand: the National Survey on Drug Use and Health reports cannabis prevalence in Oregon to have increased by almost 60% between 2014 and 2017. Colorado saw a similar evolution of its demand between 2012 and 2015, having preceded Oregon in its legalization reform.<fnref n="30" /> These

<footnote n="28">²⁸Appendix H.1 shows that the mean value of $\theta$ varies between -436.4 and -1090.9 when the elasticity varies between -0.8 and -0.5. This negative average “taste” parameter for cannabis is consistent with surveys in the US reporting negative attitudes towards cannabis consumption on average.</footnote>

<footnote n="29">²⁹Oregon commission reports from 2019 and 2021 demonstrate that the state of Oregon, where legal prices are the lowest and where licences have been flourishing, has been successful in “[offering] the illicit market steep competition” (Oregon Liquor Control Commission, 2021).</footnote>

<footnote n="30">³⁰The NSDUH bases these estimates of prevalence of cannabis use upon the extensive margin of consumption over a 12-month period, for a population aged over 12. In Colorado, the estimated prevalence was 10.41% in 2011-2012 and 16.57% in 2014-2015. In Oregon, it was 12.38% in 2013-2014, 12.73% in 2014-2015 and 19.23% in 2016-2017. These figures were retrieved online using the Substance Abuse and Mental Health Data Archive public data analysis system (https://pdas.samhsa.gov/saes/state).</footnote>
## 6.2 Eviction price of cannabis and demand increase following legalization

We first use the benchmark values and specifications discussed above to calibrate the eviction price on the U.S. cannabis market given in (18). We obtain a price for legal cannabis at around USD 97.79 per ounce. Then we compute the increase in demand following the legalization at eviction price. This requires an estimate of the price elasticity of demand of cannabis. Based on the estimates of van Ours and Williams (2007) between -0.50 and -0.70 and of Davis et al. (2016) between -0.67 and -0.79, our calibrations allow for a range of price elasticities of demand between -0.5 and -0.8. Assuming that the taste for cannabis $\theta$ is normally distributed, we calibrate in appendix H.1 the parameters of the Gaussian distribution using our model and the literature on cannabis demand.<fnref n="28" /> We find predicted increases in demand in the range of 53% to 92%, depending on the price elasticity of demand adopted.

For comparison, we present in table 1 the illegal and legal prices, $p$ and $p^L$ respectively, observed in 7 states of the U.S. in 2018. We also report the number of licensed recreational retailers, and, for comparison, the number of McDonald's restaurants, as well as each state's share of the U.S. legal market for cannabis. These figures give an idea of the degree of liberalization of the market for recreational cannabis in each state, which we discuss with the legalization reforms below.

In most states, the predicted eviction price for legal cannabis is much lower than the observed legal prices, which helps explaining why the black market is thriving, especially in California. But in the case of Colorado and Oregon prices of legal cannabis are closer to the eviction price, which explains why, in these two states, cannabis consumers have massively shifted toward the legal market.<fnref n="29" /> The research firm New Frontier Data (NFD) estimates Oregon's legal market share at 86% in 2020, just behind its share in Colorado, at 87% (New Frontier Data, 2020). In the same report, NFD forecasts that by 2025, 93% of cannabis demand in Oregon will be met with legal products.

This shift toward legal cannabis was accompanied by a bump in overall demand: the National Survey on Drug Use and Health reports cannabis prevalence in Oregon to have increased by almost 60% between 2014 and 2017. Colorado saw a similar evolution of its demand between 2012 and 2015, having preceded Oregon in its legalization reform.<fnref n="30" /> These

<footnote n="28">²⁸Appendix H.1 shows that the mean value of $\theta$ varies between -436.4 and -1090.9 when the elasticity varies between -0.8 and -0.5. This negative average “taste” parameter for cannabis is consistent with surveys in the US reporting negative attitudes towards cannabis consumption on average.</footnote>

<footnote n="29">²⁹Oregon commission reports from 2019 and 2021 demonstrate that the state of Oregon, where legal prices are the lowest and where licences have been flourishing, has been successful in “[offering] the illicit market steep competition” (Oregon Liquor Control Commission, 2021).</footnote>

<footnote n="30">³⁰The NSDUH bases these estimates of prevalence of cannabis use upon the extensive margin of consumption over a 12-month period, for a population aged over 12. In Colorado, the estimated prevalence was 10.41% in 2011-2012 and 16.57% in 2014-2015. In Oregon, it was 12.38% in 2013-2014, 12.73% in 2014-2015 and 19.23% in 2016-2017. These figures were retrieved online using the Substance Abuse and Mental Health Data Archive public data analysis system (https://pdas.samhsa.gov/saes/state).</footnote>
<table><caption>Table 1: Legal markets across the U.S.</caption><thead><tr><th>State</th><th>p</th><th>p<sup>L</sup></th><th>Recreational retailers</th><th>McDonald's restaurants</th><th>Share of US legal market</th><th>Population</th></tr></thead><tbody><tr><td>AK</td><td>298.24</td><td>361.57</td><td>123</td><td>32</td><td>0.63%</td><td>0.7</td></tr><tr><td>CA</td><td>256.57</td><td>344.45</td><td>901</td><td>1,279</td><td>34.9%</td><td>39.5</td></tr><tr><td>CO</td><td>241.75</td><td>143.07</td><td>587</td><td>209</td><td>15.1%</td><td>5.6</td></tr><tr><td>MA</td><td>339.68</td><td>354.25</td><td>113</td><td>170</td><td>4.2%</td><td>6.9</td></tr><tr><td>NV</td><td>270.57</td><td>295.54</td><td>70</td><td>134</td><td>2.6%</td><td>3.0</td></tr><tr><td>OR</td><td>210.39</td><td>127.06</td><td>661</td><td>130</td><td>7.7%</td><td>4.2</td></tr><tr><td>WA</td><td>233.73</td><td>198.45</td><td>512</td><td>167</td><td>12.8%</td><td>7.5</td></tr></tbody></table>

Prices are in USD per ounce, as of fall 2018. The legal price for Washington State is extrapolated from Lang Jones, Jeanne and Rob Smith. 2019. “Tight Regulations, High Taxes May Keep Washington State’s $1.4B Cannabis Industry from Really Blooming”. *Seattle Business*. January. https://seattlebusinessmag.com/policy/tight-regulations-high-taxes-may-keep-washington-states-14b-cannabis-industry-really-blooming (accessible through the Internet Archive Wayback Machine). All other legal prices are state averages quoted from New Frontier Data (2019), while state average black market prices are retrieved from the crowd-sourced website www.priceofweed.com, which was accessed using the Internet archive Wayback Machine. Numbers of retailers and testing facilities are retrieved from New Frontier Data’s “Cannabis Legalized States” interactive map, as of July 2020. The number of McDonald’s restaurants in each state is scraped from Google Places, as of August 2020. Shares of the US legal market are projections quoted from New Frontier Data (2017). Population is expressed in million inhabitants, as of 2018.

figures are consistent with increases in demand predicted by our model to be in the range of 53% to 92%. The evolution of the cannabis markets in Oregon and in Colorado illustrates the relevance of proposition 2, which predicts substantial increases in cannabis consumption when legalization is implemented at a price close to eviction price.

## 6.3 Effects of policies on post-legalization equilibrium

We now turn to studying how the eviction price can be adjusted depending on the enforcement of other policy instruments and how this affects predicted variations in cannabis consumption following legalization reforms. This counter-factual exercise allows us to see which instruments are the most effective depending on the objectives of the reform. Figure 4 represents eviction prices as a function of the black-market marginal cost c on the x-axis and the quality differential b on the y-axis. Yellow zones represent low prices – below USD 50 per ounce – while dark zones represent high prices – above USD 400 per ounce. To each level of eviction price represented on the color scale “Eviction price $p^L$” we associate the “Corresponding demand variation $\Delta D(p^L)$”, which is the predicted percentage increase in demand *post-legalization* as compared to the level under *status-quo* for a price elasticity
<table><caption>Table 1: Legal markets across the U.S.</caption><thead><tr><th>State</th><th>p</th><th>p<sup>L</sup></th><th>Recreational retailers</th><th>McDonald's restaurants</th><th>Share of US legal market</th><th>Population</th></tr></thead><tbody><tr><td>AK</td><td>298.24</td><td>361.57</td><td>123</td><td>32</td><td>0.63%</td><td>0.7</td></tr><tr><td>CA</td><td>256.57</td><td>344.45</td><td>901</td><td>1,279</td><td>34.9%</td><td>39.5</td></tr><tr><td>CO</td><td>241.75</td><td>143.07</td><td>587</td><td>209</td><td>15.1%</td><td>5.6</td></tr><tr><td>MA</td><td>339.68</td><td>354.25</td><td>113</td><td>170</td><td>4.2%</td><td>6.9</td></tr><tr><td>NV</td><td>270.57</td><td>295.54</td><td>70</td><td>134</td><td>2.6%</td><td>3.0</td></tr><tr><td>OR</td><td>210.39</td><td>127.06</td><td>661</td><td>130</td><td>7.7%</td><td>4.2</td></tr><tr><td>WA</td><td>233.73</td><td>198.45</td><td>512</td><td>167</td><td>12.8%</td><td>7.5</td></tr></tbody></table>

Prices are in USD per ounce, as of fall 2018. The legal price for Washington State is extrapolated from Lang Jones, Jeanne and Rob Smith. 2019. “Tight Regulations, High Taxes May Keep Washington State’s $1.4B Cannabis Industry from Really Blooming”. *Seattle Business*. January. https://seattlebusinessmag.com/policy/tight-regulations-high-taxes-may-keep-washington-states-14b-cannabis-industry-really-blooming (accessible through the Internet Archive Wayback Machine). All other legal prices are state averages quoted from New Frontier Data (2019), while state average black market prices are retrieved from the crowd-sourced website www.priceofweed.com, which was accessed using the Internet archive Wayback Machine. Numbers of retailers and testing facilities are retrieved from New Frontier Data’s “Cannabis Legalized States” interactive map, as of July 2020. The number of McDonald’s restaurants in each state is scraped from Google Places, as of August 2020. Shares of the US legal market are projections quoted from New Frontier Data (2017). Population is expressed in million inhabitants, as of 2018.

figures are consistent with increases in demand predicted by our model to be in the range of 53% to 92%. The evolution of the cannabis markets in Oregon and in Colorado illustrates the relevance of proposition 2, which predicts substantial increases in cannabis consumption when legalization is implemented at a price close to eviction price.

## 6.3 Effects of policies on post-legalization equilibrium

We now turn to studying how the eviction price can be adjusted depending on the enforcement of other policy instruments and how this affects predicted variations in cannabis consumption following legalization reforms. This counter-factual exercise allows us to see which instruments are the most effective depending on the objectives of the reform. Figure 4 represents eviction prices as a function of the black-market marginal cost $c$ on the x-axis and the quality differential $b$ on the y-axis. Yellow zones represent low prices – below USD 50 per ounce – while dark zones represent high prices – above USD 400 per ounce. To each level of eviction price represented on the color scale “Eviction price $p^L$” we associate the “Corresponding demand variation $\Delta D(p^L)$”, which is the predicted percentage increase in demand *post-legalization* as compared to the level under *status-quo* for a price elasticity
of -0.8.<fnref n="31" /> For example, at our benchmark eviction price (very close to USD 100 per ounce) the demand nearly doubles if the price elasticity is -0.8. When the eviction price is around USD 415 per ounce, because investments in repression and in quality are very large, the demand remains constant *post-legalization*. Appendix H.3 presents some robustness analysis for three other values of price elasticity, -0.7, -0.6 and -0.5 in the range supported by the evidence discussed above.

Our results show that the post-legalization equilibrium responds substantially to each policy parameter. Yet some may appear less costly to change than others. An intuitive idea to increase the eviction price *p*^L, at seemingly low costs, would be to increase the fine *F*. For example, with a USD 5000 fine for illegal purchase and other parameters set at their benchmark values then a legal price around USD 169 per ounce would evict illegal providers and contain the increase in consumption.<fnref n="32" /> However, this ignores the hidden costs discussed earlier such as the crowding of the judicial system and the punishment proportionality principle. For similar reasons, it is costly to enforce arrests of users of illegal recreational cannabis after cannabis has been legalized.<fnref n="33" />

More promising are policies enforcing sanctions against illegal providers, instead of consumers. Our simulations show that marginal costs of production for illegal providers, *c*, play a large role in the control of cannabis consumption *post-legalization*. For example, not enforcing repression against them would entail low production costs at around USD 15 per ounce and push the eviction price of cannabis down to USD 42, which would more than double the demand following legalization as illustrated in figure 4.<fnref n="34" /> We conclude that maintaining pressure on criminal networks is key to the success of any legalization reform, as it allows to control consumption of psychoactive substance *post-legalization*. This illustrates that legalization and repression (i.e., sanctions against illicit activities) are complementary policies.

Finally, the sensitivity analysis highlights the potential for investing to increase *b*, the
perceived difference between the quality of legal and illegal cannabis. From a policy per-
spective it may seem counter-intuitive to invest in quality control and marketing of legal
cannabis to limit the increase in *post-legalization* demand, especially when a large fraction
of the population is opposed to the legalization. Yet, the eviction price strongly increases

<footnote n="31">³¹In line with the theory of rational addiction (Becker and Murphy, 1988), individuals are more sensitive to price variations of addictive goods in the long run than in the short run (see Becker et al., 1990, for empirical evidence). Further, demand for legal cannabis is more price elastic (see Hollenbeck and Uetake, 2021), than for illegal cannabis, whose elasticity estimates are in the range we discuss above.</footnote>

<footnote n="32">³²Depending on the price elasticity of demand, the increase ranges between 40% and 68%, see table A7.</footnote>

<footnote n="33">³³Putting aside these constraints, enforcing the probability of arrest to remain at the prohibition level – that is around $q = 1\%$ – would entail an increase in the eviction price of legal cannabis to USD 197 per ounce, limiting the increase in consumption following legalization. Depending on the price elasticity of demand, the increase ranges between 35% and 60%, see table A7.</footnote>

<footnote n="34">³⁴Depending on the price elasticity of demand, the increase ranges between 64% and 111%, see table A7.</footnote>
of -0.8.<fnref n="31" /> For example, at our benchmark eviction price (very close to USD 100 per ounce) the demand nearly doubles if the price elasticity is -0.8. When the eviction price is around USD 415 per ounce, because investments in repression and in quality are very large, the demand remains constant *post-legalization*. Appendix H.3 presents some robustness analysis for three other values of price elasticity, -0.7, -0.6 and -0.5 in the range supported by the evidence discussed above.

Our results show that the post-legalization equilibrium responds substantially to each policy parameter. Yet some may appear less costly to change than others. An intuitive idea to increase the eviction price *p*^L, at seemingly low costs, would be to increase the fine *F*. For example, with a USD 5000 fine for illegal purchase and other parameters set at their benchmark values then a legal price around USD 169 per ounce would evict illegal providers and contain the increase in consumption.<fnref n="32" /> However, this ignores the hidden costs discussed earlier such as the crowding of the judicial system and the punishment proportionality principle. For similar reasons, it is costly to enforce arrests of users of illegal recreational cannabis after cannabis has been legalized.<fnref n="33" />

More promising are policies enforcing sanctions against illegal providers, instead of consumers. Our simulations show that marginal costs of production for illegal providers, *c*, play a large role in the control of cannabis consumption *post-legalization*. For example, not enforcing repression against them would entail low production costs at around USD 15 per ounce and push the eviction price of cannabis down to USD 42, which would more than double the demand following legalization as illustrated in figure 4.<fnref n="34" /> We conclude that maintaining pressure on criminal networks is key to the success of any legalization reform, as it allows to control consumption of psychoactive substance *post-legalization*. This illustrates that legalization and repression (i.e., sanctions against illicit activities) are complementary policies.

Finally, the sensitivity analysis highlights the potential for investing to increase *b*, the
perceived difference between the quality of legal and illegal cannabis. From a policy per-
spective it may seem counter-intuitive to invest in quality control and marketing of legal
cannabis to limit the increase in *post-legalization* demand, especially when a large fraction
of the population is opposed to the legalization. Yet, the eviction price strongly increases

<footnote n="31">³¹In line with the theory of rational addiction (Becker and Murphy, 1988), individuals are more sensitive to price variations of addictive goods in the long run than in the short run (see Becker et al., 1990, for empirical evidence). Further, demand for legal cannabis is more price elastic (see Hollenbeck and Uetake, 2021), than for illegal cannabis, whose elasticity estimates are in the range we discuss above.</footnote>

<footnote n="32">³²Depending on the price elasticity of demand, the increase ranges between 40% and 68%, see table A7.</footnote>

<footnote n="33">³³Putting aside these constraints, enforcing the probability of arrest to remain at the prohibition level – that is around $q = 1\%$ – would entail an increase in the eviction price of legal cannabis to USD 197 per ounce, limiting the increase in consumption following legalization. Depending on the price elasticity of demand, the increase ranges between 35% and 60%, see table A7.</footnote>

<footnote n="34">³⁴Depending on the price elasticity of demand, the increase ranges between 64% and 111%, see table A7.</footnote>
<figure><img src="image_4.png" /><figcaption>Figure 4: Eviction price $p^L$ as a function of the black-market marginal cost $c$ and the quality differential $b$</figcaption></figure>

Notes: Prices are in USD per ounce. All the eviction prices represented on this figure are computed with the fine amount $F$ being fixed at USD 1,000 and the probability of arrest after legalization being fixed at $q = 0.1\%$, as well as the benchmark values for the model parameters, $\alpha = 0.88$, $\lambda = 2.25$, $\gamma^+ = 0.61$ and $\gamma^- = 0.69$. The point represented by an asterisk is the benchmark eviction price of USD 97.79, which is computed from the values of the policy parameters, $c = 50$ and $b = 1.58$. The different lines represent the following isoquants: $p^L = 50$ (dashed), $p^L = 100$ (dash-dotted), $p^L = 250$ (dashed double-dotted), $p^L = 415$ (solid) and $p^L = 500$ (dotted).
<figure><img src="image_5.png" /><figcaption>Figure 4: Eviction price $p^L$ as a function of the black-market marginal cost $c$ and the quality differential $b$</figcaption></figure>

Notes: Prices are in USD per ounce. All the eviction prices represented on this figure are computed with the fine amount $F$ being fixed at USD 1,000 and the probability of arrest after legalization being fixed at $q = 0.1\%$, as well as the benchmark values for the model parameters, $\alpha = 0.88$, $\lambda = 2.25$, $\gamma^+ = 0.61$ and $\gamma^- = 0.69$. The point represented by an asterisk is the benchmark eviction price of USD 97.79, which is computed from the values of the policy parameters, $c = 50$ and $b = 1.58$. The different lines represent the following isoquants: $p^L = 50$ (dashed), $p^L = 100$ (dash-dotted), $p^L = 250$ (dashed double-dotted), $p^L = 415$ (solid) and $p^L = 500$ (dotted).
with *b*, which allows policy makers to mitigate the increase in consumption *post-legalization*. For example, doubling *b* from 1.58 to 3 pushes the eviction price of cannabis up to USD 186, limiting the increase in consumption substantially.<fnref n="35" /> Although this channel is effective at tilting consumption towards the legal sector and controlling it, efforts to improve and advertise the quality of legal products have been generally neglected by public authorities. This partly explains some countries’ disappointing experience with past reforms. It has also been largely overlooked by researchers in economics. To our knowledge we are the first to look into this aspect of cannabis legalization policies.

The policy scenarios discussed so far only affected one parameter at a time. In practice, these measures can be combined, which, with convex cost functions, is more cost-effective as discussed in section 5.<fnref n="36" /> Different examples and a discussion of the sensitivity analysis of eviction price and *post-legalization* consumption to combined measures can be found in table A8 in appendix H.3. Both sets of results highlight that, unless a government significantly invests in the quality of legal products or strongly re-enforces controls against the illegal market, the eviction price is around USD 100 or below. This leads to substantial increases in cannabis use following its legalization.

## 6.4 Policies maximizing tax revenues

This section uses our framework to predict prices on the legal and illegal markets when the government focuses on maximizing tax revenues. In addition to the benchmark values discussed above, we use a value for the marginal costs to produce in the legal sector set at USD 25 in line with Quah et al. (2014) and Caulkins (2010). Methodological detail, as well as simulations for different scenarios in terms of investment into enforcement and quality, can be found in appendix I.

The results highlight that, in most policy scenarios, the price on the legal market maximizing the tax revenue from legal sales is much higher than the eviction price. For example, for the benchmark policy parameters presented in the first row of table A9, the price maximizing tax revenue is roughly USD 297 per ounce. This is consistent with Hollenbeck and Uetake (2021) who argue that the state of Washington is on the ascending portion of the Laffer curve, with a legal price for cannabis around 200 USD per ounce (see table 1). Since the price of legal cannabis that maximizes tax revenues is generally much higher than the eviction price (i.e. USD 97.79 per ounce for the benchmark scenario), the black market survives. Depending on the policy scenario, the black market may account for 15% to up to

<footnote n="35">³⁵Depending on the price elasticity of demand the increase ranges between 37% to 63%, see table A7.</footnote>

<footnote n="36">³⁶For instance if the probability of arrest goes up to 0.5% *post-legalization* and fines are set to USD 4000, a quality differential of 2 enables to set the eviction price at USD 422, which maintains consumption at the prohibition level.</footnote>
with *b*, which allows policy makers to mitigate the increase in consumption *post-legalization*. For example, doubling *b* from 1.58 to 3 pushes the eviction price of cannabis up to USD 186, limiting the increase in consumption substantially.<fnref n="35" /> Although this channel is effective at tilting consumption towards the legal sector and controlling it, efforts to improve and advertise the quality of legal products have been generally neglected by public authorities. This partly explains some countries’ disappointing experience with past reforms. It has also been largely overlooked by researchers in economics. To our knowledge we are the first to look into this aspect of cannabis legalization policies.

The policy scenarios discussed so far only affected one parameter at a time. In practice, these measures can be combined, which, with convex cost functions, is more cost-effective as discussed in section 5.<fnref n="36" /> Different examples and a discussion of the sensitivity analysis of eviction price and *post-legalization* consumption to combined measures can be found in table A8 in appendix H.3. Both sets of results highlight that, unless a government significantly invests in the quality of legal products or strongly re-enforces controls against the illegal market, the eviction price is around USD 100 or below. This leads to substantial increases in cannabis use following its legalization.

## 6.4 Policies maximizing tax revenues

This section uses our framework to predict prices on the legal and illegal markets when the government focuses on maximizing tax revenues. In addition to the benchmark values discussed above, we use a value for the marginal costs to produce in the legal sector set at USD 25 in line with Quah et al. (2014) and Caulkins (2010). Methodological detail, as well as simulations for different scenarios in terms of investment into enforcement and quality, can be found in appendix I.

The results highlight that, in most policy scenarios, the price on the legal market maximizing the tax revenue from legal sales is much higher than the eviction price. For example, for the benchmark policy parameters presented in the first row of table A9, the price maximizing tax revenue is roughly USD 297 per ounce. This is consistent with Hollenbeck and Uetake (2021) who argue that the state of Washington is on the ascending portion of the Laffer curve, with a legal price for cannabis around 200 USD per ounce (see table 1). Since the price of legal cannabis that maximizes tax revenues is generally much higher than the eviction price (i.e. USD 97.79 per ounce for the benchmark scenario), the black market survives. Depending on the policy scenario, the black market may account for 15% to up to

<footnote n="35">³⁵Depending on the price elasticity of demand the increase ranges between 37% to 63%, see table A7.</footnote>

<footnote n="36">³⁶For instance if the probability of arrest goes up to 0.5% *post-legalization* and fines are set to USD 4000, a quality differential of 2 enables to set the eviction price at USD 422, which maintains consumption at the prohibition level.</footnote>
44% of the market. This is supported by evidence showing that the black-market represents 15% to 50% of the transactions in the state of Washington (Arcview Market Research and BDS Analytics, 2019). All these results are robust to scenarios where consumers are less price responsive, as illustrated in tables A10 to A12. As a result, increases in cannabis consumption *post-reforms* maximizing tax revenue are lower than if a legalization reform is implemented at eviction price.

Interestingly, when the quality of cannabis sold on the legal market is not different from the illegal market, the legal price that maximizes tax revenue is relatively close to the eviction price and very little black market survives. This shows a case where maximizing tax revenue and eradicating the black market are compatible. However, with a legal cannabis of low quality, the level of tax revenue is low. Tables A13 to A16 show that these results are robust to a setting with lax controls, in which, post legalization, consumers are not arrested for illegal purchases ($q = 0$).<fnref n="37" />

## 6.5 Lessons from legalization reforms in North America

Following citizens' initiative referendums in November 2012, Colorado and Washington State legalized the recreational use of cannabis. The reforms gave priority to reducing the costs of prohibition, developing a new sector of activity, and generating tax revenue.<fnref n="38" /> Since the initial goal was to meet consumers' needs, production, distribution and sale were entrusted to private operators, who invested in market-driven R&D and quality development. A legal industrial sector has since developed: as of today, each of these states accounts nearly three times more recreational cannabis retailers than McDonald's restaurants (see table 1). This booming legal market generates a substantial revenue, with a market size estimated at around USD 1 billion in 2016 in each of these states (for a population of 5.6 million in Colorado and 7.4 million in Washington State). In Washington State, where the final price is close to USD 200 per ounce, the level of taxes is high, as are quality requirements. This explains why the black market still represents 15% to 50% of the cannabis transactions (Arcview Market Research and BDS Analytics, 2019).<fnref n="39" /> Nevertheless, a few years after legalization, both states are quite happy with the impact of the reforms on

<footnote n="37">³⁷Our simulations in appendix I show for example that when the probability of arrest is zero and $b = 1.01$, the tax maximizing price is similar to the eviction price.</footnote>

<footnote n="38">³⁸The *Colorado Marijuana Legalization Amendment*, or *Amendment 64*, claims that cannabis legalization is "*in the interest of the efficient use of law enforcement resources, enhancing revenue for public purposes, and individual freedom*".</footnote>

<footnote n="39">³⁹According to New Frontier Data economist Beau Whitney, quoted by: Lang Jones, Jeanne and Rob Smith. 2019. "Tight Regulations, High Taxes May Keep Washington State's $1.4B Cannabis Industry from Really Blooming". *Seattle Business*. January. https://seattlebusinessmag.com/policy/tight-regulations-high-taxes-may-keep-washington-states-14b-cannabis-industry-really-blooming* (accessible through the Internet Archive Wayback Machine)</footnote>
44% of the market. This is supported by evidence showing that the black-market represents 15% to 50% of the transactions in the state of Washington (Arcview Market Research and BDS Analytics, 2019). All these results are robust to scenarios where consumers are less price responsive, as illustrated in tables A10 to A12. As a result, increases in cannabis consumption *post-reforms* maximizing tax revenue are lower than if a legalization reform is implemented at eviction price.

Interestingly, when the quality of cannabis sold on the legal market is not different from the illegal market, the legal price that maximizes tax revenue is relatively close to the eviction price and very little black market survives. This shows a case where maximizing tax revenue and eradicating the black market are compatible. However, with a legal cannabis of low quality, the level of tax revenue is low. Tables A13 to A16 show that these results are robust to a setting with lax controls, in which, post legalization, consumers are not arrested for illegal purchases ($q = 0$).<fnref n="37" />

## 6.5 Lessons from legalization reforms in North America

Following citizens' initiative referendums in November 2012, Colorado and Washington State legalized the recreational use of cannabis. The reforms gave priority to reducing the costs of prohibition, developing a new sector of activity, and generating tax revenue.<fnref n="38" /> Since the initial goal was to meet consumers' needs, production, distribution and sale were entrusted to private operators, who invested in market-driven R&D and quality development. A legal industrial sector has since developed: as of today, each of these states accounts nearly three times more recreational cannabis retailers than McDonald's restaurants (see table 1). This booming legal market generates a substantial revenue, with a market size estimated at around USD 1 billion in 2016 in each of these states (for a population of 5.6 million in Colorado and 7.4 million in Washington State). In Washington State, where the final price is close to USD 200 per ounce, the level of taxes is high, as are quality requirements. This explains why the black market still represents 15% to 50% of the cannabis transactions (Arcview Market Research and BDS Analytics, 2019).<fnref n="39" /> Nevertheless, a few years after legalization, both states are quite happy with the impact of the reforms on

<footnote n="37">³⁷Our simulations in appendix I show for example that when the probability of arrest is zero and $b = 1.01$, the tax maximizing price is similar to the eviction price.</footnote>

<footnote n="38">³⁸The *Colorado Marijuana Legalization Amendment*, or *Amendment 64*, claims that cannabis legalization is "*in the interest of the efficient use of law enforcement resources, enhancing revenue for public purposes, and individual freedom*".</footnote>

<footnote n="39">³⁹According to New Frontier Data economist Beau Whitney, quoted by: Lang Jones, Jeanne and Rob Smith. 2019. "Tight Regulations, High Taxes May Keep Washington State's $1.4B Cannabis Industry from Really Blooming". *Seattle Business*. January. https://seattlebusinessmag.com/policy/tight-regulations-high-taxes-may-keep-washington-states-14b-cannabis-industry-really-blooming* (accessible through the Internet Archive Wayback Machine)</footnote>
their local finances and economy and adult consumers enjoy a great variety of high quality cannabis products. These two states had a clear set of compatible priorities that were achieved by combining a market orientation for customers with relatively high taxation.

In contrast, California encounters difficulties to meet one of the main objectives of its legalization reform, raising tax revenue. In an environment where the Medical Marijuana Laws had made the grey economy prosperous, the introduction price/quality ratio of the legal cannabis was too high compared to the price/quality ratio on the illegal market. Since the cannabis industry was already well established under prohibition, consistently with our predictions, it reacted swiftly to the legal offer by lowering its prices. It has since grown, absorbing customers who previously were purchasing medical cannabis legally. Illicit transactions account for approximately 80% of the Californian cannabis market. As a result, tax revenue from the legal sector is a fraction of what was expected and the government of the state is quite disappointed by the reform.40 A better policy would have been to fix a lower introduction price of legal cannabis (i.e., lower tax rate, at least initially), combined with investments to raise quality and marketing to give a competitive edge to the legal products, and a stronger push back against illegal cannabis producers and consumers, in line with the policy mix we discuss in section 5.

The priorities of the recent legalization reform in the state of New York are markedly different from earlier reforms in the US.41 Presented as a social measure, one of its main objectives was to put an end to severe repression disproportionately affecting minorities. The relatively low point of sale retail tax rate – a 9% state tax combined with a 4% local tax – suggests that the state black market is likely to be eradicated quickly.42 It is expected to generate a tax revenue of USD 350 million *per annum* as well as to create 30,000 to 60,000 jobs.

In Canada, the federal government gave to the provinces the responsibility of implementing the new policy by regulating the retail markets, as well as setting possession, use, and cultivation limits for personal use.43 The effects of cannabis legalization in Canada on the black market are difficult to assess. Using monetary circulation, Goodhart and Ashworth (2019) show that the need for cash decreased in the country shortly after the legalization,

<footnote n="40">⁴⁰See: Murphy, Kevin. 2019. “Cannabis Black Market Problem”. *Forbes*. April 4. https://www.forbes.com/sites/kevinmurphy/2019/04/04/cannabis-black-market-problem/#76571956134f</footnote>

<footnote n="41">⁴¹Governor Cuomo signed legislation S.854-A/A.1248-A on 2021, March 31. See New York State Government, 2021. https://www.governor.ny.gov/news/governor-cuomo-signs-legislation-legalizing-adult-use-cannabis</footnote>

<footnote n="42">⁴²Interestingly, this point of sale retail tax is coupled with a THC-potency-based tax on distributors, providing a comparative advantage to low-potency products resembling medical cannabis.</footnote>

<footnote n="43">⁴³The nation-wide legalization policy adopted in 2017 and 2018 took different forms across provinces. For instance in Alberta, home-cultivation is allowed (up to four plants) and online retail sales are managed by a government monopoly, while retail sales are left to private licensed stores. In Québec, one cannot home-grow cannabis and retail sales are organized by the government through the Société Québécoise du Cannabis (SQDC).</footnote>