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>
which they interpret as a decrease in black market cannabis transactions. For them, the
country is heading towards one of the goals Trudeau had set in 2015: “[keeping] profits
out of the hands of criminals”.<fnref n="44" /> However, this optimism is contradicted by the evolution
of the market. The striking shortages at the early hours of legalization, as witnessed in
Québec,<fnref n="45" /> led legal providers to focus on increasing their supply, with no effort to improve
the quality of their products, nor the purchasing experience of the consumers (resulting in
a low *b*). As a result, a thriving black market was still satisfying the demand of over 40%
of Canadians in the third quarter of 2019.<fnref n="46" /> The black market has survived by lowering
its prices, which is consistent with the theory, and the stock market prices of the new legal
firms have plummeted.<fnref n="47" /> The overall (legal plus illegal) demand for cannabis has increased
in Canada, with the extensive margin of use rising from 22% in 2018 to 27% in 2022.<fnref n="48" />

With the objectives of eradicating the black market and drug-related crime, Canada
made the same mistake as Uruguay: the failure to anticipate the reaction of the black
market to legalization and to internalize consumers’ demand for quantity and quality led
to poorly designed reforms, at least initially.<fnref n="49" />

7 Conclusion

By modeling the decisions of cannabis consumers in a risky environment and the behavior of
black-market suppliers pre- and post-legalization, we lay out a general framework to reflect
on existing legalization reforms and design optimal policies. We show that when legalization
is not combined with enforcement of sanctions against illegal activities, it necessarily entails
an increase in cannabis use. Past and current legalization reforms illustrate the complexity
of designing legalization policies. Situations in which cannabis is legal but too expensive
(e.g., California) or rationed and of low quality (e.g., Uruguay or Canada) have resulted in
flourishing illegal businesses with no significant decrease in crime. Our analysis shows how

<footnote n="44">⁴⁴Liberal Party. 2015. “Real change: a new plan for a strong middle class”. https://liberal.ca/wp-content/uploads/sites/292/2020/09/New-plan-for-a-strong-middle-class.pdf</footnote>

<footnote n="45">⁴⁵In Québec, as of March 2019, SQDC stores only open from Wednesday to Sunday, “due to the current supply shortages (...) until product availability is more stable” (SQDC’s website, www.sqdc.ca, March 19, 2019).</footnote>

<footnote n="46">⁴⁶See: Beaulieu, Marie-Cristina. 2020. “Cannabis Black Market”. *Public Safety Canada*. June 15. https://www publicsafety gc ca cnt trnsprnc brfng mtrls prlmntry bndrs 20200930/026/index-en aspx. Updated February 8, 2021.</footnote>

<footnote n="47">⁴⁷Levinson-King, Robin. 2019. “Why Canada’s cannabis bubble burst”. *BBC News*. December 29. https://www.bbc.com/news/world-us-canada-50664578</footnote>

<footnote n="48">⁴⁸See: Government of Canada, Health Infobase. 2022. “Cannabis use for non-medical purposes among Canadians (aged 16+)”. December 16. https://health-infobase.canada.ca/cannabis/#a4</footnote>

<footnote n="49">⁴⁹Since then, public authorities seem to have turned to investing in quality. See: Tomesco, Frédéric. 2022. “4 years after legalization, Quebec’s cannabis stores want to smoke the black market”. *The Montreal Gazette*. October 17. https://montrealgazette.com/business/local-business/4-years-after-legalization-quebecs-cannabis-stores-want-to-smoke-the-black-market</footnote>
which they interpret as a decrease in black market cannabis transactions. For them, the
country is heading towards one of the goals Trudeau had set in 2015: “[keeping] profits
out of the hands of criminals”.<fnref n="44" /> However, this optimism is contradicted by the evolution
of the market. The striking shortages at the early hours of legalization, as witnessed in
Québec,<fnref n="45" /> led legal providers to focus on increasing their supply, with no effort to improve
the quality of their products, nor the purchasing experience of the consumers (resulting in
a low *b*). As a result, a thriving black market was still satisfying the demand of over 40%
of Canadians in the third quarter of 2019.<fnref n="46" /> The black market has survived by lowering
its prices, which is consistent with the theory, and the stock market prices of the new legal
firms have plummeted.<fnref n="47" /> The overall (legal plus illegal) demand for cannabis has increased
in Canada, with the extensive margin of use rising from 22% in 2018 to 27% in 2022.<fnref n="48" />

With the objectives of eradicating the black market and drug-related crime, Canada
made the same mistake as Uruguay: the failure to anticipate the reaction of the black
market to legalization and to internalize consumers’ demand for quantity and quality led
to poorly designed reforms, at least initially.<fnref n="49" />

# 7 Conclusion

By modeling the decisions of cannabis consumers in a risky environment and the behavior of
black-market suppliers pre- and post-legalization, we lay out a general framework to reflect
on existing legalization reforms and design optimal policies. We show that when legalization
is not combined with enforcement of sanctions against illegal activities, it necessarily entails
an increase in cannabis use. Past and current legalization reforms illustrate the complexity
of designing legalization policies. Situations in which cannabis is legal but too expensive
(e.g., California) or rationed and of low quality (e.g., Uruguay or Canada) have resulted in
flourishing illegal businesses with no significant decrease in crime. Our analysis shows how

<footnote n="44">⁴⁴Liberal Party. 2015. “Real change: a new plan for a strong middle class”. https://liberal.ca/wp-content/uploads/sites/292/2020/09/New-plan-for-a-strong-middle-class.pdf</footnote>

<footnote n="45">⁴⁵In Québec, as of March 2019, SQDC stores only open from Wednesday to Sunday, “due to the current supply shortages (...) until product availability is more stable” (SQDC’s website, www.sqdc.ca, March 19, 2019).</footnote>

<footnote n="46">⁴⁶See: Beaulieu, Marie-Cristina. 2020. “Cannabis Black Market”. *Public Safety Canada*. June 15. https://www publicsafety gc ca cnt trnsprnc brfng mtrls prlmntry bndrs 20200930/026/index-en aspx. Updated February 8, 2021.</footnote>

<footnote n="47">⁴⁷Levinson-King, Robin. 2019. “Why Canada’s cannabis bubble burst”. *BBC News*. December 29. https://www.bbc.com/news/world-us-canada-50664578</footnote>

<footnote n="48">⁴⁸See: Government of Canada, Health Infobase. 2022. “Cannabis use for non-medical purposes among Canadians (aged 16+)”. December 16. https://health-infobase.canada.ca/cannabis/#a4</footnote>

<footnote n="49">⁴⁹Since then, public authorities seem to have turned to investing in quality. See: Tomesco, Frédéric. 2022. “4 years after legalization, Quebec’s cannabis stores want to smoke the black market”. *The Montreal Gazette*. October 17. https://montrealgazette.com/business/local-business/4-years-after-legalization-quebecs-cannabis-stores-want-to-smoke-the-black-market</footnote>
to avoid these unexpected effects. We characterize the *eviction* price for legal cannabis and show how this predatory price can be embedded in a policy mix, such that the government can “weed the dealers out” of the market while curbing the – legal – demand for cannabis by raising its price.

Our findings highlight the complementarities between legalization of high quality cannabis (in terms of purchasing experience, gustatory quality of the product, potency and purity) and sanctions against illegal trade, providing policymakers with guidelines to overcome the legalization/consumption increase trade-off. Legalization will be effective at regulating the demand for cannabis if consumers are compelled to buy on a legal market products of good quality rather than uncertified illegal products, and, at the same time, if illegal suppliers are targeted by repressive measures that drive them out of business. Raising the level of punishment and enforcing sanctions, not only against users of illegal drugs but more effectively against suppliers, enable authorities to implement higher legal prices for cannabis while undermining dealers.

Although our analysis focuses on how to achieve full legalization by eliminating the black market while containing consumption *post-legalization*, our general framework can be used to study a broader set of objectives. The optimal combinations of instruments depend on the policy objectives. These vary across settings and, in some cases, lead to the *status-quo* equilibrium where the market is regulated by dealers: prohibition is optimal when the government seeks to minimize the total consumption of cannabis. In other cases, coupling eviction pricing of legal cannabis with other policy instruments enables governments to reach desirable compounds of consumption and tax revenue targets. Extensions we discuss show how our policy mix can be fine-tuned to minimize the negative externalities entailed by cannabis use, to minimize the enforcement costs of policies, to maximize the consumer surplus or to maximize public resources raised through taxation of a legal sector. They highlight the (in)compatibility of some of these objectives, which is likely to give rise to unexpected or undesirable policy effects.

Finally, to shed more light on consumption behavior *post-legalization*, future research should account for the large heterogeneity of consumers, in particular regarding their risk aversion, intensive margin of consumption and liquidity constraints.

## References

Amlung, Michael, Derek D Reed, Vanessa Morris, Elizabeth R Aston, Jane Metrik, and James MacKillop, “Price elasticity of illegal versus legal cannabis: A behavioral economic substitutability analysis,” *Addiction*, 2019, 114 (1), 112–118.
to avoid these unexpected effects. We characterize the *eviction* price for legal cannabis and show how this predatory price can be embedded in a policy mix, such that the government can “weed the dealers out” of the market while curbing the – legal – demand for cannabis by raising its price.

Our findings highlight the complementarities between legalization of high quality cannabis (in terms of purchasing experience, gustatory quality of the product, potency and purity) and sanctions against illegal trade, providing policymakers with guidelines to overcome the legalization/consumption increase trade-off. Legalization will be effective at regulating the demand for cannabis if consumers are compelled to buy on a legal market products of good quality rather than uncertified illegal products, and, at the same time, if illegal suppliers are targeted by repressive measures that drive them out of business. Raising the level of punishment and enforcing sanctions, not only against users of illegal drugs but more effectively against suppliers, enable authorities to implement higher legal prices for cannabis while undermining dealers.

Although our analysis focuses on how to achieve full legalization by eliminating the black market while containing consumption *post-legalization*, our general framework can be used to study a broader set of objectives. The optimal combinations of instruments depend on the policy objectives. These vary across settings and, in some cases, lead to the *status-quo* equilibrium where the market is regulated by dealers: prohibition is optimal when the government seeks to minimize the total consumption of cannabis. In other cases, coupling eviction pricing of legal cannabis with other policy instruments enables governments to reach desirable compounds of consumption and tax revenue targets. Extensions we discuss show how our policy mix can be fine-tuned to minimize the negative externalities entailed by cannabis use, to minimize the enforcement costs of policies, to maximize the consumer surplus or to maximize public resources raised through taxation of a legal sector. They highlight the (in)compatibility of some of these objectives, which is likely to give rise to unexpected or undesirable policy effects.

Finally, to shed more light on consumption behavior *post-legalization*, future research should account for the large heterogeneity of consumers, in particular regarding their risk aversion, intensive margin of consumption and liquidity constraints.

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Caulkins, Jonathan P, “Zero-tolerance policies: do they inhibit or stimulate illicit drug consumption?,” *Management Science*, 1993, **39** (4), 458–476.

Caulkins, Jonathan P, “Estimated cost of production for legalized cannabis,” *RAND, Drug Policy Research Center*. http://www.rand.org/content/dam/rand/pubs/working_papers/2010/RAND_WR764.pdf, 2010.

Caulkins, Jonathan P and Rosalie Liccardo Pacula, “Marijuana markets: Inferences from reports by the household population,” *Journal of Drug Issues*, 2006, **36** (1), 173–200.

Center for Behavioral Health Statistics and Quality, “2017 National Survey on Drug Use and Health: Detailed Tables,” Technical Report, Substance Abuse and Mental Health Services Administration 2018.

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# Appendix

## A Cannabis laws in the U.S.

As of February 2023, nineteen states and the District of Columbia have legalized the use of recreational cannabis. Cannabis possession remains a felony in other states such as Arizona, where sanctions and fines to enforce the law differ a lot. For example in Arizona, there is no guideline for punishment regarding small amounts of cannabis and possessing 2 pounds or less entails a risk of incarceration of up to 2 years and a fine of up to USD 150,000. In contrast, any amount on a first offense in Iowa is only a misdemeanor punishable by a maximum prison sentence of 6 months and a USD 1,000 fine.

The table below offers a synthetic overview of state cannabis laws across the United States. For each state, we reported the year during which cannabis was decriminalized in the second column. The third column records the year of the first ballot to legalize the use of medical cannabis, i.e. to instate a *Medical Marijuana Law* (MML), while the fourth column gives the year during which such a law was passed. The fifth column lists the year of the first ballot to legalize the recreational use of cannabis, and the sixth column the year of such a law being passed. The final column reports the year of the first legal retail sales of cannabis. Dashes represent the absence of the event described in the corresponding column.

<table><thead><tr><th>State</th><th>Decrim.</th><th>1st MML ballot</th><th>MML</th><th>1st rec. ballot</th><th>Rec.</th><th>Retail</th></tr></thead><tbody><tr><td>AL</td><td>-</td><td>-<sup>a</sup></td><td>2021</td><td>-</td><td>-</td><td>-</td></tr><tr><td>AK</td><td>1975<sup>b</sup></td><td>1998</td><td>1998</td><td>2000</td><td>2014</td><td>2016</td></tr><tr><td>AZ</td><td>-</td><td>1996</td><td>2010</td><td>2016</td><td>2020</td><td>2021</td></tr><tr><td>AR</td><td>-<sup>c</sup></td><td>2012</td><td>2016</td><td>2022</td><td>-</td><td>-</td></tr><tr><td>CA</td><td>1975</td><td>1996</td><td>1996</td><td>1972</td><td>2016</td><td>2018</td></tr><tr><td>CO</td><td>1975</td><td>2000</td><td>2000</td><td>2012</td><td>2012</td><td>2014</td></tr><tr><td>CT</td><td>2011</td><td>-<sup>a</sup></td><td>2012</td><td>-<sup>d</sup></td><td>2021</td><td>2023</td></tr><tr><td>DE</td><td>2015</td><td>-<sup>a</sup></td><td>2011</td><td>-</td><td>-</td><td>-</td></tr></tbody></table>

<footnote><sup>a</sup> *Medical Marijuana* was not on the ballot: instead, it was signed into law after legislative approval.</footnote>

<footnote><sup>b</sup>Alaska issued a cannabis decriminalization bill on May 16, 1975, which is two weeks before the famous *Ravin* decision, protecting the possession of small amounts under constitutional privacy rights, was issued. Decriminalization of cannabis came into effect on June 5, 1975. The timeline of cannabis policy in Alaska then becomes fuzzy: further decriminalization was billed in 1982, then cannabis was recriminalized in 1990, decriminalized in 2003, then recriminalized in 2006; while the *Ravin* caselaw would still interact with the criminal state law (Brandeis, 2012). Legalization approved in 2014 ended this confusion.</footnote>

<footnote><sup>c</sup>Although cannabis use remains a crime under state law, it is decriminalized locally.</footnote>

<footnote><sup>d</sup> The recreational use of cannabis was not on the ballot: instead, it was signed into law after legislative approval.</footnote>
# Appendix

## A Cannabis laws in the U.S.

As of February 2023, nineteen states and the District of Columbia have legalized the use of recreational cannabis. Cannabis possession remains a felony in other states such as Arizona, where sanctions and fines to enforce the law differ a lot. For example in Arizona, there is no guideline for punishment regarding small amounts of cannabis and possessing 2 pounds or less entails a risk of incarceration of up to 2 years and a fine of up to USD 150,000. In contrast, any amount on a first offense in Iowa is only a misdemeanor punishable by a maximum prison sentence of 6 months and a USD 1,000 fine.

The table below offers a synthetic overview of state cannabis laws across the United States. For each state, we reported the year during which cannabis was decriminalized in the second column. The third column records the year of the first ballot to legalize the use of medical cannabis, i.e. to instate a *Medical Marijuana Law* (MML), while the fourth column gives the year during which such a law was passed. The fifth column lists the year of the first ballot to legalize the recreational use of cannabis, and the sixth column the year of such a law being passed. The final column reports the year of the first legal retail sales of cannabis. Dashes represent the absence of the event described in the corresponding column.

<table><thead><tr><th>State</th><th>Decrim.</th><th>1st MML ballot</th><th>MML</th><th>1st rec. ballot</th><th>Rec.</th><th>Retail</th></tr></thead><tbody><tr><td>AL</td><td>-</td><td>-<sup>a</sup></td><td>2021</td><td>-</td><td>-</td><td>-</td></tr><tr><td>AK</td><td>1975<sup>b</sup></td><td>1998</td><td>1998</td><td>2000</td><td>2014</td><td>2016</td></tr><tr><td>AZ</td><td>-</td><td>1996</td><td>2010</td><td>2016</td><td>2020</td><td>2021</td></tr><tr><td>AR</td><td>-<sup>c</sup></td><td>2012</td><td>2016</td><td>2022</td><td>-</td><td>-</td></tr><tr><td>CA</td><td>1975</td><td>1996</td><td>1996</td><td>1972</td><td>2016</td><td>2018</td></tr><tr><td>CO</td><td>1975</td><td>2000</td><td>2000</td><td>2012</td><td>2012</td><td>2014</td></tr><tr><td>CT</td><td>2011</td><td>-<sup>a</sup></td><td>2012</td><td>-<sup>d</sup></td><td>2021</td><td>2023</td></tr><tr><td>DE</td><td>2015</td><td>-<sup>a</sup></td><td>2011</td><td>-</td><td>-</td><td>-</td></tr></tbody></table>

<footnote><sup>a</sup> *Medical Marijuana* was not on the ballot: instead, it was signed into law after legislative approval.</footnote>

<footnote><sup>b</sup>Alaska issued a cannabis decriminalization bill on May 16, 1975, which is two weeks before the famous *Ravin* decision, protecting the possession of small amounts under constitutional privacy rights, was issued. Decriminalization of cannabis came into effect on June 5, 1975. The timeline of cannabis policy in Alaska then becomes fuzzy: further decriminalization was billed in 1982, then cannabis was recriminalized in 1990, decriminalized in 2003, then recriminalized in 2006; while the *Ravin* caselaw would still interact with the criminal state law (Brandeis, 2012). Legalization approved in 2014 ended this confusion.</footnote>

<footnote><sup>c</sup>Although cannabis use remains a crime under state law, it is decriminalized locally.</footnote>

<footnote><sup>d</sup> The recreational use of cannabis was not on the ballot: instead, it was signed into law after legislative approval.</footnote>
<table><thead><tr><th>State</th><th>Decrim.</th><th>1st MML ballot</th><th>MML</th><th>1st rec. ballot</th><th>Rec.</th><th>Retail</th></tr></thead><tbody><tr><td>D.C.</td><td>2014</td><td>1998</td><td>2010</td><td>2014</td><td>2014</td><td>-<sup>e</sup></td></tr><tr><td>FL</td><td>-<sup>f</sup></td><td>2014</td><td>2016</td><td>-<sup>g</sup></td><td>-</td><td>-</td></tr><tr><td>GA</td><td>-<sup>f</sup></td><td>-</td><td>-<sup>h</sup></td><td>-</td><td>-</td><td>-</td></tr><tr><td>HI</td><td>2020</td><td>-<sup>a</sup></td><td>2000</td><td>-</td><td>-</td><td>-</td></tr><tr><td>ID</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>IL</td><td>2016</td><td>-<sup>a</sup></td><td>2013</td><td>-<sup>d</sup></td><td>2019</td><td>2020</td></tr><tr><td>IN</td><td>-<sup>i</sup></td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>IA</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>KS</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>KY</td><td>-<sup>f</sup></td><td>-</td><td>-<sup>j</sup></td><td>-</td><td>-</td><td>-</td></tr><tr><td>LA</td><td>2021</td><td>-<sup>a</sup></td><td>2015<sup>k</sup></td><td>-</td><td>-</td><td>-</td></tr><tr><td>ME</td><td>1975</td><td>1999</td><td>1999</td><td>2016</td><td>2016</td><td>2020</td></tr><tr><td>MD</td><td>2014</td><td>-<sup>a</sup></td><td>2013</td><td>2022</td><td>2022</td><td>-<sup>l</sup></td></tr><tr><td>MA</td><td>2008</td><td>2012</td><td>2012</td><td>2016</td><td>2016</td><td>2018</td></tr><tr><td>MI</td><td>2018</td><td>2008</td><td>2008</td><td>2018</td><td>2018</td><td>2019</td></tr><tr><td>MN</td><td>1976</td><td>-<sup>a</sup></td><td>2014</td><td>-</td><td>-<sup>m</sup></td><td>-</td></tr><tr><td>MS</td><td>1978</td><td>2020</td><td>2020</td><td>-</td><td>-</td><td>-</td></tr><tr><td>MO</td><td>2014</td><td>2018</td><td>2018</td><td>2022</td><td>2022</td><td>2023</td></tr><tr><td>MT</td><td>-<sup>f</sup></td><td>2004</td><td>2004</td><td>2020</td><td>2020</td><td>2022</td></tr><tr><td>NE</td><td>1979</td><td>-<sup>n</sup></td><td>-</td><td>-</td><td>-</td><td>-</td></tr></tbody></table>

<footnote><sup>e</sup>Implementation still pending.</footnote>

<footnote><sup>f</sup>Although cannabis use remains a crime under state law, it is decriminalized locally.</footnote>

<footnote><sup>g</sup>A cannabis legalization initiative was expected to be on the ballot in November 2022 and is now expected for November 2024 (“Marijuana on the ballot”, *Ballotpedia*. Retrieved online June 2022 and February 2023, https://ballotpedia.org/Marijuana_on_the-ballot)</footnote>

<footnote><sup>h</sup>A bill was passed in 2015, legalizing the use of *light cannabis*, i.e. cannabis products featuring low THC potency (see Georgia General Assembly, https://www.legis.ga.gov/legislation/42674).</footnote>

<footnote><sup>i</sup>Decriminalized in Marion County as of 2019 (see https://web.archive.org/web/20190930193952/ https://www.wthr.com/article/marion-county-will-no-longer-prosecute-simple-marijuana-cases).</footnote>

<footnote><sup>j</sup>A *Medical Marijuana* bill was presented to the House of Kentucky in January 2020. It is presently under evaluation by the Senate Judiciary Committee (Kentucky General Assembly, *House Bill 136*; retrieved online 3rd December 2020, url: https://apps.legislature.ky.gov/record/20rs/hb136.html).</footnote>

<footnote><sup>k</sup>Although *Medical Marijuana* was signed into law in 2015, it was unlawful to inhale cannabis until 2019 (see https://www.mpp.org/states/louisiana/overview-of-louisianas-medical-cannabis-law/).</footnote>

<footnote><sup>l</sup>Expected July 2023.</footnote>

<footnote><sup>m</sup>In January 2023, the Minnesota House of Representatives introduced bill HF 100, which plans the legalization and regulation of adult-use cannabis (Minnesota House of Representatives, *HF 100*; retrieved online 8th February 2023, url: https://wdoc.house.leg.state.mn.us/leg/LS93/HF0100.0.pdf).</footnote>

<footnote><sup>n</sup>A *Medical Marijuana* ballot is expected to be on the ballot in November 2022 (“Marijuana on the ballot”)</footnote>
<table><thead><tr><th>State</th><th>Decrim.</th><th>1st MML ballot</th><th>MML</th><th>1st rec. ballot</th><th>Rec.</th><th>Retail</th></tr></thead><tbody><tr><td>D.C.</td><td>2014</td><td>1998</td><td>2010</td><td>2014</td><td>2014</td><td>-<sup>e</sup></td></tr><tr><td>FL</td><td>-<sup>f</sup></td><td>2014</td><td>2016</td><td>-<sup>g</sup></td><td>-</td><td>-</td></tr><tr><td>GA</td><td>-<sup>f</sup></td><td>-</td><td>-<sup>h</sup></td><td>-</td><td>-</td><td>-</td></tr><tr><td>HI</td><td>2020</td><td>-<sup>a</sup></td><td>2000</td><td>-</td><td>-</td><td>-</td></tr><tr><td>ID</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>IL</td><td>2016</td><td>-<sup>a</sup></td><td>2013</td><td>-<sup>d</sup></td><td>2019</td><td>2020</td></tr><tr><td>IN</td><td>-<sup>i</sup></td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>IA</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>KS</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>KY</td><td>-<sup>f</sup></td><td>-</td><td>-<sup>j</sup></td><td>-</td><td>-</td><td>-</td></tr><tr><td>LA</td><td>2021</td><td>-<sup>a</sup></td><td>2015<sup>k</sup></td><td>-</td><td>-</td><td>-</td></tr><tr><td>ME</td><td>1975</td><td>1999</td><td>1999</td><td>2016</td><td>2016</td><td>2020</td></tr><tr><td>MD</td><td>2014</td><td>-<sup>a</sup></td><td>2013</td><td>2022</td><td>2022</td><td>-<sup>l</sup></td></tr><tr><td>MA</td><td>2008</td><td>2012</td><td>2012</td><td>2016</td><td>2016</td><td>2018</td></tr><tr><td>MI</td><td>2018</td><td>2008</td><td>2008</td><td>2018</td><td>2018</td><td>2019</td></tr><tr><td>MN</td><td>1976</td><td>-<sup>a</sup></td><td>2014</td><td>-</td><td>-<sup>m</sup></td><td>-</td></tr><tr><td>MS</td><td>1978</td><td>2020</td><td>2020</td><td>-</td><td>-</td><td>-</td></tr><tr><td>MO</td><td>2014</td><td>2018</td><td>2018</td><td>2022</td><td>2022</td><td>2023</td></tr><tr><td>MT</td><td>-<sup>f</sup></td><td>2004</td><td>2004</td><td>2020</td><td>2020</td><td>2022</td></tr><tr><td>NE</td><td>1979</td><td>-<sup>n</sup></td><td>-</td><td>-</td><td>-</td><td>-</td></tr></tbody></table>

<footnote><sup>e</sup>Implementation still pending.</footnote>

<footnote><sup>f</sup>Although cannabis use remains a crime under state law, it is decriminalized locally.</footnote>

<footnote><sup>g</sup> A cannabis legalization initiative was expected to be on the ballot in November 2022 and is now expected for November 2024 ("Marijuana on the ballot", *Ballotpedia*. Retrieved online June 2022 and February 2023, https://ballotpedia.org/Marijuana_on_the-ballot)</footnote>

<footnote><sup>h</sup>A bill was passed in 2015, legalizing the use of *light cannabis*, i.e. cannabis products featuring low THC potency (see Georgia General Assembly, https://www.legis.ga.gov/legislation/42674).</footnote>

<footnote><sup>i</sup>Decriminalized in Marion County as of 2019 (see https://web.archive.org/web/20190930193952/ https://www.wthr.com/article/marion-county-will-no-longer-prosecute-simple-marijuana-cases).</footnote>

<footnote><sup>j</sup>A *Medical Marijuana* bill was presented to the House of Kentucky in January 2020. It is presently under evaluation by the Senate Judiciary Committee (Kentucky General Assembly, *House Bill 136*; retrieved online 3rd December 2020, url: https://apps.legislature.ky.gov/record/20rs/hb136.html).</footnote>

<footnote><sup>k</sup>Although *Medical Marijuana* was signed into law in 2015, it was unlawful to inhale cannabis until 2019 (see https://www.mpp.org/states/louisiana/overview-of-louisianas-medical-cannabis-law/).</footnote>

<footnote><sup>l</sup>Expected July 2023.</footnote>

<footnote><sup>m</sup>In January 2023, the Minnesota House of Representatives introduced bill HF 100, which plans the legalization and regulation of adult-use cannabis (Minnesota House of Representatives, *HF 100*; retrieved online 8th February 2023, url: https://wdoc.house.leg.state.mn.us/leg/LS93/HF0100.0.pdf).</footnote>

<footnote><sup>n</sup> A *Medical Marijuana* ballot is expected to be on the ballot in November 2022 ("Marijuana on the ballot").</footnote>
<table><thead><tr><th>State</th><th>Decrim.</th><th>1st MML ballot</th><th>MML</th><th>1st rec. ballot</th><th>Rec.</th><th>Retail</th></tr></thead><tbody><tr><td>NV</td><td>2016</td><td>1998</td><td>1998</td><td>2006</td><td>2016</td><td>2017</td></tr><tr><td>NH</td><td>2017</td><td>-<sup>a</sup></td><td>2013</td><td>-</td><td>-</td><td>-</td></tr><tr><td>NJ</td><td>-</td><td>-<sup>a</sup></td><td>2010</td><td>2020</td><td>2020</td><td>2022</td></tr><tr><td>NM</td><td>2019</td><td>-<sup>a</sup></td><td>2007</td><td><sup>d</sup></td><td>2021</td><td>2022</td></tr><tr><td>NY</td><td>1977</td><td>-<sup>a</sup></td><td>2014</td><td>-<sup>d</sup></td><td>2021</td><td>2022</td></tr><tr><td>NC</td><td>1977</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>ND</td><td>2019</td><td>2016</td><td>2016</td><td>2018</td><td>-</td><td>-</td></tr><tr><td>OH</td><td>1975</td><td>-<sup>a</sup></td><td>2016</td><td>2015</td><td>-</td><td>-</td></tr><tr><td>OK</td><td>-<sup>o</sup></td><td>2018</td><td>2018</td><td>-<sup>p</sup></td><td>-</td><td>-</td></tr><tr><td>OR</td><td>1973</td><td>1998</td><td>1998</td><td>2012</td><td>2014</td><td>2015</td></tr><tr><td>PA</td><td>-<sup>f</sup></td><td>-<sup>a</sup></td><td>2016</td><td>-</td><td>-</td><td>-</td></tr><tr><td>RI</td><td>2012</td><td>-<sup>a</sup></td><td>2005</td><td>-<sup>d</sup></td><td>2022</td><td>-</td></tr><tr><td>SC</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>SD</td><td>-</td><td>2006</td><td>2020</td><td>2020</td><td>-<sup>q</sup></td><td>-</td></tr><tr><td>TN</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>TX</td><td>-<sup>f</sup></td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>UT</td><td>-</td><td>2018</td><td>2018</td><td>-</td><td>-</td><td>-</td></tr><tr><td>VT</td><td>2013</td><td>-<sup>a</sup></td><td>2004</td><td>-<sup>d</sup></td><td>2018</td><td>2020</td></tr><tr><td>VA</td><td>-</td><td>-</td><td>-</td><td>-<sup>d</sup></td><td>2021</td><td>-<sup>r</sup></td></tr><tr><td>WA</td><td>2012</td><td>1998</td><td>1998</td><td>2012</td><td>2012</td><td>2014</td></tr><tr><td>WV</td><td>-</td><td>-</td><td>2017<sup>s</sup></td><td>-</td><td>-</td><td>-</td></tr><tr><td>WI</td><td>-<sup>f</sup></td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>WY</td><td>-<sup>t</sup></td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr></tbody></table>

ballot”, *Ballotpedia*. Retrieved online June 2022, https://ballotpedia.org/Marijuana_on_the-ballot).

<sup>o</sup>A cannabis decriminalization initiative is expected to be on the ballot in November 2022 (“Okla-homa State Question 812, Marijuana Decriminalization Initiative (2022)”, retrieved online on Ballot-pedia; url: https://ballotpedia.org/Oklahoma_State_Question_812,_Marijuana_Decriminalization-Initiative_(2022)).

<sup>p</sup> A cannabis legalization initiative was expected to be on the ballot in November 2022 and is now expected for March 2023 (“Marijuana on the ballot”, *Ballotpedia*. Retrieved online June 2022 and February 2023, https://ballotpedia.org/Marijuana_on_the-ballot)

<sup>q</sup>The recreational use of cannabis was legalized by the 2020 ballot. However, in 2021, the South Dakota Supreme Court ruled the amendment responsible for the legalization of recreational as unconstitutional.

<sup>r</sup>Expected in 2024.

<sup>s</sup>Although a bill regulating medical use of cannabis was signed in April 2017, Medical Marijuana Laws were not implemented in West Virginia before 2019.

<sup>t</sup>Expected to be on the ballot in 2024 (“Marijuana on the ballot”, *Ballotpedia*. Retrieved online June 2022, https://ballotpedia.org/Marijuana_on_the-ballot)
<table><thead><tr><th>State</th><th>Decrim.</th><th>1st MML ballot</th><th>MML</th><th>1st rec. ballot</th><th>Rec.</th><th>Retail</th></tr></thead><tbody><tr><td>NV</td><td>2016</td><td>1998</td><td>1998</td><td>2006</td><td>2016</td><td>2017</td></tr><tr><td>NH</td><td>2017</td><td>-<sup>a</sup></td><td>2013</td><td>-</td><td>-</td><td>-</td></tr><tr><td>NJ</td><td>-</td><td>-<sup>a</sup></td><td>2010</td><td>2020</td><td>2020</td><td>2022</td></tr><tr><td>NM</td><td>2019</td><td>-<sup>a</sup></td><td>2007</td><td><sup>d</sup></td><td>2021</td><td>2022</td></tr><tr><td>NY</td><td>1977</td><td>-<sup>a</sup></td><td>2014</td><td>-<sup>d</sup></td><td>2021</td><td>2022</td></tr><tr><td>NC</td><td>1977</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>ND</td><td>2019</td><td>2016</td><td>2016</td><td>2018</td><td>-</td><td>-</td></tr><tr><td>OH</td><td>1975</td><td>-<sup>a</sup></td><td>2016</td><td>2015</td><td>-</td><td>-</td></tr><tr><td>OK</td><td>-<sup>o</sup></td><td>2018</td><td>2018</td><td>-<sup>p</sup></td><td>-</td><td>-</td></tr><tr><td>OR</td><td>1973</td><td>1998</td><td>1998</td><td>2012</td><td>2014</td><td>2015</td></tr><tr><td>PA</td><td>-<sup>f</sup></td><td>-<sup>a</sup></td><td>2016</td><td>-</td><td>-</td><td>-</td></tr><tr><td>RI</td><td>2012</td><td>-<sup>a</sup></td><td>2005</td><td>-<sup>d</sup></td><td>2022</td><td>-</td></tr><tr><td>SC</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>SD</td><td>-</td><td>2006</td><td>2020</td><td>2020</td><td>-<sup>q</sup></td><td>-</td></tr><tr><td>TN</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>TX</td><td>-<sup>f</sup></td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>UT</td><td>-</td><td>2018</td><td>2018</td><td>-</td><td>-</td><td>-</td></tr><tr><td>VT</td><td>2013</td><td>-<sup>a</sup></td><td>2004</td><td>-<sup>d</sup></td><td>2018</td><td>2020</td></tr><tr><td>VA</td><td>-</td><td>-</td><td>-</td><td>-<sup>d</sup></td><td>2021</td><td>-<sup>r</sup></td></tr><tr><td>WA</td><td>2012</td><td>1998</td><td>1998</td><td>2012</td><td>2012</td><td>2014</td></tr><tr><td>WV</td><td>-</td><td>-</td><td>2017<sup>s</sup></td><td>-</td><td>-</td><td>-</td></tr><tr><td>WI</td><td>-<sup>f</sup></td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>WY</td><td>-<sup>t</sup></td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr></tbody></table>

ballot”, *Ballotpedia*. Retrieved online June 2022, https://ballotpedia.org/Marijuana_on_the-ballot).

°A cannabis decriminalization initiative is expected to be on the ballot in November 2022 (“Okla-homa State Question 812, Marijuana Decriminalization Initiative (2022)”, retrieved online on Ballot-pedia; url: https://ballotpedia.org/Oklahoma_State_Question_812,_Marijuana_Decriminalization_ Initiative_(2022)).

P A cannabis legalization initiative was expected to be on the ballot in November 2022 and is now expected for March 2023 (“Marijuana on the ballot”, *Ballotpedia*. Retrieved online June 2022 and February 2023, https://ballotpedia.org/Marijuana_on_the-ballot)

qThe recreational use of cannabis was legalized by the 2020 ballot. However, in 2021, the South Dakota Supreme Court ruled the amendment responsible for the legalization of recreational as unconstitutional.

rExpected in 2024.

sAlthough a bill regulating medical use of cannabis was signed in April 2017, Medical Marijuana Laws were not implemented in West Virginia before 2019.

tExpected to be on the ballot in 2024 (“Marijuana on the ballot”, *Ballotpedia*. Retrieved online June 2022, https://ballotpedia.org/Marijuana_on_the-ballot
## B Characterizing the marginal type of consumer $\theta^I$, indifferent between no consumption and illegal consumption

An individual of type $\theta$ deciding between illegal consumption and no consumption considers the lottery $[-p - F, \theta v - p; q, 1 - q]$. Not consuming entails a zero payoff. The utility associated with illegal consumption is given by: $w^+(1-q)u(\theta v - p) + w^-(q)u(-p - F)$, where $u$ is a value function which is continuous, derivable and strictly increasing on $\mathbb{R}$, and such that $u(0) = 0$.

The consumption condition is written as: $w^+(1-q)u(\theta v - p) + w^-(q)u(-p - F) > 0$.

Let us define $V_I(\theta) = w^+(1-q)u(\theta v - p) + w^-(q)u(-p - F)$.

The marginal individual $\theta^I$, indifferent between illegal consumption and no consumption, is characterized by:

$$V_I(\theta) = 0 \qquad (A1)$$

Since the value function $u$ from not consuming is such that $u(0) = 0$, this condition is the same, whether $\theta^I$ is derived using expected utility theory or prospect theory. The only difference is that under expected utility theory, the weighting functions $w^+$ and $w^-$ are equal to the identity. Since $u$ is a function which is continuous, derivable, strictly increasing on $\mathbb{R}$, it admits a reciprocal function $u^{-1}$ which is also strictly increasing and such that $u^{-1}(0) = 0$. Since $v > 0$, condition (A1) is equivalent to:

$$\theta^I = u^{-1} \left( - \frac{w^-(q)}{w^+(1-q)} u(-p-F) \right) + \frac{p}{v} \qquad (A2)$$

We deduce that $\theta^I$ exists and is unique, with $\theta^I > \frac{p}{v}$ if $q > 0$ and $\theta^I = \frac{p}{v}$ if $q = 0$.

Expression (A2) clearly shows that $\theta^I$ increases with $q$, $p$ and $F$, since the value function $u$, its reciprocal and the weight functions are strictly increasing.

Finally, we focus on the absolute value of the price elasticity of demand, $\epsilon_{D,p}$, as defined in (4). After differentiating $\epsilon_{D,p}$ with respect to $q$, one can check that:

$$\frac{d\epsilon_{D^I, p}}{dq} = \frac{d\left\{\frac{g(\theta^I)}{1-G(\theta^I)}\right\}}{d\theta^I} \frac{d^2\theta^I}{dpdq} p + \frac{g(\theta^I)}{1-G(\theta^I)} \frac{d^2\theta^I}{dpdq} p. \qquad (A3)$$

As $\theta^I$ increases with $p$ and $q$ it follows that $\epsilon_{D^I, p}$ increases with $q \in [0, 1]$ if the cross-derivative of $\theta^I$ with $p$ and $q$ is positive and if the distribution $G(\theta)$ satisfies the monotone hazard rate (MHR) property. We next check under what condition this cross derivative is positive.
## B Characterizing the marginal type of consumer $\theta^I$, indifferent between no consumption and illegal consumption

An individual of type $\theta$ deciding between illegal consumption and no consumption considers the lottery $[-p - F, \theta v - p; q, 1 - q]$. Not consuming entails a zero payoff. The utility associated with illegal consumption is given by: $w^+(1-q)u(\theta v - p) + w^-(q)u(-p - F)$, where $u$ is a value function which is continuous, derivable and strictly increasing on $\mathbb{R}$, and such that $u(0) = 0$.

The consumption condition is written as: $w^+(1-q)u(\theta v - p) + w^-(q)u(-p - F) > 0$.

Let us define $V_I(\theta) = w^+(1-q)u(\theta v - p) + w^-(q)u(-p - F)$.

The marginal individual $\theta^I$, indifferent between illegal consumption and no consumption, is characterized by:

$$V_I(\theta) = 0 \qquad (A1)$$

Since the value function $u$ from not consuming is such that $u(0) = 0$, this condition is the same, whether $\theta^I$ is derived using expected utility theory or prospect theory. The only difference is that under expected utility theory, the weighting functions $w^+$ and $w^-$ are equal to the identity. Since $u$ is a function which is continuous, derivable, strictly increasing on $\mathbb{R}$, it admits a reciprocal function $u^{-1}$ which is also strictly increasing and such that $u^{-1}(0) = 0$. Since $v > 0$, condition (A1) is equivalent to:

$$\theta^I = u^{-1} \left( - \frac{w^-(q)}{w^+(1-q)} u(-p-F) \right) + \frac{p}{v} \qquad (A2)$$

We deduce that $\theta^I$ exists and is unique, with $\theta^I > \frac{p}{v}$ if $q > 0$ and $\theta^I = \frac{p}{v}$ if $q = 0$.

Expression (A2) clearly shows that $\theta^I$ increases with $q, p$ and $F$, since the value function $u$, its reciprocal and the weight functions are strictly increasing.

Finally, we focus on the absolute value of the price elasticity of demand, $\epsilon_{D,p}$, as defined in (4). After differentiating $\epsilon_{D,p}$ with respect to $q$, one can check that:

$$\frac{d\epsilon_{D^I, p}}{dq} = \frac{d\left\{\frac{g(\theta^I)}{1-G(\theta^I)}\right\}}{d\theta^I} \frac{d^2\theta^I}{dpdq} p + \frac{g(\theta^I)}{1-G(\theta^I)} \frac{d^2\theta^I}{dpdq} p. \qquad (A3)$$

As $\theta^I$ increases with $p$ and $q$ it follows that $\epsilon_{D^I, p}$ increases with $q \in [0, 1]$ if the cross-derivative of $\theta^I$ with $p$ and $q$ is positive and if the distribution $G(\theta)$ satisfies the monotone hazard rate (MHR) property. We next check under what condition this cross derivative is positive.
Differentiating equation (A1) yields: $\sum_{i \in \{p,q,\theta,F\}} \alpha_i d_i = 0$, with

$$ 
\left\{ 
\begin{aligned}
\alpha_{\theta} &= vw^{+}(1-q)u'(\theta v - p) \\
\alpha_{q} &= -w^{+'}(1-q)u(\theta v - p) + w^{-'}(q)u(-p-F) \\
\alpha_{p} &= -w^{+}(1-q)u'(\theta v - p) - w^{-}(q)u'(-p-F) \\
\alpha_{F} &= -w^{-}(q)u'(-p-F)
\end{aligned}
\right. 
$$

In particular, it yields $\frac{d^2\theta^I}{dp^2} = -\frac{\alpha_p}{\alpha_\theta}$. From this follows that

$$ \frac{d^2\theta^I}{dpdq} = \frac{\alpha_p\alpha_{\theta q} - \alpha_{pq}\alpha_\theta}{\alpha_\theta^2} $$

where

$$ 
\left\{ 
\begin{aligned}
\alpha_{pq} &= \frac{\partial \alpha_p}{\partial q} = w^{+'}(1-q)u'(\theta v - p) - w^{-'}(q)u'(-p-F) \\
\alpha_{\theta q} &= \frac{\partial \alpha_\theta}{\partial q} = -vw^{+'}(1-q)u'(\theta v - p)
\end{aligned}
\right. 
$$

Since the function $u$ is increasing and the weight functions are positive and increasing, we show that $\alpha_p\alpha_{\theta q} - \alpha_{pq}\alpha_\theta > 0$ as follows:

$$ 
\begin{aligned}
&[w^{-}(q)w^{+'}(1-q) + w^{-'}(q)w^{+}(1-q)]vu'(\theta v - p)u'(-p-F) > 0 \\
\Rightarrow \quad &w^{-}(q)u'(-p-F)vw^{+'}(1-q)u'(\theta v - p) + w^{-'}(q)u'(-p-F)vw^{+}(1-q)u'(\theta v - p) > 0 \\
\Rightarrow \quad &\alpha_p\alpha_{\theta q} - \alpha_{pq}\alpha_\theta > 0
\end{aligned}
$$

We conclude that $\frac{d^2\theta^I}{dpdq} > 0$ and that $\epsilon_{D^I,p}$ increases with $q \in [0,1]$ if the distribution $G(\theta)$ satisfies the monotone hazard rate (MHR) property.

## C Characterizing the marginal consumer $\theta^L(p, p^L)$, indifferent between legal and illegal consumption

A consumer of type $\theta$ deciding between legal and illegal consumption faces a choice between a certain payoff of $\theta bv - p^L$ and the lottery $[-p-F, \theta v - p; q, 1-q]$. Note first that individuals with $\theta \le 0$ will never purchase cannabis, whether it is legal or not. Second if $\theta v - p \le \theta bv - p^L$ the only possibility is that the individual buys either the legal product or nothing. Symmetrically if $\theta v - p > 0 > \theta bv - p^L$ the only possibility is that he/she either purchases on the black market or not at all. It implies that a necessary condition for some consumers being willing to purchase cannabis illegally, while others prefer to purchase it legally, is that there exists some $\theta > 0$ such that $\theta v - p > \theta bv - p^L > 0$, or equivalently
Differentiating equation (A1) yields: $\sum_{i \in \{p,q,\theta,F\}} \alpha_i d_i = 0$, with

$$ 
\left\{ 
\begin{aligned}
\alpha_{\theta} &= vw^{+}(1-q)u'(\theta v - p) \\
\alpha_{q} &= -w^{+'}(1-q)u(\theta v - p) + w^{-'}(q)u(-p-F) \\
\alpha_{p} &= -w^{+}(1-q)u'(\theta v - p) - w^{-}(q)u'(-p-F) \\
\alpha_{F} &= -w^{-}(q)u'(-p-F)
\end{aligned}
\right. 
$$

In particular, it yields $\frac{d\theta^I}{dp} = -\frac{\alpha_p}{\alpha_\theta}$. From this follows that

$$ \frac{d^2\theta^I}{dpdq} = \frac{\alpha_p\alpha_{\theta q} - \alpha_{pq}\alpha_\theta}{\alpha_\theta^2} $$

where

$$ 
\left\{ 
\begin{aligned}
\alpha_{pq} &= \frac{\partial \alpha_p}{\partial q} = w^{+'}(1-q)u'(\theta v - p) - w^{-'}(q)u'(-p-F) \\
\alpha_{\theta q} &= \frac{\partial \alpha_\theta}{\partial q} = -vw^{+'}(1-q)u'(\theta v - p)
\end{aligned}
\right. 
$$

Since the function $u$ is increasing and the weight functions are positive and increasing, we show that $\alpha_p\alpha_{\theta q} - \alpha_{pq}\alpha_\theta > 0$ as follows:

$$ 
\begin{aligned}
&[w^{-}(q)w^{+'}(1-q) + w^{-'}(q)w^{+}(1-q)]vu'(\theta v - p)u'(-p-F) > 0 \\
&\Rightarrow w^{-}(q)u'(-p-F)vw^{+'}(1-q)u'(\theta v - p) + w^{-'}(q)u'(-p-F)vw^{+}(1-q)u'(\theta v - p) > 0 \\
&\Rightarrow \alpha_p\alpha_{\theta q} - \alpha_{pq}\alpha_\theta > 0
\end{aligned} 
$$

We conclude that $\frac{d^2\theta^I}{dpdq} > 0$ and that $\epsilon_{D^I,p}$ increases with $q \in [0,1]$ if the distribution $G(\theta)$ satisfies the monotone hazard rate (MHR) property.

## C Characterizing the marginal consumer $\theta^L(p, p^L)$, indifferent between legal and illegal consumption

A consumer of type $\theta$ deciding between legal and illegal consumption faces a choice between a certain payoff of $\theta bv - p^L$ and the lottery $[-p-F, \theta v - p; q, 1-q]$. Note first that individuals with $\theta \le 0$ will never purchase cannabis, whether it is legal or not. Second if $\theta v - p \le \theta bv - p^L$ the only possibility is that the individual buys either the legal product or nothing. Symmetrically if $\theta v - p > 0 > \theta bv - p^L$ the only possibility is that he/she either purchases on the black market or not at all. It implies that a necessary condition for some consumers being willing to purchase cannabis illegally, while others prefer to purchase it legally, is that there exists some $\theta > 0$ such that $\theta v - p > \theta bv - p^L > 0$, or equivalently
$\frac{p^L-p}{(b-1)v} > \theta > \frac{p^L}{bv}$. This requires that $\frac{p^L-p}{(b-1)v} > \frac{p^L}{bv}$ or equivalently $p^L > bp$.

## C.1 Under expected utility theory

If individuals are expected utility maximizers the marginal consumer, indifferent between legal and illegal consumption, solves the following equation: $(1-q)u(\theta v - p) + qu(-p-F) = u(\theta bv - p^L)$. Let

$$V_1(\theta) = (1-q)u(\theta v - p) + qu(-p-F) - u(\theta bv - p^L) \quad (A4)$$

If $\theta^L > 0$ exists, it is such that $V_1(\theta) = 0$.

We deduce that for $\frac{p^L-p}{(b-1)v} > \theta > \frac{p^L}{bv}$, $V_1'(\theta) = (1-q)vu'(\theta v - p) - bvu'(\theta bv - p^L) < 0$ since $u'$ is decreasing (i.e., $u$ is concave) and $1-q \le 1$, $\theta v - p > \theta bv - p^L$, $b > 1$. Hence, if $\theta^L > 0$ exists, it is unique. We have that: $V_1(\frac{p^L-p}{(b-1)v}) = -q[u(\frac{p^L-bp}{b-1}) - u(-p-F)] < 0$. Since $V_1(\theta)$ is decreasing for $\theta \in [\frac{p^L}{bv}, \frac{p^L-p}{(b-1)v}]$, to finish the proof we need to find the condition under which $V_1(\frac{p^L}{bv}) > 0$. Therefore, whenever

$$(1-q)u\left(p^L - \frac{bp}{b}\right) > -qu(-p-F) \quad (A5)$$

the equation $V_1(\theta) = 0$ admits a unique solution.

Differentiating equation A4 yields $\alpha_q dq + \alpha_{p^L} dp^L + \alpha_p dp + \alpha_F dF + \alpha_{\theta^L} d\theta^L + \alpha_b dd = 0$ with

$$\left\{
\begin{array}{l}
\alpha_q = u(-p-F) - u(\theta^L v - p) < 0 \\
\alpha_{p^L} = u'(\theta^L v - p^L) > 0 \\
\alpha_p = -qu'(-p-F) - (1-q)u'(\theta^L v - p) < 0 \\
\alpha_F = -qu'(-p-F) < 0 \\
\alpha_{\theta^L} = v(1-q)u'(\theta^L v - p) - bvu'(\theta^L bv - p^L) < 0 \\
\alpha_b = -\theta^L v u'(\theta^L bv - p^L) < 0
\end{array}
\right.$$

It is straightforward to show that $\theta^L$ decreases with $q$, $p$, $F$ and $b$, while it increases with $p^L$.

## C.2 Under prospect theory

Under CPT the consumer's reference level of wealth is provided by the risk free option, $\theta bv - p^L$. A potential cannabis consumer deciding between buying from the black market or from the legal sector considers the lottery $[p^L - p - F - \theta bv, p^L - p + \theta(1-b)v; q, 1-q]$.
$\frac{p^L-p}{(b-1)v} > \theta > \frac{p^L}{bv}$. This requires that $\frac{p^L-p}{(b-1)v} > \frac{p^L}{bv}$ or equivalently $p^L > bp$.

## C.1 Under expected utility theory

If individuals are expected utility maximizers the marginal consumer, indifferent between legal and illegal consumption, solves the following equation: $(1-q)u(\theta v - p) + qu(-p-F) = u(\theta bv - p^L)$. Let

$$V_1(\theta) = (1-q)u(\theta v - p) + qu(-p-F) - u(\theta bv - p^L) \quad (A4)$$

If $\theta^L > 0$ exists, it is such that $V_1(\theta) = 0$.

We deduce that for $\frac{p^L-p}{(b-1)v} > \theta > \frac{p^L}{bv}$, $V_1'(\theta) = (1-q)vu'(\theta v - p) - bvu'(\theta bv - p^L) < 0$ since $u'$ is decreasing (i.e., $u$ is concave) and $1-q \le 1$, $\theta v - p > \theta bv - p^L$, $b > 1$. Hence, if $\theta^L > 0$ exists, it is unique. We have that: $V_1(\frac{p^L-p}{(b-1)v}) = -q[u(\frac{p^L-bp}{b-1}) - u(-p-F)] < 0$. Since $V_1(\theta)$ is decreasing for $\theta \in [\frac{p^L}{bv}, \frac{p^L-p}{(b-1)v}]$, to finish the proof we need to find the condition under which $V_1(\frac{p^L}{bv}) > 0$. Therefore, whenever

$$(1-q)u\left(p^L - \frac{bp}{b}\right) > -qu(-p-F) \quad (A5)$$

the equation $V_1(\theta) = 0$ admits a unique solution.

Differentiating equation A4 yields $\alpha_q dq + \alpha_{p^L} dp^L + \alpha_p dp + \alpha_F dF + \alpha_{\theta^L} d\theta^L + \alpha_b dd = 0$ with

$$\left\{
\begin{array}{l}
\alpha_q = u(-p-F) - u(\theta^L v - p) < 0 \\
\alpha_{p^L} = u'(\theta^L v - p^L) > 0 \\
\alpha_p = -qu'(-p-F) - (1-q)u'(\theta^L v - p) < 0 \\
\alpha_F = -qu'(-p-F) < 0 \\
\alpha_{\theta^L} = v(1-q)u'(\theta^L v - p) - bvu'(\theta^L bv - p^L) < 0 \\
\alpha_b = -\theta^L v u'(\theta^L bv - p^L) < 0
\end{array}
\right.$$

It is straightforward to show that $\theta^L$ decreases with $q$, $p$, $F$ and $b$, while it increases with $p^L$.

## C.2 Under prospect theory

Under CPT the consumer's reference level of wealth is provided by the risk free option, $\theta bv - p^L$. A potential cannabis consumer deciding between buying from the black market or from the legal sector considers the lottery $[p^L - p - F - \theta bv, p^L - p + \theta(1-b)v; q, 1-q]$.
Let

$$V_2(\theta) = w^+(1-q)u(p^L - p - (b-1)v\theta) + w^-(q)u(-p - F - \theta bv + p^L) \quad (A6)$$

The marginal consumer, $\theta^L(p, p^L)$, indifferent between legal and illegal consumption solves $V_2(\theta) = 0$. Since $b \ge 1$ and $u$ is strictly increasing, we have

$$V_2'(\theta) = -(b-1)vw^+(1-q)u'\left(\theta(1-b)v - p + p^L\right) - bvw^-(q)u'\left(-p - F - \theta bv + p^L\right) < 0$$

We have: $V_2\left(\frac{p^L-p}{(b-1)v}\right) = w^-(q)u(p - p^L - (b-1)F) < 0$ since $p^L > bp \ge p$. The strict monotonicity of $V_2(\theta)$ implies that $\theta^L$ exists and is unique whenever $V_2\left(\frac{p^L}{bv}\right) > 0$. This is equivalent to:

$$w^+(1-q)u\left(p^L - \frac{bp}{b}\right) > -w^-(q)u(-p-F) \quad (A7)$$

Condition (A7) under CPT is equivalent to (A5) under EUT, where the probability weighting function is the identity. In both cases these conditions imply that $\theta^L > 0$ exists and is unique.

Differentiating equation (A6) yields: $\alpha_{\theta^L}d\theta^L + \alpha_qdq + \alpha_{p^L}dp^L + \alpha_pdp + \alpha_FdF + \alpha_ddd = 0$ with

$$\left\{
\begin{array}{l}
\alpha_{\theta^L} = -w^-(q)vu' (p^L - p - F - \theta^L bv) - w^+(1-q)(d-1)vu' (p^L - p + \theta^L(1-b)v) < 0 \\
\alpha_q = w^-(q)u (p^L - p - F - \theta^L bv) - w^+(1-q)u (p^L - p + \theta^L(1-b)v) < 0 \\
\alpha_{p^L} = w^-(q)u' (p^L - p - F - \theta^L bv) + w^+(1-q)u' (p^L - p + \theta^L(1-b)v) > 0 \\
\alpha_p = -w^-(q)u' (p^L - p - F - \theta^L bv) - w^+(1-q)u' (p^L - p + \theta^L(1-b)v) < 0 \\
\alpha_F = -w^-(q)u' (p^L - p - F - \theta^L bv) < 0 \\
\alpha_b = -\theta^L vw^+(1-q)u' (p^L - p + \theta^L(1-b)v) - \theta v qu' (-p - F - \theta bv + p^L) < 0
\end{array}
\right.$$

It is straightforward to show that $\theta^L$ decreases with $q$, $p$, $F$ and $b$, while it increases with $p^L$.

### C.3 On the sensitivity of the price elasticity on the illegal market to the legal price

Finally, let us focus on the absolute value of the price elasticity of demand on the illegal market, $\epsilon_{D,p}$, when both the illegal and the legal markets are active and its sensitivity to the legal price $p^L$. To this purpose, we differentiate $\epsilon_{D,p}$ with respect to $p^L$.

$$\frac{d\epsilon_{D,p}}{dp^L} = \frac{d\frac{g(\theta^L)}{G(\theta^L)-G(\theta^I)}}{d\theta^L} \frac{d\theta^L}{dp^L} \frac{d\theta^I}{dp} p - \frac{d\frac{g(\theta^L)}{G(\theta^L)-G(\theta^I)}}{d\theta^L} \frac{d^2\theta^L}{dpdp^L} p - \frac{g(\theta^L)}{G(\theta^L)-G(\theta^I)} \frac{d^2\theta^L}{dpdp^L} p \quad (A8)$$
Let

$$V_2(\theta) = w^+(1-q)u(p^L - p - (b-1)v\theta) + w^-(q)u(-p - F - \theta bv + p^L) \quad (A6)$$

The marginal consumer, $\theta^L(p, p^L)$, indifferent between legal and illegal consumption solves $V_2(\theta) = 0$. Since $b \ge 1$ and $u$ is strictly increasing, we have

$$V_2'(\theta) = -(b-1)vw^+(1-q)u'\left(\theta(1-b)v - p + p^L\right) - bvw^-(q)u'\left(-p - F - \theta bv + p^L\right) < 0$$

We have: $V_2\left(\frac{p^L-p}{(b-1)v}\right) = w^-(q)u(p-p^L - (b-1)F) < 0$ since $p^L > bp \ge p$. The strict monotonicity of $V_2(\theta)$ implies that $\theta^L$ exists and is unique whenever $V_2\left(\frac{p^L}{bv}\right) > 0$. This is equivalent to:

$$w^+(1-q)u\left(p^L - \frac{bp}{b}\right) > -w^-(q)u(-p-F) \quad (A7)$$

Condition (A7) under CPT is equivalent to (A5) under EUT, where the probability weighting function is the identity. In both cases these conditions imply that $\theta^L > 0$ exists and is unique.

Differentiating equation (A6) yields: $\alpha_{\theta^L}d\theta^L + \alpha_qdq + \alpha_{p^L}dp^L + \alpha_pdp + \alpha_FdF + \alpha_ddd = 0$ with

$$\left\{
\begin{array}{l}
\alpha_{\theta^L} = -w^-(q)vu' (p^L - p - F - \theta^L bv) - w^+(1-q)(d-1)vu' (p^L - p + \theta^L(1-b)v) < 0 \\
\alpha_q = w^-(q)u (p^L - p - F - \theta^L bv) - w^+(1-q)u (p^L - p + \theta^L(1-b)v) < 0 \\
\alpha_{p^L} = w^-(q)u' (p^L - p - F - \theta^L bv) + w^+(1-q)u' (p^L - p + \theta^L(1-b)v) > 0 \\
\alpha_p = -w^-(q)u' (p^L - p - F - \theta^L bv) - w^+(1-q)u' (p^L - p + \theta^L(1-b)v) < 0 \\
\alpha_F = -w^-(q)u' (p^L - p - F - \theta^L bv) < 0 \\
\alpha_b = -\theta^L vw^+(1-q)u' (p^L - p + \theta^L(1-b)v) - \theta v qu' (-p - F - \theta bv + p^L) < 0
\end{array}
\right.$$

It is straightforward to show that $\theta^L$ decreases with $q$, $p$, $F$ and $b$, while it increases with $p^L$.

### C.3 On the sensitivity of the price elasticity on the illegal market to the legal price

Finally, let us focus on the absolute value of the price elasticity of demand on the illegal market, $\epsilon_{D,p}$, when both the illegal and the legal markets are active and its sensitivity to the legal price $p^L$. To this purpose, we differentiate $\epsilon_{D,p}$ with respect to $p^L$.

$$\frac{d\epsilon_{D,p}}{dp^L} = \frac{d\frac{g(\theta^L)}{G(\theta^L)-G(\theta^I)}}{d\theta^L} \frac{d\theta^L}{dp^L} \frac{d\theta^I}{dp} p - \frac{d\frac{g(\theta^L)}{G(\theta^L)-G(\theta^I)}}{d\theta^L} \frac{d^2\theta^L}{dpdp^L} p - \frac{g(\theta^L)}{G(\theta^L)-G(\theta^I)} \frac{d^2\theta^L}{dpdp^L} p \quad (A8)$$
Since, $\frac{d\frac{g(\theta^I)}{G(\theta^I)-G(\theta^I)}}{d\theta^L} < 0$, $\frac{d\theta^L}{dp^L} > 0$ and $\frac{d\theta^I}{dp} > 0$, the first term of (A8) is negative.

When both the legal and the illegal sectors are active, $\theta^I < \theta^L$ and hence $G(\theta^I) < G(\theta^L) < 1$. It follows that $\frac{g(\theta^L)}{G(\theta^I)-G(\theta^L)} < 0$. Assuming the distribution $G(\theta)$ satisfies the monotone hazard rate (MHR) property as verified by a large class of distributions, $\frac{g(\theta^L)}{1-G(\theta^L)} > 0$ increases with $\theta^L$. Therefore, $\frac{g(\theta^L)}{G(\theta^I)-G(\theta^L)}$ decreases with $\theta^L$: $\frac{d\frac{g(\theta^L)}{G(\theta^I)-G(\theta^L)}}{d\theta^L} < 0$.

Further, $\frac{d^2\theta^L}{dpdp^L} > 0$. Indeed, the differentiation of equations (A4) or alternatively (A6) yields $\frac{d\theta^L}{dp} = -\frac{\alpha_p}{\alpha_\theta^L}$, where the quantities $\alpha_p$ and $\alpha_\theta^L$ are defined in sections C.1 and C.2 respectively. From this follows that

$$ \frac{d^2\theta^L}{dpdp^L} = \frac{\alpha_p\alpha_{\theta^L p^L} - \alpha_{pp^L}\alpha_{\theta^L}}{\alpha_{\theta^L}^2} $$

We show below that $\alpha_p\alpha_{\theta^L p^L} - \alpha_{pp^L}\alpha_{\theta^L} > 0$ and $\frac{d^2\theta^L}{dpdp^L} > 0$. We conclude that $\frac{d\epsilon_{D^I p}}{dp^L} < 0$: as the price on the legal market $p^L$ increases, consumers become less elastic to the black-market price $p$.

## Under EUT

$$ \left\{ \begin{array}{l} \alpha_{pp^L} = 0 \\ \alpha_{\theta^L p^L} = bvu'' (\theta^L bv - p^L) \end{array} \right. < 0 $$

Since $\alpha_p < 0$, it is straightforward that $\frac{d^2\theta^L}{dpdp^L} > 0$.

## Under CPT

$$ \left\{ \begin{array}{l} \alpha_{pp^L} = \frac{\partial \alpha_p}{\partial p^L} = -w^{-}(q)u''(p^L - p - F - \theta^L bv) - w^{+}(1-q)u''(p^L - p + \theta^L(1-b)v) \\ \alpha_{\theta^L p^L} = \frac{\partial \alpha_\theta^L}{\partial p^L} = v\alpha_{pp^L} - w^{+}(1-q)(d-2)vu''(p^L - p + \theta^L(1-b)v) \end{array} \right. $$

Since $\alpha_{\theta^L} = v\alpha_p - w^+(1-q)(d-2)vu'(p^L - p + \theta^L(1-b)v)$, we can rewrite

$$ \begin{aligned} \alpha_p \alpha_{\theta^L p^L} - \alpha_{pp^L} \alpha_{\theta^L} &= \alpha_p (v \alpha_{pp^L} - w^+(1-q)(d-2)vu''(p^L - p + \theta^L(1-b)v)) \\ &\quad - \alpha_{pp^L} (v \alpha_p - w^+(1-q)(d-2)vu'(p^L - p + \theta^L(1-b)v)) \\ &= - \alpha_p w^+(1-q)(d-2)vu''(p^L - p + \theta^L(1-b)v) \\ &\quad + \alpha_{pp^L} w^+(1-q)(d-2)vu'(p^L - p + \theta^L(1-b)v) \end{aligned} $$

Besides,

$$ - \alpha_p u'' (p^L - p + \theta^L(1-b)v) + \alpha_{pp^L} u' (p^L - p + \theta^L(1-b)v) $$
Since, $\frac{d\frac{g(\theta^I)}{G(\theta^I)-G(\theta^I)}}{d\theta^L} < 0$, $\frac{d\theta^L}{dp^L} > 0$ and $\frac{d\theta^I}{dp} > 0$, the first term of (A8) is negative.

When both the legal and the illegal sectors are active, $\theta^I < \theta^L$ and hence $G(\theta^I) < G(\theta^L) < 1$. It follows that $\frac{g(\theta^L)}{G(\theta^I)-G(\theta^L)} < 0$. Assuming the distribution $G(\theta)$ satisfies the monotone hazard rate (MHR) property as verified by a large class of distributions, $\frac{g(\theta^L)}{1-G(\theta^L)} > 0$ increases with $\theta^L$. Therefore, $\frac{g(\theta^L)}{G(\theta^I)-G(\theta^L)}$ decreases with $\theta^L$: $\frac{d\frac{g(\theta^L)}{G(\theta^I)-G(\theta^L)}}{d\theta^L} < 0$.

Further, $\frac{d^2\theta^L}{dpdp^L} > 0$. Indeed, the differentiation of equations (A4) or alternatively (A6) yields $\frac{d\theta^L}{dp} = -\frac{\alpha_p}{\alpha_\theta^L}$, where the quantities $\alpha_p$ and $\alpha_\theta^L$ are defined in sections C.1 and C.2 respectively. From this follows that

$$ \frac{d^2\theta^L}{dpdp^L} = \frac{\alpha_p\alpha_{\theta^L p^L} - \alpha_{pp^L}\alpha_{\theta^L}}{\alpha_{\theta^L}^2} $$

We show below that $\alpha_p\alpha_{\theta^L p^L} - \alpha_{pp^L}\alpha_{\theta^L} > 0$ and $\frac{d^2\theta^L}{dpdp^L} > 0$. We conclude that $\frac{d\epsilon_{D^I p}}{dp^L} < 0$: as the price on the legal market $p^L$ increases, consumers become less elastic to the black-market price $p$.

## Under EUT

$$ \left\{ \begin{array}{l} \alpha_{pp^L} = 0 \\ \alpha_{\theta^L p^L} = bvu'' (\theta^L bv - p^L) \end{array} \right. < 0 $$

Since $\alpha_p < 0$, it is straightforward that $\frac{d^2\theta^L}{dpdp^L} > 0$.

## Under CPT

$$ \left\{ \begin{array}{l} \alpha_{pp^L} = \frac{\partial \alpha_p}{\partial p^L} = -w^{-}(q)u''(p^L - p - F - \theta^L bv) - w^{+}(1-q)u''(p^L - p + \theta^L(1-b)v) \\ \alpha_{\theta^L p^L} = \frac{\partial \alpha_\theta^L}{\partial p^L} = v\alpha_{pp^L} - w^{+}(1-q)(d-2)vu''(p^L - p + \theta^L(1-b)v) \end{array} \right. $$

Since $\alpha_{\theta^L} = v\alpha_p - w^+(1-q)(d-2)vu'(p^L - p + \theta^L(1-b)v)$, we can rewrite

$$ \begin{align*} \alpha_p \alpha_{\theta^L p^L} - \alpha_{pp^L} \alpha_{\theta^L} &= \alpha_p (v \alpha_{pp^L} - w^+(1-q)(d-2)vu''(p^L - p + \theta^L(1-b)v)) \\ &\quad - \alpha_{pp^L} (v \alpha_p - w^+(1-q)(d-2)vu'(p^L - p + \theta^L(1-b)v)) \\ &= - \alpha_p w^+(1-q)(d-2)vu''(p^L - p + \theta^L(1-b)v) \\ &\quad + \alpha_{pp^L} w^+(1-q)(d-2)vu'(p^L - p + \theta^L(1-b)v) \end{align*} $$

Besides,

$$ - \alpha_p u'' (p^L - p + \theta^L(1-b)v) + \alpha_{pp^L} u' (p^L - p + \theta^L(1-b)v) $$
$$ 
\begin{aligned}
&=w^{-}(q)u' (p^{L}-p-F-\theta^{L}bv)u'' (p^{L}-p+\theta^{L}(1-b)v) \\
&\quad +w^{+}(1-q)u' (p^{L}-p+\theta^{L}(1-b)v)u'' (p^{L}-p+\theta^{L}(1-b)v) \\
&\quad -w^{-}(q)u'' (p^{L}-p-F-\theta^{L}bv)u' (p^{L}-p+\theta^{L}(1-b)v) \\
&\quad -w^{+}(1-q)u'' (p^{L}-p+\theta^{L}(1-b)v)u' (p^{L}-p+\theta^{L}(1-b)v) \\
&=w^{-}(q)u' (p^{L}-p-F-\theta^{L}bv)u'' (p^{L}-p+\theta^{L}(1-b)v) \\
&\quad -w^{-}(q)u'' (p^{L}-p-F-\theta^{L}bv)u' (p^{L}-p+\theta^{L}(1-b)v) \\
&< 0
\end{aligned}
$$

Hence, $\alpha_p\alpha_{\theta^L p^L} - \alpha_{pp^L}\alpha_{\theta^L} > 0$ and $\frac{d^2\theta^L}{dp^L dp^L} > 0$.

# D Consumers facing legalization

## D.1 Consumer choices

This appendix shows that $\tilde{p}^L(p) = \theta^I bv$, with $\theta^I$ solution of (2), is the threshold price of legal cannabis under which the dealers exit the market if they sell their product at price $p$.

Appendix B shows that any consumer with type higher than $\theta^I$, solution of (2) – that is solution of $w^+(1-q)u(\theta^I v - p) + w^-(q)u(-p-F) = 0$ – prefers to purchase cannabis on the illegal market than not to consume cannabis.

Appendix C shows that any consumer with type higher than $\theta^L$, solution of $w^+(1-q)u(p^L - p - \theta(b-1)v) + w^-(q)u(-p-F-\theta bv + p^L) = 0$, prefers to purchase cannabis legally than illegally.

Therefore to push dealers out of the market when they sell illegal products at price $p$, $\theta^L$ must be pushed under $\theta^I$. The maximum price of legal cannabis such that dealers are pushed out of business at price $p$ is the solution of $w^+(1-q)u(p^L - p - \theta(b-1)v) + w^-(q)u(-p-F-\theta bv + p^L) = 0$, for $\theta^I$, solution of (2).

Replacing $p^L = \theta^I bv$ in the equation above, we can write $w^+(1-q)u(p^L - p - \theta(b-1)v) + w^-(q)u(-p-F-\theta bv + p^L) = w^+(1-q)u(\theta^I v - p) + w^-(q)u(-p-F)$, which is equal to 0 since $\theta^I$, is solution of (2).

This demonstrates that $\tilde{p}^L(p) = \theta^I bv$, with $\theta^I$ solution of (2), is this threshold price.

We next compare $\theta^0$, $\theta^L$ and $\theta^I$ depending on whether the legal price, $p^L$, is higher than $\tilde{p}^L(p)$ or not.

Under legalization, the consumer $\theta^0$, indifferent between legal consumption and no consumption, is characterized by $u(\theta^0 bv - p^L) = 0$. Any consumer with type higher than $\theta^0 = \frac{p^L}{bv}$ prefers to purchase cannabis legally than not consume cannabis.
$$ 
\begin{align*}
&=w^{-}(q)u' (p^{L} - p - F - \theta^{L}bv) u'' (p^{L} - p + \theta^{L}(1-b)v) \\
&\quad + w^{+}(1-q)u' (p^{L} - p + \theta^{L}(1-b)v) u'' (p^{L} - p + \theta^{L}(1-b)v) \\
&\quad - w^{-}(q)u'' (p^{L} - p - F - \theta^{L}bv) u' (p^{L} - p + \theta^{L}(1-b)v) \\
&\quad - w^{+}(1-q)u'' (p^{L} - p + \theta^{L}(1-b)v) u' (p^{L} - p + \theta^{L}(1-b)v) \\
&=w^{-}(q)u' (p^{L} - p - F - \theta^{L}bv) u'' (p^{L} - p + \theta^{L}(1-b)v) \\
&\quad - w^{-}(q)u'' (p^{L} - p - F - \theta^{L}bv) u' (p^{L} - p + \theta^{L}(1-b)v) \\
&< 0
\end{align*}
$$

Hence, $\alpha_p \alpha_{\theta^L p^L} - \alpha_{pp^L} \alpha_{\theta^L} > 0$ and $\frac{d^2 \theta^L}{dp^L dp^L} > 0$.

# D Consumers facing legalization

## D.1 Consumer choices

This appendix shows that $\tilde{p}^L(p) = \theta^I bv$, with $\theta^I$ solution of (2), is the threshold price of legal cannabis under which the dealers exit the market if they sell their product at price $p$.

Appendix B shows that any consumer with type higher than $\theta^I$, solution of (2) – that is solution of $w^+(1-q)u(\theta^I v - p) + w^-(q)u(-p-F) = 0$ – prefers to purchase cannabis on the illegal market than not to consume cannabis.

Appendix C shows that any consumer with type higher than $\theta^L$, solution of $w^+(1-q)u(p^L - p - \theta(b-1)v) + w^-(q)u(-p-F-\theta bv + p^L) = 0$, prefers to purchase cannabis legally than illegally.

Therefore to push dealers out of the market when they sell illegal products at price $p$, $\theta^L$ must be pushed under $\theta^I$. The maximum price of legal cannabis such that dealers are pushed out of business at price $p$ is the solution of $w^+(1-q)u(p^L - p - \theta(b-1)v) + w^-(q)u(-p-F-\theta bv + p^L) = 0$, for $\theta^I$, solution of (2).

Replacing $p^L = \theta^I bv$ in the equation above, we can write $w^+(1-q)u(p^L - p - \theta(b-1)v) + w^-(q)u(-p-F-\theta bv + p^L) = w^+(1-q)u(\theta^I v - p) + w^-(q)u(-p-F)$, which is equal to 0 since $\theta^I$, is solution of (2).

This demonstrates that $\tilde{p}^L(p) = \theta^I bv$, with $\theta^I$ solution of (2), is this threshold price.

We next compare $\theta^0$, $\theta^L$ and $\theta^I$ depending on whether the legal price, $p^L$, is higher than $\tilde{p}^L(p)$ or not.

Under legalization, the consumer $\theta^0$, indifferent between legal consumption and no consumption, is characterized by $u(\theta^0 bv - p^L) = 0$. Any consumer with type higher than $\theta^0 = \frac{p^L}{bv}$ prefers to purchase cannabis legally than not consume cannabis.
Appendix C shows that consumer $\theta^L$, indifferent between legal and illegal consumption, solves under

$$ \bullet \text{ EUT: } V_1(\theta) = (1-q)u(\theta v - p) + qu(-p-F) - u(\theta bv - p^L) = 0; $$

$$ \bullet \text{ CPT: } V_2(\theta) = w^+(1-q)u(p^L - p - \theta(b-1)v) + w^-(q)u(-p-F - \theta bv + p^L) = 0. $$

Two cases may follow the implementation of a legal market.

**Condition $p^L \le \tilde{p}^L(p)$ holds.**

We can write, for $i = 1, 2$, $V_i(\theta^0) = w^+(1-q)u(\frac{p^L}{b} - p) + w^-(q)u(-p-F)$, with the weighting functions being the identity function under EUT.

By definition of $\theta^L$, $V_i(\theta^L) = 0$. If $p^L \le \theta^Ibv$ then $\frac{p^L}{b} \le \theta^Iv$. $\theta^I$ is solution of $w^+(1-q)u(\theta^Iv - p) + w^-(q)u(-p-F) = 0$. Since the function $u(\cdot)$ is increasing, $\frac{p^L}{b} \le \theta^Iv$, implies that: $w^+(1-q)u(\frac{p^L}{b} - p) + w^-(q)u(-p-F) = V_i(\theta^0) < 0$.

Since the function $V_i(\theta)$ is decreasing in $\theta$, $V_i(\theta^L) = 0$ and $V_i(\theta^0) < 0$ imply $\theta^L \le \theta^0$.

Finally, since $V_I(\theta)$ is strictly increasing in $\theta$, $\theta^0 < \theta^I \Leftrightarrow V_I(\theta^0) = w^+(1-q)u(\frac{p^L}{b} - p) + w^-(q)u(-p-F) < V_I(\theta^I)$. Since $V_I(\theta^I) = 0$ and $V_I(\theta^0) < 0$, we deduce that $\theta^0 < \theta^I$.

We have demonstrated in this condition that $\theta^L < \theta^0 < \theta^I$: the legalization has the effect of drying up the illegal market.

**Condition $p^L > \tilde{p}^L(p)$ holds.**

The reasoning is similar to the previous case but the inequalities are inverted.

The condition $p^L > \theta^Ibv$, leads to $V_i(\theta^0) > V_i(\theta^L) = 0$ such that $\theta^0 < \theta^I$.

Similarly, since $V_I(\theta)$ is strictly increasing in $\theta$, $V_I(\theta^0) = w^+(1-q)u(p^L - \frac{bp}{b}) + w^-(q)u(-p-F) > 0$ and $V_I(\theta^I) = 0$ imply that $\theta^I < \theta^0$. We have demonstrated in this condition that $\theta^I < \theta^0 < \theta^L$: the illegal market survives.

## D.2 Proof of proposition 1 (the demand)

The black market responds strategically to the legal market by lowering its price to $p^N(p^L)$, 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), which depends on $p^L$. The price reaction function of the black market sellers solves the following equation:

$$ p(p^L) = \begin{cases} p^N(p^L) & \text{if } c \le p^N(p^L) < \frac{p^L}{b} \\ \emptyset & \text{otherwise} \end{cases} \qquad (A9) $$

Since $\theta$ is distributed on $\mathbb{R}$, as long as $p^L < \infty$, there is a positive demand for legal cannabis $(1 - G(\theta^L(p, p^L)) > 0)$.
Appendix C shows that consumer $\theta^L$, indifferent between legal and illegal consumption, solves under

* EUT: $V_1(\theta) = (1-q)u(\theta v - p) + qu(-p-F) - u(\theta bv - p^L) = 0$;

* CPT: $V_2(\theta) = w^+(1-q)u(p^L - p - \theta(b-1)v) + w^-(q)u(-p-F - \theta bv + p^L) = 0$.

Two cases may follow the implementation of a legal market.

**Condition $p^L \le \tilde{p}^L(p)$ holds.**

We can write, for $i = 1, 2$, $V_i(\theta^0) = w^+(1-q)u(\frac{p^L}{b} - p) + w^-(q)u(-p-F)$, with the weighting functions being the identity function under EUT.

By definition of $\theta^L$, $V_i(\theta^L) = 0$. If $p^L \le \theta^Ibv$ then $\frac{p^L}{b} \le \theta^Iv$. $\theta^I$ is solution of $w^+(1-q)u(\theta^Iv - p) + w^-(q)u(-p-F) = 0$. Since the function $u(\cdot)$ is increasing, $\frac{p^L}{b} \le \theta^Iv$, implies that: $w^+(1-q)u(\frac{p^L}{b} - p) + w^-(q)u(-p-F) = V_i(\theta^0) < 0$.

Since the function $V_i(\theta)$ is decreasing in $\theta$, $V_i(\theta^L) = 0$ and $V_i(\theta^0) < 0$ imply $\theta^L \le \theta^0$.

Finally, since $V_I(\theta)$ is strictly increasing in $\theta$, $\theta^0 < \theta^I \Leftrightarrow V_I(\theta^0) = w^+(1-q)u(\frac{p^L}{b} - p) + w^-(q)u(-p-F) < V_I(\theta^I)$. Since $V_I(\theta^I) = 0$ and $V_I(\theta^0) < 0$, we deduce that $\theta^0 < \theta^I$.

We have demonstrated in this condition that $\theta^L < \theta^0 < \theta^I$: the legalization has the effect of drying up the illegal market.

**Condition $p^L > \tilde{p}^L(p)$ holds.**

The reasoning is similar to the previous case but the inequalities are inverted.

The condition $p^L > \theta^Ibv$, leads to $V_i(\theta^0) > V_i(\theta^L) = 0$ such that $\theta^0 < \theta^I$.

Similarly, since $V_I(\theta)$ is strictly increasing in $\theta$, $V_I(\theta^0) = w^+(1-q)u(p^L - \frac{bp}{b}) + w^-(q)u(-p-F) > 0$ and $V_I(\theta^I) = 0$ imply that $\theta^I < \theta^0$. We have demonstrated in this condition that $\theta^I < \theta^0 < \theta^L$: the illegal market survives.

## D.2 Proof of proposition 1 (the demand)

The black market responds strategically to the legal market by lowering its price to $p^N(p^L)$, 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), which depends on $p^L$. The price reaction function of the black market sellers solves the following equation:

$$p(p^L) = \begin{cases} p^N(p^L) & \text{if } c \le p^N(p^L) < \frac{p^L}{b} \\ \emptyset & \text{otherwise} \end{cases} \qquad (A9)$$

Since $\theta$ is distributed on $\mathbb{R}$, as long as $p^L < \infty$, there is a positive demand for legal cannabis $(1 - G(\theta^L(p, p^L)) > 0)$.
If $p^L > \tilde{p}^L(p)$ ($\theta^I < \theta^0 < \theta^L$) and other policy parameters ($c, b, q, F$) are held constant, the demand for the black-market product decreases following legalization and the absolute value of the price elasticity of the black-market demand increases. Therefore, for any finite legal retail price $p^L$, the black-market price $p$ decreases after legalization. This implies that the demand for cannabis increases ($\theta^I$ decreases).

If $p^L \le \tilde{p}^L(p)$ ($\theta^L \le \theta^0 \le \theta^I$), it is obvious that the overall demand for legal cannabis increases following legalization. We deduce that legalization always increases the overall demand for cannabis, when the operation costs of illegal providers, the quality differential and the repression of demand on the black market are held constant.

# E Pricing out the dealers

## E.1 Proof of proposition 2 (characterization of the eviction price)

Under prospect theory the threshold price, denoted $\underline{p}^L$, below which the criminals exit the market is such that $\theta^L(c, \underline{p}^L) = \theta^I(c)$, where $\theta^I(c)$ and $\theta^L(c, \underline{p}^L)$ are defined in equations (2) and (7) with $p = c$. Therefore, $\theta^I(c)$ (or equivalently $\theta^L(c, \underline{p}^L)$) is determined by the following system of equations:

$$ egin{cases} w^+(1-q)u(\theta v - c) + w^-(q)u(-c-F) = 0 \\ w^+(1-q)u(\theta v - \theta b v + \underline{p}^L - c) + w^-(q)u(-\theta b v + \underline{p}^L - c - F) = 0 \end{cases} $$

Under expected utility theory, the same reasoning yields the following system of equations:

$$ egin{cases} (1-q)u(\theta v - c) + qu(-c-F) = 0 \\ (1-q)u(\theta v - c) + qu(-c-F) = u(\theta b v - \underline{p}^L) \end{cases} $$

In both cases, this yields $\underline{p}^L = dv\theta^I(c)$.

The legal demand is at the same level as if illegal suppliers were pricing at marginal cost:

$$ D^L(\underline{p}^L) = \int_{\theta^L(\underline{p}^L, c)}^{+\infty} g(\theta) d\theta = 1 - G(\theta^L(\underline{p}^L, c)) = 1 - G(\theta^I(c)) = D^I(c). \quad (A10) $$

## E.2 Proof of the corollary to proposition 2

The price $\underline{p}^L = bv\theta^I(c)$ being linear in the quality differential $b$ and the parameters $\theta^I$ and $v$ being positive, it is straightforward that $\underline{p}^L$ increases with $b$. Regarding the other parameters, comparative statics are derived in appendix B with $p = c$.
If $p^L > \tilde{p}^L(p)$ ($\theta^I < \theta^0 < \theta^L$) and other policy parameters $(c, b, q, F)$ are held constant, the demand for the black-market product decreases following legalization and the absolute value of the price elasticity of the black-market demand increases. Therefore, for any finite legal retail price $p^L$, the black-market price $p$ decreases after legalization. This implies that the demand for cannabis increases ($\theta^I$ decreases).

If $p^L \le \tilde{p}^L(p)$ ($\theta^L \le \theta^0 \le \theta^I$), it is obvious that the overall demand for legal cannabis increases following legalization. We deduce that legalization always increases the overall demand for cannabis, when the operation costs of illegal providers, the quality differential and the repression of demand on the black market are held constant.

# E Pricing out the dealers

## E.1 Proof of proposition 2 (characterization of the eviction price)

Under prospect theory the threshold price, denoted $\underline{p}^L$, below which the criminals exit the market is such that $\theta^L(c, \underline{p}^L) = \theta^I(c)$, where $\theta^I(c)$ and $\theta^L(c, \underline{p}^L)$ are defined in equations (2) and (7) with $p = c$. Therefore, $\theta^I(c)$ (or equivalently $\theta^L(c, \underline{p}^L)$) is determined by the following system of equations:

$$ 
\begin{cases} 
w^+(1-q)u(\theta v - c) + w^-(q)u(-c-F) = 0 \\ 
w^+(1-q)u(\theta v - \theta bv + \underline{p}^L - c) + w^-(q)u(-\theta bv + \underline{p}^L - c - F) = 0 
\end{cases} 
$$

Under expected utility theory, the same reasoning yields the following system of equations:

$$ 
\begin{cases} 
(1-q)u(\theta v - c) + qu(-c-F) = 0 \\ 
(1-q)u(\theta v - c) + qu(-c-F) = u(\theta bv - \underline{p}^L) 
\end{cases} 
$$

In both cases, this yields $\underline{p}^L = dv\theta^I(c)$.

The legal demand is at the same level as if illegal suppliers were pricing at marginal cost:

$$ D^L(\underline{p}^L) = \int_{\theta^L(\underline{p}^L, c)}^{+\infty} g(\theta) d\theta = 1 - G(\theta^L(\underline{p}^L, c)) = 1 - G(\theta^I(c)) = D^I(c). \quad (A10) $$

## E.2 Proof of the corollary to proposition 2

The price $\underline{p}^L = bv\theta^I(c)$ being linear in the quality differential $b$ and the parameters $\theta^I$ and $v$ being positive, it is straightforward that $\underline{p}^L$ increases with $b$. Regarding the other parameters, comparative statics are derived in appendix B with $p = c$.
# F Enlarging the set of objectives

## F.1 Proof of proposition 3 (cost effectiveness under a demand target)

Consider the case of a government interested in eradicating the illegal market while containing the (legal) use of cannabis to a level $D^L(p^L) = \bar{D}$. Such a government then applies the eviction price $p^L$ defined in proposition 2 and such that $D^L(p^L) \le \bar{D}$.

In this case, the optimal combination of policy instruments, minimizing the net enforcement cost $C(e, b, \tau) = E(\delta, q)$, is solution of the following program:

$$ \begin{array}{ll} \min_{\delta,q} & E(\delta, q) \\ \text{s.t.} & D^L(p^L) \le \bar{D} \text{ with } p^L = bv\theta^I((1+\delta)c^L) \end{array} \qquad (A11) $$

The Lagrangian of this optimization problem is

$$ \mathcal{L} = E(\delta, q) + \lambda [\bar{D} - D^L(p^L)] $$

The Lagrangian derivatives with respect of $\delta$ and $q$ are given as follows

$$ \frac{\partial E(\delta, q)}{\partial \delta} - \lambda \frac{\partial D^L(p^L)}{\partial \delta} = 0 $$

$$ \frac{\partial E(\delta, q)}{\partial q} - \lambda \frac{\partial D^L(p^L)}{\partial q} = 0 $$

Focusing on interior solutions, these yield $\frac{\partial D^L(p^L)}{\partial q} = \frac{\partial E(\delta, q)}{\partial q}$, i.e. the optimality condition (12) and, at the optimum, the demand constraint $D^L(p^L) = \bar{D}$ is binding.

## F.2 Maximizing tax revenue

### Proof of proposition 5

In this section we aim to derive the optimal tax rate when the government seeks to maximize tax revenue. It solves: $\max_{\tau} \tau c^L D^L(p, (1+\tau)c^L|b)$. The first order condition of this optimization program is:

$$ c^L D^L(p, (1+\tau)c^L|b) + \tau c^L \frac{\partial D^L}{\partial \tau} = 0 $$

which is equivalent to:

$$ D^L(p, (1+\tau)c^L|b) + \tau \frac{\partial D^L}{\partial \tau} = 0 $$
# F Enlarging the set of objectives

## F.1 Proof of proposition 3 (cost effectiveness under a demand target)

Consider the case of a government interested in eradicating the illegal market while containing the (legal) use of cannabis to a level $D^L(p^L) = \bar{D}$. Such a government then applies the eviction price $p^L$ defined in proposition 2 and such that $D^L(p^L) \le \bar{D}$.

In this case, the optimal combination of policy instruments, minimizing the net enforcement cost $C(e, b, \tau) = E(\delta, q)$, is solution of the following program:

$$ \begin{array}{ll} \min_{\delta,q} & E(\delta, q) \\ \text{s.t.} & D^L(p^L) \le \bar{D} \text{ with } p^L = bv\theta^I((1+\delta)c^L) \end{array} \qquad (A11) $$

The Lagrangian of this optimization problem is

$$ \mathcal{L} = E(\delta, q) + \lambda [\bar{D} - D^L(p^L)] $$

The Lagrangian derivatives with respect of $\delta$ and $q$ are given as follows

$$ \frac{\partial E(\delta, q)}{\partial \delta} - \lambda \frac{\partial D^L(p^L)}{\partial \delta} = 0 $$

$$ \frac{\partial E(\delta, q)}{\partial q} - \lambda \frac{\partial D^L(p^L)}{\partial q} = 0 $$

Focusing on interior solutions, these yield $\frac{\partial D^L(p^L)}{\partial q} = \frac{\partial E(\delta, q)}{\partial q}$, i.e. the optimality condition (12) and, at the optimum, the demand constraint $D^L(p^L) = \bar{D}$ is binding.

## F.2 Maximizing tax revenue

### Proof of proposition 5

In this section we aim to derive the optimal tax rate when the government seeks to maximize tax revenue. It solves: $\max_{\tau} \tau c^L D^L(p, (1+\tau)c^L|b)$. The first order condition of this optimization program is:

$$ c^L D^L(p, (1+\tau)c^L|b) + \tau c^L \frac{\partial D^L}{\partial \tau} = 0 $$

which is equivalent to :

$$ D^L(p, (1+\tau)c^L|b) + \tau \frac{\partial D^L}{\partial \tau} = 0 $$
If $p^L > \tilde{p}^L$, $D^L(p, (1+\tau)c^L|b) = 1 - G(\theta^0)$, with $\theta^0 = \frac{p^L}{bv}$ (cf. 4.2).

$$
\begin{align*}
& D^L(p, (1+\tau)c^L|b) + \tau \frac{\partial D^L}{\partial \tau} = 0 \\
\Leftrightarrow & 1 - G\left(\frac{p^L}{bv}\right) + \tau \frac{\partial \left\{1 - G\left(\frac{p^L}{bv}\right)\right\}}{\partial \tau} = 0 \\
\Leftrightarrow & 1 - G\left(\frac{p^L}{bv}\right) = \tau \frac{\partial \left\{G\left(\frac{p^L}{bv}\right)\right\}}{\partial \tau} \\
\Leftrightarrow & 1 - G\left(\frac{p^L}{bv}\right) = \tau \frac{\partial \left\{G\left(\frac{(1+\tau)c^L}{bv}\right)\right\}}{\partial \tau} \\
\Leftrightarrow & 1 - G\left(\frac{p^L}{bv}\right) = \tau \frac{c^L}{bv} g\left(\frac{(1+\tau)c^L}{bv}\right) \\
\Leftrightarrow & 1 - G(\theta^0) = \tau c^L \underbrace{\frac{1}{bv} g(\theta^0)}_{= \frac{\partial \theta^0}{\partial p^L}}
\end{align*}
$$

Otherwise, $D^L(p, (1+\tau)c^L|b) = 1 - G(\theta^L)$ and

$$
\begin{align*}
& D^L(p, (1+\tau)c^L|b) + \tau \frac{\partial D^L}{\partial \tau} = 0 \\
\Leftrightarrow & 1 - G(\theta^L) + \tau \frac{\partial \{1 - G(\theta^L)\}}{\partial \tau} = 0 \\
\Leftrightarrow & 1 - G(\theta^L) = \tau \frac{\partial \{G(\theta^L)\}}{\partial \tau} \\
\Leftrightarrow & 1 - G(\theta^L) = \tau \frac{\partial \theta^L}{\partial \tau} g(\theta^L) \\
\Leftrightarrow & 1 - G(\theta^L) = \tau \frac{\partial \theta^L}{\partial p^L} \frac{\partial p^L}{\partial \tau} g(\theta^L) \\
\Leftrightarrow & 1 - G(\theta^L) = \tau \frac{\partial \theta^L}{\partial p^L} c^L g(\theta^L)
\end{align*}
$$

This yields equation (15).

Maximizing tax revenue when $\theta$ follows an exponential distribution

Let us assume that on the positive real line, $\theta$ follows an exponential distribution $G(\theta) \equiv 1 - e^{-\eta\theta}$, with $0 < \eta < 1$, equation (15) becomes

$$1 = \eta c^L \tau \frac{\partial \theta^L}{\partial p^L}. \qquad (A12)$$
If $p^L > \tilde{p}^L$, $D^L(p, (1+\tau)c^L|b) = 1 - G(\theta^0)$, with $\theta^0 = \frac{p^L}{bv}$ (cf. 4.2).

$$
\begin{align*}
& D^L(p, (1+\tau)c^L|b) + \tau \frac{\partial D^L}{\partial \tau} = 0 \\
\Leftrightarrow & 1 - G\left(\frac{p^L}{bv}\right) + \tau \frac{\partial \left\{1 - G\left(\frac{p^L}{bv}\right)\right\}}{\partial \tau} = 0 \\
\Leftrightarrow & 1 - G\left(\frac{p^L}{bv}\right) = \tau \frac{\partial \left\{G\left(\frac{p^L}{bv}\right)\right\}}{\partial \tau} \\
\Leftrightarrow & 1 - G\left(\frac{p^L}{bv}\right) = \tau \frac{\partial \left\{G\left(\frac{(1+\tau)c^L}{bv}\right)\right\}}{\partial \tau} \\
\Leftrightarrow & 1 - G\left(\frac{p^L}{bv}\right) = \tau \frac{c^L}{bv} g\left(\frac{(1+\tau)c^L}{bv}\right) \\
\Leftrightarrow & 1 - G(\theta^0) = \tau c^L \underbrace{\frac{1}{bv} g(\theta^0)}_{= \frac{\partial \theta^0}{\partial p^L}}
\end{align*}
$$

Otherwise, $D^L(p, (1+\tau)c^L|b) = 1 - G(\theta^L)$ and

$$
\begin{align*}
& D^L(p, (1+\tau)c^L|b) + \tau \frac{\partial D^L}{\partial \tau} = 0 \\
\Leftrightarrow & 1 - G(\theta^L) + \tau \frac{\partial \{1 - G(\theta^L)\}}{\partial \tau} = 0 \\
\Leftrightarrow & 1 - G(\theta^L) = \tau \frac{\partial \{G(\theta^L)\}}{\partial \tau} \\
\Leftrightarrow & 1 - G(\theta^L) = \tau \frac{\partial \theta^L}{\partial \tau} g(\theta^L) \\
\Leftrightarrow & 1 - G(\theta^L) = \tau \frac{\partial \theta^L}{\partial p^L} \frac{\partial p^L}{\partial \tau} g(\theta^L) \\
\Leftrightarrow & 1 - G(\theta^L) = \tau \frac{\partial \theta^L}{\partial p^L} c^L g(\theta^L)
\end{align*}
$$

This yields equation (15).

Maximizing tax revenue when $\theta$ follows an exponential distribution

Let us assume that on the positive real line, $\theta$ follows an exponential distribution $G(\theta) \equiv 1 - e^{-\eta\theta}$, with $0 < \eta < 1$, equation (15) becomes

$$1 = \eta c^L \tau \frac{\partial \theta^L}{\partial p^L}. \qquad (A12)$$
If the black market has been initially shut down, then (A12) yields $\tau_0^{\alpha_T} = \frac{bv}{\eta c^L}$. If the black market is not shut down, with risk-neutral consumers we have $\theta^L = \frac{p^L-p-qF}{(b+q-1)v}$, so that (A12) yields: $\tau^{\alpha_T} = \frac{b+q-1}{\eta c^L}v \ge 0$. This is the optimal solution if the demand for cannabis is strictly positive for this level of taxes which requires that $\theta^L(\tau^{\alpha_T}) = \frac{(1+\tau^{\alpha_T})c^L-p-qF}{(b+q-1)v} > 0$. This is equivalent to $\eta < \frac{v(b+q-1)}{qF+p-c^L} \le \frac{v(b+q-1)}{qF+\delta c^L} = \eta^{\alpha_T}$. We deduce 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="50" /> which is intuitive.

When the government does not have to deal with competition it can impose higher taxes, as the consumers are captive. In both cases, the tax rate increases with $vb$, the quality of the legal product, and decreases with $c^L$, the marginal cost of production of legal cannabis, and with $\eta$, the distribution of consumers' type parameter. Indeed, a higher $\eta$ implies that the distribution of taste is skewed towards the low values of $\theta$: few people are willing to pay a high price for cannabis, which implies that the tax rate should be relatively low.

Next, we check under which conditions the optimal tax level $\tau^{\alpha_T}$ is such that the final price $p^L(\tau^{\alpha_T}) = (1+\tau^{\alpha_T})c^L$ is lower than the eviction price $\underline{p}^L = bv\theta^I((1+\delta)c^L) = b\frac{(1+\delta)c^L+qF}{1-q}$. Let $\eta^{evic} = \frac{(1-q)(b+q-1)v}{b(\delta c^L+qF)+(b+q-1)c^L} > 0$. It is easy to check that if $\eta \ge \eta^{evic}$, then $p^L(\tau^{\alpha_T}) \le \underline{p}^L$. Under our assumptions, $0 < \eta^{evic} < \eta^{\alpha_T}$. Only when $\eta^{evic} \le \eta < \eta^{\alpha_T}$ is it possible to maximize tax revenues while simultaneously eradicating the black market through an eviction price.

Based on the number of users of cannabis worldwide, it is unrealistic to assume that the distribution of tastes for cannabis in the general population is skewed towards the low values of $\theta$ (i.e., it is unrealistic to consider large values for $\eta$). Yet, if $\eta < \eta^{evic} < \eta^{\alpha_T}$, then the price that maximizes tax revenue is higher than the eviction price. In other words, when there is a large demand for cannabis, maximizing tax revenue implies setting the price of the legal products relatively high, such that the black market can survive by selling illegal cannabis at a discount.

## Taxation and survival of the black market

After the government chooses the price of the legal cannabis, $p^L = (1+\tau)c^L$, the repression (i.e. the probability of arrest $q$, the fine $F$ and the increase in marginal cost to produce illegally $\delta \ge 0$), as well as the quality differential between legal and illegal products, $b \ge 1$, the consumers decide whether to consume or not, and on which market. From here, two cases may occur.

1. Taxes are set low enough such that, given the level of repression on both the demand and supply sides and the quality differential, the black market does not survive.

<footnote n="50">⁵⁰They are equal only when $q = 1$.</footnote>
If the black market has been initially shut down, then (A12) yields $\tau_0^{\alpha_T} = \frac{bv}{\eta c^L}$. If the black market is not shut down, with risk-neutral consumers we have $\theta^L = \frac{p^L-p-qF}{(b+q-1)v}$, so that (A12) yields: $\tau^{\alpha_T} = \frac{b+q-1}{\eta c^L}v \ge 0$. This is the optimal solution if the demand for cannabis is strictly positive for this level of taxes which requires that $\theta^L(\tau^{\alpha_T}) = \frac{(1+\tau^{\alpha_T})c^L-p-qF}{(b+q-1)v} > 0$. This is equivalent to $\eta < \frac{v(b+q-1)}{qF+p-c^L} \le \frac{v(b+q-1)}{qF+\delta c^L} = \eta^{\alpha_T}$. We deduce 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="50" /> which is intuitive.

When the government does not have to deal with competition it can impose higher taxes, as the consumers are captive. In both cases, the tax rate increases with $vb$, the quality of the legal product, and decreases with $c^L$, the marginal cost of production of legal cannabis, and with $\eta$, the distribution of consumers' type parameter. Indeed, a higher $\eta$ implies that the distribution of taste is skewed towards the low values of $\theta$: few people are willing to pay a high price for cannabis, which implies that the tax rate should be relatively low.

Next, we check under which conditions the optimal tax level $\tau^{\alpha_T}$ is such that the final price $p^L(\tau^{\alpha_T}) = (1+\tau^{\alpha_T})c^L$ is lower than the eviction price $\underline{p}^L = bv\theta^I((1+\delta)c^L) = b\frac{(1+\delta)c^L+qF}{1-q}$. Let $\eta^{evic} = \frac{(1-q)(b+q-1)v}{b(\delta c^L+qF)+(b+q-1)c^L} > 0$. It is easy to check that if $\eta \ge \eta^{evic}$, then $p^L(\tau^{\alpha_T}) \le \underline{p}^L$. Under our assumptions, $0 < \eta^{evic} < \eta^{\alpha_T}$. Only when $\eta^{evic} \le \eta < \eta^{\alpha_T}$ is it possible to maximize tax revenues while simultaneously eradicating the black market through an eviction price.

Based on the number of users of cannabis worldwide, it is unrealistic to assume that the distribution of tastes for cannabis in the general population is skewed towards the low values of $\theta$ (i.e., it is unrealistic to consider large values for $\eta$). Yet, if $\eta < \eta^{evic} < \eta^{\alpha_T}$, then the price that maximizes tax revenue is higher than the eviction price. In other words, when there is a large demand for cannabis, maximizing tax revenue implies setting the price of the legal products relatively high, such that the black market can survive by selling illegal cannabis at a discount.

## Taxation and survival of the black market

After the government chooses the price of the legal cannabis, $p^L = (1+\tau)c^L$, the repression (i.e. the probability of arrest $q$, the fine $F$ and the increase in marginal cost to produce illegally $\delta \ge 0$), as well as the quality differential between legal and illegal products, $b \ge 1$, the consumers decide whether to consume or not, and on which market. From here, two cases may occur.

1. Taxes are set low enough such that, given the level of repression on both the demand and supply sides and the quality differential, the black market does not survive.

<footnote n="50">⁵⁰They are equal only when $q = 1$.</footnote>
In this case $\tau$ satisfies $1 + \tau \le bv \frac{\theta^I((1+\delta)c^L)}{c^L}$ where $\theta^I((1+\delta)c^L)$ is defined in (2). Let $\theta^0 = \frac{(1+\tau)c^L}{vb}$ be the agent indifferent between consuming legal cannabis at price $p^L = (1 + \tau)c^L$ and not consuming. The demand for (legal) cannabis is given by: $D^L((1 + \tau)c^L) = 1 - G(\frac{(1+\tau)c^L}{vb})$.

2. If the government sets taxes too high, such that $(1 + \tau)c^L > bv\theta^I((1 + \delta)c^L)$, then the demand is split between the legal and illegal markets, as follows:

$$D^L(p, (1+\tau)c^L|b) = 1 - G(\theta^L(p, (1+\tau)c^L|b)) \\ D^I(p, (1+\tau)c^L|b) = G(\theta^L(p, (1+\tau)c^L|b)) - G(\theta^I(p))$$

where $\theta^I(p)$ is defined in (2) and $\theta^L(p, (1+\tau)c^L|b)$ in (7). Illegal providers set the black market price $p$ as defined in (6). The price reaction function of the illegal sector is analogous to the best response described in (10) with $p^L = (1 + \tau)c^L$.

## G Application to Tversky and Kahneman (1992)

Tversky and Kahneman (1992) introduces a model featuring loss aversion, diminishing sensitivity for gains and losses and diminishing sensitivity regarding probabilities. Agents' appreciation for gains and losses is represented by a value function $u(x)$, which is S-shaped and has an inflection point in zero. This describes individuals being empirically risk-averse for gains and risk-seeking for losses; called by Kahneman and Tversky (1979) the reflection effect.

More specifically, the authors calibrate the following functional form for the value function:

$$u(x) = \begin{cases} x^{\alpha}, & \text{if } x > 0 \\ -\lambda(-x)^{\beta}, & \text{if } x \le 0 \end{cases} \qquad (A13)$$

where $\alpha, \beta \in (0, 1)$ capture the degree of risk preference of individuals who are risk-averse for gains and risk-seeking for losses. $\lambda \ge 1$ is the coefficient of loss aversion, which reflects that the decrease in utility from a loss is greater than the increase in utility from a gain of the same amount. In line with Tversky and Kahneman (1992) estimates, we assume $\alpha = \beta$.

The weighting functions $w^+$, for gains, $w^-$, for losses are concave near 0 and convex near 1 to capture diminishing sensitivity for probabilities. Tversky and Kahneman (1992) specify the weighting functions as follows:

$$w^x(q) = \frac{q^{\gamma^x}}{(q^{\gamma^x} + (1-q)^{\gamma^x})^{\frac{1}{\gamma^x}}} \quad \text{with } x = +, -.$$
In this case $\tau$ satisfies $1 + \tau \le bv \frac{\theta^I((1+\delta)c^L)}{c^L}$ where $\theta^I((1+\delta)c^L)$ is defined in (2). Let $\theta^0 = \frac{(1+\tau)c^L}{vb}$ be the agent indifferent between consuming legal cannabis at price $p^L = (1+\tau)c^L$ and not consuming. The demand for (legal) cannabis is given by: $D^L((1+\tau)c^L) = 1 - G(\frac{(1+\tau)c^L}{vb})$.

2. If the government sets taxes too high, such that $(1 + \tau)c^L > bv\theta^I((1 + \delta)c^L)$, then the demand is split between the legal and illegal markets, as follows:

$$D^L(p, (1+\tau)c^L|b) = 1 - G(\theta^L(p, (1+\tau)c^L|b)) \\ D^I(p, (1+\tau)c^L|b) = G(\theta^L(p, (1+\tau)c^L|b)) - G(\theta^I(p))$$

where $\theta^I(p)$ is defined in (2) and $\theta^L(p, (1+\tau)c^L|b)$ in (7). Illegal providers set the black market price $p$ as defined in (6). The price reaction function of the illegal sector is analogous to the best response described in (10) with $p^L = (1+\tau)c^L$.

## G Application to Tversky and Kahneman (1992)

Tversky and Kahneman (1992) introduces a model featuring loss aversion, diminishing sensitivity for gains and losses and diminishing sensitivity regarding probabilities. Agents' appreciation for gains and losses is represented by a value function $u(x)$, which is S-shaped and has an inflection point in zero. This describes individuals being empirically risk-averse for gains and risk-seeking for losses; called by Kahneman and Tversky (1979) the reflection effect.

More specifically, the authors calibrate the following functional form for the value function:

$$u(x) = \begin{cases} x^{\alpha}, & \text{if } x > 0 \\ -\lambda(-x)^{\beta}, & \text{if } x \le 0 \end{cases} \qquad (A13)$$

where $\alpha, \beta \in (0, 1)$ capture the degree of risk preference of individuals who are risk-averse for gains and risk-seeking for losses. $\lambda \ge 1$ is the coefficient of loss aversion, which reflects that the decrease in utility from a loss is greater than the increase in utility from a gain of the same amount. In line with Tversky and Kahneman (1992) estimates, we assume $\alpha = \beta$.

The weighting functions $w^+$, for gains, $w^-$, for losses are concave near 0 and convex near 1 to capture diminishing sensitivity for probabilities. Tversky and Kahneman (1992) specify the weighting functions as follows:

$$w^x(q) = \frac{q^{\gamma^x}}{(q^{\gamma^x} + (1-q)^{\gamma^x})^{\frac{1}{\gamma^x}}} \quad \text{with } x = +, -.$$
The form of such weighting functions is represented in figure A1. For $\gamma = 1$, $w^x : q \mapsto \frac{q^\gamma}{(q^\gamma+(1-q)^\gamma)^{\frac{1}{\gamma}}}$ is the identity. The closer $\gamma$ is to 0, the more distorted the probability weights are. When $\gamma \to 0$, the function $w^x$ has an L-shape.

<figure><img src="image_5.png" /><figcaption>Figure A1: Probability weighting functions for $\gamma \in (0, 1]$</figcaption></figure>

In line with Tversky and Kahneman (1992), we assume that $\gamma^+ < \gamma^-$.

## Eviction price under Tversky and Kahneman (1992)

Substituting in equation (A2) the value function $u$ specified in (A13), the type $\theta^I$ indifferent between consuming illegally and not consuming is given by:

$$ \theta^I = \frac{1}{v} \left[ \left( \lambda \frac{w^{-}(q)}{w^{+}(1-q)} \right)^{\frac{1}{\alpha}} (F+p) + p \right] \quad (A14) $$

This implies that:

$$ \frac{\partial \theta^I}{\partial p} = \frac{1}{v} \left[ \left( \lambda \frac{w^{-}(q)}{w^{+}(1-q)} \right)^{\frac{1}{\alpha}} + 1 \right] > 0 $$

Let us note $\omega(q) \equiv \frac{w^{-}(q)}{w^{+}(1-q)}$, which is strictly increasing since $w^x$ is increasing for $x = +, -$. It yields:

$$ \frac{\partial \theta^I}{\partial q} = \frac{\lambda^{\frac{1}{\alpha}} (F+p)}{\alpha v} \omega'(q) [\omega(q)]^{\frac{1-\alpha}{\alpha}} > 0. $$

We deduce that the eviction price $p^L = bv\theta^I(c)$ under Tversky and Kahneman (1992)'s
The form of such weighting functions is represented in figure A1. For $\gamma = 1$, $w^x : q \mapsto \frac{q^\gamma}{(q^\gamma+(1-q)^\gamma)^{\frac{1}{\gamma}}}$ is the identity. The closer $\gamma$ is to 0, the more distorted the probability weights are. When $\gamma \to 0$, the function $w^x$ has an L-shape.

<figure><img src="image_6.png" /><figcaption>Figure A1: Probability weighting functions for $\gamma \in (0, 1]$</figcaption></figure>

In line with Tversky and Kahneman (1992), we assume that $\gamma^+ < \gamma^-$.

## Eviction price under Tversky and Kahneman (1992)

Substituting in equation (A2) the value function $u$ specified in (A13), the type $\theta^I$ indifferent between consuming illegally and not consuming is given by:

$$ \theta^I = \frac{1}{v} \left[ \left( \lambda \frac{w^{-}(q)}{w^{+}(1-q)} \right)^{\frac{1}{\alpha}} (F+p) + p \right] \quad (A14) $$

This implies that:

$$ \frac{\partial \theta^I}{\partial p} = \frac{1}{v} \left[ \left( \lambda \frac{w^{-}(q)}{w^{+}(1-q)} \right)^{\frac{1}{\alpha}} + 1 \right] > 0 $$

Let us note $\omega(q) \equiv \frac{w^{-}(q)}{w^{+}(1-q)}$, which is strictly increasing since $w^x$ is increasing for $x = +, -$. It yields:

$$ \frac{\partial \theta^I}{\partial q} = \frac{\lambda^{\frac{1}{\alpha}} (F+p)}{\alpha v} \omega'(q) [\omega(q)]^{\frac{1-\alpha}{\alpha}} > 0. $$

We deduce that the eviction price $p^L = bv\theta^I(c)$ under Tversky and Kahneman (1992)'s
specification is:

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

## Comparative statics of the eviction price

We can check straightforwardly how the eviction price varies when the policy parameters change (see corollary to proposition 2 already demonstrated in the general case).

$$ \frac{\partial \underline{p}^L}{\partial F} = b \left( \lambda \frac{w^{-}(q)}{w^{+}(1-q)} \right)^{\frac{1}{\alpha}} > 0 $$

$$ \frac{\partial \underline{p}^L}{\partial c} = b \left[ \left( \lambda \frac{w^{-}(q)}{w^{+}(1-q)} \right)^{\frac{1}{\alpha}} + 1 \right] > 0 $$

$$ \frac{\partial \underline{p}^L}{\partial b} = \left[ \left( \lambda \frac{w^{-}(q)}{w^{+}(1-q)} \right)^{\frac{1}{\alpha}} (F+c) + c \right] > 0 $$

$$ \frac{\partial \underline{p}^L}{\partial q} = -b \frac{(F+c)\lambda^{\frac{1}{\alpha}} \omega'(q)}{\alpha \omega^2(q)} > 0 $$

## Marginal consumer indifferent between legal and illegal consumption

Under the Tversky and Kahneman (1992) specification, one can solve for the type $\theta^L$ indifferent between consuming legal and black market cannabis, substituting the function (A13) in equation (7). This parameter is given as follows.

$$ \theta^L = \left[ \left( \lambda \frac{w^{-}(q)}{w^{+}(1-q)} \right)^{\frac{1}{\alpha}} b + b - 1 \right]^{-1} \left[ (p^L - p) \left( 1 + \left( \lambda \frac{w^{-}(q)}{w^{+}(1-q)} \right)^{\frac{1}{\alpha}} \right) - \left( \lambda \frac{w^{-}(q)}{w^{+}(1-q)} \right)^{\frac{1}{\alpha}} F \right] \quad (A15) $$

## H The policy mix: a numerical application

This appendix completes the policy implications discussed in section 6 with further explanations of the calibrations, as well as with sensitivity analyses of the post-legalization equilibrium to the behavioral and policy parameters.
specification is:

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

## Comparative statics of the eviction price

We can check straightforwardly how the eviction price varies when the policy parameters change (see corollary to proposition 2 already demonstrated in the general case).

$$ \frac{\partial \underline{p}^L}{\partial F} = b \left( \lambda \frac{w^{-}(q)}{w^{+}(1-q)} \right)^{\frac{1}{\alpha}} > 0 $$

$$ \frac{\partial \underline{p}^L}{\partial c} = b \left[ \left( \lambda \frac{w^{-}(q)}{w^{+}(1-q)} \right)^{\frac{1}{\alpha}} + 1 \right] > 0 $$

$$ \frac{\partial \underline{p}^L}{\partial b} = \left[ \left( \lambda \frac{w^{-}(q)}{w^{+}(1-q)} \right)^{\frac{1}{\alpha}} (F+c) + c \right] > 0 $$

$$ \frac{\partial \underline{p}^L}{\partial q} = -b \frac{(F+c)\lambda^{\frac{1}{\alpha}} \omega'(q)}{\alpha \omega^2(q)} > 0 $$

## Marginal consumer indifferent between legal and illegal consumption

Under the Tversky and Kahneman (1992) specification, one can solve for the type $\theta^L$ indifferent between consuming legal and black market cannabis, substituting the function (A13) in equation (7). This parameter is given as follows.

$$ \theta^L = \left[ \left( \lambda \frac{w^{-}(q)}{w^{+}(1-q)} \right)^{\frac{1}{\alpha}} b + b - 1 \right]^{-1} \left[ (p^L - p) \left( 1 + \left( \lambda \frac{w^{-}(q)}{w^{+}(1-q)} \right)^{\frac{1}{\alpha}} \right) - \left( \lambda \frac{w^{-}(q)}{w^{+}(1-q)} \right)^{\frac{1}{\alpha}} F \right] \quad (A15) $$

## H The policy mix: a numerical application

This appendix completes the policy implications discussed in section 6 with further explanations of the calibrations, as well as with sensitivity analyses of the *post-legalization* equilibrium to the behavioral and policy parameters.
The sensitivity analyses rely on comparisons with the benchmark scenario in which the model parameters are set at the values calibrated by Tversky and Kahneman (1992) and policy parameters are set at benchmark values $q_L = 0.1\%$, $F = 1,000$, $b = 1.58$, and $c = 50$, which yields the benchmark eviction price $\underline{p}^L = 97.79$, using the closed-form expression (18).

## H.1 Calibration of the distribution of “taste” for cannabis

We calibrate the distribution of the “taste” for cannabis using our model and the literature on demand for cannabis, which estimates the range of price elasticities of demand, $\epsilon_{D^I p}$, between -0.5 and -0.8. Let us assume the “taste” for cannabis, $\theta \in \mathbb{R}$, is drawn from a normal distribution $N(\mu, \sigma^2)$. The expression of the price elasticity of demand in equation (4) becomes

$$ \epsilon_{D^I p} = \frac{p}{v} \left[ \left( \lambda \frac{w^{-}(q)}{w^{+}(1-q)} \right)^{\frac{1}{\alpha}} + 1 \right] \frac{1}{\sigma \sqrt{2\pi}} \frac{e^{-\frac{(\theta^I - \mu)^2}{2\sigma^2}}}{1 - \phi(\frac{\theta^I - \mu}{\sigma})} \quad (A16) $$

In 2017, 15% of Americans are estimated to have used cannabis in the past year (CBHSQ, 2018). This margin is simply given by:

$$ \zeta = 1 - \phi \left( \frac{\theta^I - \mu}{\sigma} \right) \quad (A17) $$

Using the estimates of $\epsilon$ and $\zeta$ discussed in the literature, we calibrate the parameters $\mu$ and $\sigma$ solving the system defined by equations (A16) and (A17), normalizing $v \equiv 1$ and using the benchmark values for the model parameters described in section 6.1. Using an iterative solver, we obtain the set of solutions described in table A2 for $\mu$ and $\sigma$, as well as the benchmark values for the post-legalization increase in consumption implementing the eviction price $\underline{p}^L = 97.79$,$^{51}$ $\Delta D(\underline{p}^L)$. As the demand becomes more inelastic, the distribution tail becomes fatter and the mean taste lower. The more inelastic the demand, the lower the post-legalization increase in demand.

The 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. This appendix also shows that small variations around the values calibrated by Tversky and Kahneman (1992) induce relatively little change in the predicted policy price $\underline{p}^L$ and subsequent increases in consumption.

<footnote>$^{51}$This eviction price assumes that, under legalization, the probability of arrest is ten times smaller ($q_L = 0.1\%$) than under prohibition ($q = 1\%$); and that the marginal cost on the black market is USD 50 post-legalization.</footnote>
The sensitivity analyses rely on comparisons with the benchmark scenario in which the model parameters are set at the values calibrated by Tversky and Kahneman (1992) and policy parameters are set at benchmark values $q_L = 0.1\%$, $F = 1,000$, $b = 1.58$, and $c = 50$, which yields the benchmark eviction price $\underline{p}^L = 97.79$, using the closed-form expression (18).

## H.1 Calibration of the distribution of “taste” for cannabis

We calibrate the distribution of the “taste” for cannabis using our model and the literature on demand for cannabis, which estimates the range of price elasticities of demand, $\epsilon_{D^I p}$, between -0.5 and -0.8. Let us assume the “taste” for cannabis, $\theta \in \mathbb{R}$, is drawn from a normal distribution $N(\mu, \sigma^2)$. The expression of the price elasticity of demand in equation (4) becomes

$$ \epsilon_{D^I p} = \frac{p}{v} \left[ \left( \lambda \frac{w^{-}(q)}{w^{+}(1-q)} \right)^{\frac{1}{\alpha}} + 1 \right] \frac{1}{\sigma \sqrt{2\pi}} \frac{e^{-\frac{(\theta^I - \mu)^2}{2\sigma^2}}}{1 - \phi \left( \frac{\theta^I - \mu}{\sigma} \right)} \quad (A16) $$

In 2017, 15% of Americans are estimated to have used cannabis in the past year (CBHSQ, 2018). This margin is simply given by:

$$ \zeta = 1 - \phi \left( \frac{\theta^I - \mu}{\sigma} \right) \quad (A17) $$

Using the estimates of $\epsilon$ and $\zeta$ discussed in the literature, we calibrate the parameters $\mu$ and $\sigma$ solving the system defined by equations (A16) and (A17), normalizing $v \equiv 1$ and using the benchmark values for the model parameters described in section 6.1. Using an iterative solver, we obtain the set of solutions described in table A2 for $\mu$ and $\sigma$, as well as the benchmark values for the post-legalization increase in consumption implementing the eviction price $\underline{p}^L = 97.79$,$^{51}$ $\Delta D(\underline{p}^L)$. As the demand becomes more inelastic, the distribution tail becomes fatter and the mean taste lower. The more inelastic the demand, the lower the post-legalization increase in demand.

The 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. This appendix also shows that small variations around the values calibrated by Tversky and Kahneman (1992) induce relatively little change in the predicted policy price $\underline{p}^L$ and subsequent increases in consumption.

<footnote>$^{51}$This eviction price assumes that, under legalization, the probability of arrest is ten times smaller ($q_L = 0.1\%$) than under prohibition ($q = 1\%$); and that the marginal cost on the black market is USD 50 post-legalization.</footnote>
<table><caption>Table A2: Distribution parameters and *post-legalization* increases in consumption</caption><thead><tr><th>ε<sub>D<sup>I</sup><sub>p</sub></sub></th><th>μ̂</th><th>σ̂</th><th>ΔD (p<sup>L</sup>)</th></tr></thead><tbody><tr><td>0.5</td><td>-690.4</td><td>1065.8</td><td>53%</td></tr><tr><td>0.6</td><td>-506.3</td><td>888.1</td><td>65%</td></tr><tr><td>0.7</td><td>-374.8</td><td>761.3</td><td>78%</td></tr><tr><td>0.8</td><td>-276.2</td><td>666.1</td><td>91%</td></tr></tbody></table>

Notes: Behavioral parameters are set based on Tversky and Kahneman (1992): $λ = 2.25$, $α = 0.88$, $γ^+ = 0.61$, $γ^- = 0.69$. Variation in demand relies on the baseline estimate of $p^L = 97.79$.

## H.2 Sensitivity analysis of $p^L$ to the behavioral parameters

Policy parameters are set at benchmark values $q_L = 0.1\%$, $F = 1,000$, $b = 1.58$, and $c = 50$. Prices and costs are for one ounce of cannabis. $\Delta D(p^L)$ is the percentage predicted increase in consumption following a legalization process that drives dealers out of business.

We study the sensitivity of the eviction price, $p^L$, to the exogenous behavioral parameters $γ^+$, $γ^-$, $α$ and $λ$. The benchmark values are: $α = 0.88$, $λ = 2.25$, $γ^+ = 0.61$ and $γ^- = 0.69$.

Tables A3 to A6 present in columns 3 and 4 the sensitivity of the distribution parameters, and in columns 5 and 6 the sensitivity of both the eviction price and the subsequent increase in consumption *post-legalization*. The magnitude of variations of the behavioral parameters around the benchmark values are presented in column 2.

Overall, the distribution parameters are not very sensitive to the variations in the behavioral parameters: variations in the behavioral parameters by 10% entail variations in the distribution parameters of less than 8% for most cases. The eviction price is fairly sensitive to the parameter $γ^-$: a 10% variation in this parameter causes a change in price of up to 13.5%. This is also true for the parameter $α$. Finally, *post-legalization* cannabis consumption is not very responsive to small variations in the behavioral parameters (by less than 10%) as it changes by less than 2% in most cases.

## H.3 Sensitivity analysis to policy instruments

This section studies the sensitivity of the eviction price and of the *post-legalization* demand to parameters that can be influenced by policies. Several instruments are considered: reinforcing sanctions may increase the marginal cost of operations for illegal suppliers, $c$, the probability of arrest, $q$, or fines to illegal consumers, $F$. Moreover, investing in the quality of the legal cannabis, including the purchasing experience, taste of the product, certification of potency and of the healthiness of the production process, and information/education cam-
<table><caption>Table A2: Distribution parameters and *post-legalization* increases in consumption</caption><thead><tr><th>ε<sub>D<sup>I</sup><sub>p</sub></sub></th><th>μ̂</th><th>σ̂</th><th>ΔD (p<sup>L</sup>)</th></tr></thead><tbody><tr><td>0.5</td><td>-690.4</td><td>1065.8</td><td>53%</td></tr><tr><td>0.6</td><td>-506.3</td><td>888.1</td><td>65%</td></tr><tr><td>0.7</td><td>-374.8</td><td>761.3</td><td>78%</td></tr><tr><td>0.8</td><td>-276.2</td><td>666.1</td><td>91%</td></tr></tbody></table>

Notes: Behavioral parameters are set based on Tversky and Kahneman (1992): $λ = 2.25$, $α = 0.88$, $γ^+ = 0.61$, $γ^- = 0.69$. Variation in demand relies on the baseline estimate of $p^L = 97.79$.

## H.2 Sensitivity analysis of $p^L$ to the behavioral parameters

Policy parameters are set at benchmark values $q_L = 0.1\%$, $F = 1,000$, $b = 1.58$, and $c = 50$. Prices and costs are for one ounce of cannabis. $\Delta D(p^L)$ is the percentage predicted increase in consumption following a legalization process that drives dealers out of business.

We study the sensitivity of the eviction price, $p^L$, to the exogenous behavioral parameters $γ^+$, $γ^-$, $α$ and $λ$. The benchmark values are: $α = 0.88$, $λ = 2.25$, $γ^+ = 0.61$ and $γ^- = 0.69$.

Tables A3 to A6 present in columns 3 and 4 the sensitivity of the distribution parameters, and in columns 5 and 6 the sensitivity of both the eviction price and the subsequent increase in consumption *post-legalization*. The magnitude of variations of the behavioral parameters around the benchmark values are presented in column 2.

Overall, the distribution parameters are not very sensitive to the variations in the behavioral parameters: variations in the behavioral parameters by 10% entail variations in the distribution parameters of less than 8% for most cases. The eviction price is fairly sensitive to the parameter $γ^-$: a 10% variation in this parameter causes a change in price of up to 13.5%. This is also true for the parameter $α$. Finally, *post-legalization* cannabis consumption is not very responsive to small variations in the behavioral parameters (by less than 10%) as it changes by less than 2% in most cases.

## H.3 Sensitivity analysis to policy instruments

This section studies the sensitivity of the eviction price and of the *post-legalization* demand to parameters that can be influenced by policies. Several instruments are considered: reinforcing sanctions may increase the marginal cost of operations for illegal suppliers, $c$, the probability of arrest, $q$, or fines to illegal consumers, $F$. Moreover, investing in the quality of the legal cannabis, including the purchasing experience, taste of the product, certification of potency and of the healthiness of the production process, and information/education cam-
<table><caption>Table A3: Sensitivity of eviction price and demand to behavioral parameters for $\epsilon = -0.5$</caption><thead><tr><th>parameter</th><th>variation</th><th>μ̂</th><th>σ̂</th><th>p̄<sup>L</sup></th><th>ΔD(p̄<sup>L</sup>)</th></tr></thead><tbody><tr><td rowspan="4">γ<sup>+</sup> = 0.61</td><td>+10%</td><td>0.1%</td><td>-0.22%</td><td>-0.21%</td><td>-0.3%</td></tr><tr><td>+5%</td><td>0.06%</td><td>-0.12%</td><td>-0.12%</td><td>-0.16%</td></tr><tr><td>-5%</td><td>-0.06%</td><td>0.15%</td><td>0.16%</td><td>0.2%</td></tr><tr><td>-10%</td><td>-0.14%</td><td>0.33%</td><td>0.36%</td><td>0.46%</td></tr><tr><td rowspan="4">γ<sup>-</sup> = 0.69</td><td>+10%</td><td>0.86%</td><td>-1.91%</td><td>-7.97%</td><td>-2.63%</td></tr><tr><td>+5%</td><td>0.47%</td><td>-1.03%</td><td>-4.51%</td><td>-1.41%</td></tr><tr><td>-5%</td><td>-0.53%</td><td>1.19%</td><td>5.86%</td><td>1.61%</td></tr><tr><td>-10%</td><td>-1.15%</td><td>2.57%</td><td>13.45%</td><td>3.44%</td></tr><tr><td rowspan="4">α = 0.88</td><td>+10%</td><td>-0.8%</td><td>1.8%</td><td>9.66%</td><td>2.43%</td></tr><tr><td>+5%</td><td>-0.39%</td><td>0.89%</td><td>4.57%</td><td>1.21%</td></tr><tr><td>-5%</td><td>0.39%</td><td>-0.87%</td><td>-4.04%</td><td>-1.18%</td></tr><tr><td>-10%</td><td>0.77%</td><td>-1.7%</td><td>-7.54%</td><td>-2.33%</td></tr><tr><td rowspan="4">λ = 2.25</td><td>+10%</td><td>-0.33%</td><td>0.76%</td><td>2.2%</td><td>1.03%</td></tr><tr><td>+5%</td><td>-0.16%</td><td>0.38%</td><td>1.1%</td><td>0.52%</td></tr><tr><td>-5%</td><td>0.18%</td><td>-0.38%</td><td>-1.09%</td><td>-0.51%</td></tr><tr><td>-10%</td><td>0.34%</td><td>-0.75%</td><td>-2.17%</td><td>-1.03%</td></tr></tbody></table>

Benchmark values in column 1 are $\hat{\mu} = -690.4$, $\hat{\sigma} = 1065.8$, $p̄^L = 97.79$ and $\Delta D(p̄^L) = 53.18\%$.

<table><caption>Table A4: Sensitivity of eviction price and demand to behavioral parameters for $\epsilon = -0.6$</caption><thead><tr><th>parameter</th><th>variation</th><th>μ̂</th><th>σ̂</th><th>p̄<sup>L</sup></th><th>ΔD(p̄<sup>L</sup>)</th></tr></thead><tbody><tr><td rowspan="4">γ<sup>+</sup> = 0.61</td><td>+10%</td><td>0.22%</td><td>-0.21%</td><td>-0.21%</td><td>-0.34%</td></tr><tr><td>+5%</td><td>0.13%</td><td>-0.12%</td><td>-0.12%</td><td>-0.19%</td></tr><tr><td>-5%</td><td>-0.14%</td><td>0.15%</td><td>0.16%</td><td>0.24%</td></tr><tr><td>-10%</td><td>-0.32%</td><td>0.34%</td><td>0.36%</td><td>0.53%</td></tr><tr><td rowspan="4">γ<sup>-</sup> = 0.69</td><td>+10%</td><td>1.87%</td><td>-1.91%</td><td>-7.97%</td><td>-3.05%</td></tr><tr><td>+5%</td><td>1.01%</td><td>-1.03%</td><td>-4.51%</td><td>-1.63%</td></tr><tr><td>-5%</td><td>-1.16%</td><td>1.2%</td><td>5.86%</td><td>1.87%</td></tr><tr><td>-10%</td><td>-2.5%</td><td>2.57%</td><td>13.45%</td><td>3.99%</td></tr><tr><td rowspan="4">α = 0.88</td><td>+10%</td><td>-1.75%</td><td>1.81%</td><td>9.66%</td><td>2.82%</td></tr><tr><td>+5%</td><td>-0.86%</td><td>0.9%</td><td>4.57%</td><td>1.4%</td></tr><tr><td>-5%</td><td>0.85%</td><td>-0.86%</td><td>-4.04%</td><td>-1.37%</td></tr><tr><td>-10%</td><td>1.66%</td><td>-1.69%</td><td>-7.54%</td><td>-2.7%</td></tr><tr><td rowspan="4">λ = 2.25</td><td>+10%</td><td>-0.73%</td><td>0.77%</td><td>2.2%</td><td>1.2%</td></tr><tr><td>+5%</td><td>-0.36%</td><td>0.38%</td><td>1.1%</td><td>0.6%</td></tr><tr><td>-5%</td><td>0.38%</td><td>-0.37%</td><td>-1.09%</td><td>-0.6%</td></tr><tr><td>-10%</td><td>0.74%</td><td>-0.75%</td><td>-2.17%</td><td>-1.19%</td></tr></tbody></table>

Benchmark values in column 1 $\hat{\mu} = -506.3$, $\hat{\sigma} = 888.1$, $p̄^L = 97.79$ and $\Delta D(p̄^L) = 65.45\%$.
<table><caption>Table A3: Sensitivity of eviction price and demand to behavioral parameters for $\epsilon = -0.5$</caption><thead><tr><th>parameter</th><th>variation</th><th>μ̂</th><th>σ̂</th><th>p̄<sup>L</sup></th><th>ΔD(p̄<sup>L</sup>)</th></tr></thead><tbody><tr><td rowspan="4">γ<sup>+</sup> = 0.61</td><td>+10%</td><td>0.1%</td><td>-0.22%</td><td>-0.21%</td><td>-0.3%</td></tr><tr><td>+5%</td><td>0.06%</td><td>-0.12%</td><td>-0.12%</td><td>-0.16%</td></tr><tr><td>-5%</td><td>-0.06%</td><td>0.15%</td><td>0.16%</td><td>0.2%</td></tr><tr><td>-10%</td><td>-0.14%</td><td>0.33%</td><td>0.36%</td><td>0.46%</td></tr><tr><td rowspan="4">γ<sup>-</sup> = 0.69</td><td>+10%</td><td>0.86%</td><td>-1.91%</td><td>-7.97%</td><td>-2.63%</td></tr><tr><td>+5%</td><td>0.47%</td><td>-1.03%</td><td>-4.51%</td><td>-1.41%</td></tr><tr><td>-5%</td><td>-0.53%</td><td>1.19%</td><td>5.86%</td><td>1.61%</td></tr><tr><td>-10%</td><td>-1.15%</td><td>2.57%</td><td>13.45%</td><td>3.44%</td></tr><tr><td rowspan="4">α = 0.88</td><td>+10%</td><td>-0.8%</td><td>1.8%</td><td>9.66%</td><td>2.43%</td></tr><tr><td>+5%</td><td>-0.39%</td><td>0.89%</td><td>4.57%</td><td>1.21%</td></tr><tr><td>-5%</td><td>0.39%</td><td>-0.87%</td><td>-4.04%</td><td>-1.18%</td></tr><tr><td>-10%</td><td>0.77%</td><td>-1.7%</td><td>-7.54%</td><td>-2.33%</td></tr><tr><td rowspan="4">λ = 2.25</td><td>+10%</td><td>-0.33%</td><td>0.76%</td><td>2.2%</td><td>1.03%</td></tr><tr><td>+5%</td><td>-0.16%</td><td>0.38%</td><td>1.1%</td><td>0.52%</td></tr><tr><td>-5%</td><td>0.18%</td><td>-0.38%</td><td>-1.09%</td><td>-0.51%</td></tr><tr><td>-10%</td><td>0.34%</td><td>-0.75%</td><td>-2.17%</td><td>-1.03%</td></tr></tbody></table>

Benchmark values in column 1 are $\hat{\mu} = -690.4$, $\hat{\sigma} = 1065.8$, $p̄^L = 97.79$ and $\Delta D(p̄^L) = 53.18\%$.

<table><caption>Table A4: Sensitivity of eviction price and demand to behavioral parameters for $\epsilon = -0.6$</caption><thead><tr><th>parameter</th><th>variation</th><th>μ̂</th><th>σ̂</th><th>p̄<sup>L</sup></th><th>ΔD(p̄<sup>L</sup>)</th></tr></thead><tbody><tr><td rowspan="4">γ<sup>+</sup> = 0.61</td><td>+10%</td><td>0.22%</td><td>-0.21%</td><td>-0.21%</td><td>-0.34%</td></tr><tr><td>+5%</td><td>0.13%</td><td>-0.12%</td><td>-0.12%</td><td>-0.19%</td></tr><tr><td>-5%</td><td>-0.14%</td><td>0.15%</td><td>0.16%</td><td>0.24%</td></tr><tr><td>-10%</td><td>-0.32%</td><td>0.34%</td><td>0.36%</td><td>0.53%</td></tr><tr><td rowspan="4">γ<sup>-</sup> = 0.69</td><td>+10%</td><td>1.87%</td><td>-1.91%</td><td>-7.97%</td><td>-3.05%</td></tr><tr><td>+5%</td><td>1.01%</td><td>-1.03%</td><td>-4.51%</td><td>-1.63%</td></tr><tr><td>-5%</td><td>-1.16%</td><td>1.2%</td><td>5.86%</td><td>1.87%</td></tr><tr><td>-10%</td><td>-2.5%</td><td>2.57%</td><td>13.45%</td><td>3.99%</td></tr><tr><td rowspan="4">α = 0.88</td><td>+10%</td><td>-1.75%</td><td>1.81%</td><td>9.66%</td><td>2.82%</td></tr><tr><td>+5%</td><td>-0.86%</td><td>0.9%</td><td>4.57%</td><td>1.4%</td></tr><tr><td>-5%</td><td>0.85%</td><td>-0.86%</td><td>-4.04%</td><td>-1.37%</td></tr><tr><td>-10%</td><td>1.66%</td><td>-1.69%</td><td>-7.54%</td><td>-2.7%</td></tr><tr><td rowspan="4">λ = 2.25</td><td>+10%</td><td>-0.73%</td><td>0.77%</td><td>2.2%</td><td>1.2%</td></tr><tr><td>+5%</td><td>-0.36%</td><td>0.38%</td><td>1.1%</td><td>0.6%</td></tr><tr><td>-5%</td><td>0.38%</td><td>-0.37%</td><td>-1.09%</td><td>-0.6%</td></tr><tr><td>-10%</td><td>0.74%</td><td>-0.75%</td><td>-2.17%</td><td>-1.19%</td></tr></tbody></table>

Benchmark values in column 1 $\hat{\mu} = -506.3$, $\hat{\sigma} = 888.1$, $p̄^L = 97.79$ and $\Delta D(p̄^L) = 65.45\%$.
<table><caption>Table A5: Sensitivity of eviction price and demand to behavioral parameters for $\epsilon = -0.7$</caption><thead><tr><th>parameter</th><th>variation</th><th>μ̂</th><th>σ̂</th><th>p̄<sup>L</sup></th><th>ΔD(p̄<sup>L</sup>)</th></tr></thead><tbody><tr><td rowspan="4">γ<sup>+</sup> = 0.61</td><td>+10%</td><td>0.37%</td><td>-0.22%</td><td>-0.21%</td><td>-0.39%</td></tr><tr><td>+5%</td><td>0.21%</td><td>-0.12%</td><td>-0.12%</td><td>-0.21%</td></tr><tr><td>-5%</td><td>-0.24%</td><td>0.14%</td><td>0.16%</td><td>0.27%</td></tr><tr><td>-10%</td><td>-0.55%</td><td>0.33%</td><td>0.36%</td><td>0.6%</td></tr><tr><td rowspan="4">γ<sup>-</sup> = 0.69</td><td>+10%</td><td>3.2%</td><td>-1.92%</td><td>-7.97%</td><td>-3.43%</td></tr><tr><td>+5%</td><td>1.73%</td><td>-1.03%</td><td>-4.51%</td><td>-1.84%</td></tr><tr><td>-5%</td><td>-1.98%</td><td>1.19%</td><td>5.86%</td><td>2.11%</td></tr><tr><td>-10%</td><td>-4.27%</td><td>2.56%</td><td>13.45%</td><td>4.49%</td></tr><tr><td rowspan="4">α = 0.88</td><td>+10%</td><td>-3.0%</td><td>1.8%</td><td>9.66%</td><td>3.17%</td></tr><tr><td>+5%</td><td>-1.48%</td><td>0.89%</td><td>4.57%</td><td>1.58%</td></tr><tr><td>-5%</td><td>1.45%</td><td>-0.87%</td><td>-4.04%</td><td>-1.54%</td></tr><tr><td>-10%</td><td>2.84%</td><td>-1.7%</td><td>-7.54%</td><td>-3.03%</td></tr><tr><td rowspan="4">λ = 2.25</td><td>+10%</td><td>-1.26%</td><td>0.76%</td><td>2.2%</td><td>1.35%</td></tr><tr><td>+5%</td><td>-0.62%</td><td>0.37%</td><td>1.1%</td><td>0.67%</td></tr><tr><td>-5%</td><td>0.64%</td><td>-0.38%</td><td>-1.09%</td><td>-0.67%</td></tr><tr><td>-10%</td><td>1.27%</td><td>-0.76%</td><td>-2.17%</td><td>-1.34%</td></tr></tbody></table>

Benchmark values in column 1 $\hat{\mu} = -374.8$, $\hat{\sigma} = 761.3$, $\underline{p}^L = 97.79$ and $\Delta D(\underline{p}^L) = 78.23\%$.

<table><caption>Table A6: Sensitivity of eviction price and demand to the behavioral parameters for $\epsilon = -0.8$</caption><thead><tr><th>parameter</th><th>variation</th><th>μ̂</th><th>σ̂</th><th>p̄<sup>L</sup></th><th>ΔD(p̄<sup>L</sup>)</th></tr></thead><tbody><tr><td rowspan="4">γ<sup>+</sup> = 0.61</td><td>+10%</td><td>0.58%</td><td>-0.22%</td><td>-0.21%</td><td>-0.42%</td></tr><tr><td>+5%</td><td>0.32%</td><td>-0.12%</td><td>-0.12%</td><td>-0.23%</td></tr><tr><td>-5%</td><td>-0.38%</td><td>0.15%</td><td>0.16%</td><td>0.29%</td></tr><tr><td>-10%</td><td>-0.88%</td><td>0.34%</td><td>0.36%</td><td>0.66%</td></tr><tr><td rowspan="4">γ<sup>-</sup> = 0.69</td><td>+10%</td><td>5.02%</td><td>-1.91%</td><td>-7.97%</td><td>-3.78%</td></tr><tr><td>+5%</td><td>2.71%</td><td>-1.03%</td><td>-4.51%</td><td>-2.02%</td></tr><tr><td>-5%</td><td>-3.12%</td><td>1.2%</td><td>5.86%</td><td>2.32%</td></tr><tr><td>-10%</td><td>-6.72%</td><td>2.57%</td><td>13.45%</td><td>4.95%</td></tr><tr><td rowspan="4">α = 0.88</td><td>+10%</td><td>-4.73%</td><td>1.81%</td><td>9.66%</td><td>3.5%</td></tr><tr><td>+5%</td><td>-2.33%</td><td>0.89%</td><td>4.57%</td><td>1.74%</td></tr><tr><td>-5%</td><td>2.27%</td><td>-0.86%</td><td>-4.04%</td><td>-1.7%</td></tr><tr><td>-10%</td><td>4.44%</td><td>-1.69%</td><td>-7.54%</td><td>-3.34%</td></tr><tr><td rowspan="4">λ = 2.25</td><td>+10%</td><td>-1.99%</td><td>0.76%</td><td>2.2%</td><td>1.48%</td></tr><tr><td>+5%</td><td>-0.99%</td><td>0.38%</td><td>1.1%</td><td>0.74%</td></tr><tr><td>-5%</td><td>1.0%</td><td>-0.38%</td><td>-1.09%</td><td>-0.74%</td></tr><tr><td>-10%</td><td>1.98%</td><td>-0.75%</td><td>-2.17%</td><td>-1.47%</td></tr></tbody></table>

Benchmark values in column 1 $\hat{\mu} = -276.2$, $\hat{\sigma} = 666.1$, $\underline{p}^L = 97.79$, $\Delta D(\underline{p}^L) = 91.49\%$.
<table><caption>Table A5: Sensitivity of eviction price and demand to behavioral parameters for $\epsilon = -0.7$</caption><thead><tr><th>parameter</th><th>variation</th><th>μ̂</th><th>σ̂</th><th>p̄<sup>L</sup></th><th>ΔD(p̄<sup>L</sup>)</th></tr></thead><tbody><tr><td rowspan="4">γ<sup>+</sup> = 0.61</td><td>+10%</td><td>0.37%</td><td>-0.22%</td><td>-0.21%</td><td>-0.39%</td></tr><tr><td>+5%</td><td>0.21%</td><td>-0.12%</td><td>-0.12%</td><td>-0.21%</td></tr><tr><td>-5%</td><td>-0.24%</td><td>0.14%</td><td>0.16%</td><td>0.27%</td></tr><tr><td>-10%</td><td>-0.55%</td><td>0.33%</td><td>0.36%</td><td>0.6%</td></tr><tr><td rowspan="4">γ<sup>-</sup> = 0.69</td><td>+10%</td><td>3.2%</td><td>-1.92%</td><td>-7.97%</td><td>-3.43%</td></tr><tr><td>+5%</td><td>1.73%</td><td>-1.03%</td><td>-4.51%</td><td>-1.84%</td></tr><tr><td>-5%</td><td>-1.98%</td><td>1.19%</td><td>5.86%</td><td>2.11%</td></tr><tr><td>-10%</td><td>-4.27%</td><td>2.56%</td><td>13.45%</td><td>4.49%</td></tr><tr><td rowspan="4">α = 0.88</td><td>+10%</td><td>-3.0%</td><td>1.8%</td><td>9.66%</td><td>3.17%</td></tr><tr><td>+5%</td><td>-1.48%</td><td>0.89%</td><td>4.57%</td><td>1.58%</td></tr><tr><td>-5%</td><td>1.45%</td><td>-0.87%</td><td>-4.04%</td><td>-1.54%</td></tr><tr><td>-10%</td><td>2.84%</td><td>-1.7%</td><td>-7.54%</td><td>-3.03%</td></tr><tr><td rowspan="4">λ = 2.25</td><td>+10%</td><td>-1.26%</td><td>0.76%</td><td>2.2%</td><td>1.35%</td></tr><tr><td>+5%</td><td>-0.62%</td><td>0.37%</td><td>1.1%</td><td>0.67%</td></tr><tr><td>-5%</td><td>0.64%</td><td>-0.38%</td><td>-1.09%</td><td>-0.67%</td></tr><tr><td>-10%</td><td>1.27%</td><td>-0.76%</td><td>-2.17%</td><td>-1.34%</td></tr></tbody></table>

Benchmark values in column 1 $\hat{\mu} = -374.8$, $\hat{\sigma} = 761.3$, $p̄^L = 97.79$ and $\Delta D(p̄^L) = 78.23\%$.

<table><caption>Table A6: Sensitivity of eviction price and demand to the behavioral parameters for $\epsilon = -0.8$</caption><thead><tr><th>parameter</th><th>variation</th><th>μ̂</th><th>σ̂</th><th>p̄<sup>L</sup></th><th>ΔD(p̄<sup>L</sup>)</th></tr></thead><tbody><tr><td rowspan="4">γ<sup>+</sup> = 0.61</td><td>+10%</td><td>0.58%</td><td>-0.22%</td><td>-0.21%</td><td>-0.42%</td></tr><tr><td>+5%</td><td>0.32%</td><td>-0.12%</td><td>-0.12%</td><td>-0.23%</td></tr><tr><td>-5%</td><td>-0.38%</td><td>0.15%</td><td>0.16%</td><td>0.29%</td></tr><tr><td>-10%</td><td>-0.88%</td><td>0.34%</td><td>0.36%</td><td>0.66%</td></tr><tr><td rowspan="4">γ<sup>-</sup> = 0.69</td><td>+10%</td><td>5.02%</td><td>-1.91%</td><td>-7.97%</td><td>-3.78%</td></tr><tr><td>+5%</td><td>2.71%</td><td>-1.03%</td><td>-4.51%</td><td>-2.02%</td></tr><tr><td>-5%</td><td>-3.12%</td><td>1.2%</td><td>5.86%</td><td>2.32%</td></tr><tr><td>-10%</td><td>-6.72%</td><td>2.57%</td><td>13.45%</td><td>4.95%</td></tr><tr><td rowspan="4">α = 0.88</td><td>+10%</td><td>-4.73%</td><td>1.81%</td><td>9.66%</td><td>3.5%</td></tr><tr><td>+5%</td><td>-2.33%</td><td>0.89%</td><td>4.57%</td><td>1.74%</td></tr><tr><td>-5%</td><td>2.27%</td><td>-0.86%</td><td>-4.04%</td><td>-1.7%</td></tr><tr><td>-10%</td><td>4.44%</td><td>-1.69%</td><td>-7.54%</td><td>-3.34%</td></tr><tr><td rowspan="4">λ = 2.25</td><td>+10%</td><td>-1.99%</td><td>0.76%</td><td>2.2%</td><td>1.48%</td></tr><tr><td>+5%</td><td>-0.99%</td><td>0.38%</td><td>1.1%</td><td>0.74%</td></tr><tr><td>-5%</td><td>1.0%</td><td>-0.38%</td><td>-1.09%</td><td>-0.74%</td></tr><tr><td>-10%</td><td>1.98%</td><td>-0.75%</td><td>-2.17%</td><td>-1.47%</td></tr></tbody></table>

Benchmark values in column 1 $\hat{\mu} = -276.2$, $\hat{\sigma} = 666.1$, $p̄^L = 97.79$, $\Delta D(p̄^L) = 91.49\%$.
paigns about the danger of consuming illegal cannabis will increase the relative valuation of consumption of legal cannabis, *b*. This aspect is generally overlooked by proponents of cannabis legalization. Yet our simulations show that it is an important instrument of any successful reform.

The first row of table A7 presents the benchmark values of the policy parameters in columns 1 to 4, as well as the resulting eviction legal price $p^L$ around USD 98, and the resulting relative increase in the extensive margin of consumption *post-legalization* – which depends on the values of price elasticities of demand – in columns 5 to 8.

Rows 2 to 7 of table A7 present several scenarios regarding the marginal cost of operating on the black market. In the first scenario, the marginal cost for illegal production and distribution of cannabis drops to 15$ per ounce. This captures a situation in which controls are very lax and hence are not inflating the marginal cost of operation for illegal suppliers, which comes close to the estimates given by Caulkins (2010). We then present other cases where increasing and enforcing the sanctions against illegal producers and retailers raises the marginal cost of production on the black market up to 250$.

Another parameter whose evolution is hard to predict is $b$. Indeed, when retail sales for cannabis are legal, certified products appear, which is likely to increase $b$. Moreover, legalization decreases search costs, which also contributes to raising $b$. Meanwhile, being challenged by a newly legalized market, black market producers and retailers may decide to invest in better products and services. For instance, some consumers may not want to be seen coming in person to a dispensary, due to social stigma or professional constraints that strictly forbid them to consume cannabis (in the case of truck drivers for example), and may turn to a black market delivery service. This may reduce the relative value of legal cannabis. Starting from our benchmark value, $b = 1.58$, rows 8 to 12 consider alternative cases, for $b$ increasing to 3.00 or falling to 0.50.<fnref n="52" />

Rows 13 to 18 vary the probability of being caught on the black market, $q$. Once a legal market is established, it may become more costly to detect consumers of illegal cannabis than it was under strict prohibition, such that $q$ may decrease. On the other hand, it may be politically more feasible to be tough on consumers of illegal cannabis, such that $q$ may increase. Rows 19 to 23 allow for several values of fines, $F$. For similar reasons, it may or may not be easier to implement higher fines with legalization, which is captured by the range of values chosen for the sensitivity analysis. In particular, it might be politically easier to implement higher fines when a legal alternative exists.

**Response to the policy mix** To illustrate how governments may use a combination of policy instruments to regulate the market for cannabis *post-legalization*, table A8 exploits

<footnote n="52">⁵²Appendix H.4 discusses the case with $b < 1$.</footnote>
paigns about the danger of consuming illegal cannabis will increase the relative valuation of consumption of legal cannabis, b. This aspect is generally overlooked by proponents of cannabis legalization. Yet our simulations show that it is an important instrument of any successful reform.

The first row of table A7 presents the benchmark values of the policy parameters in columns 1 to 4, as well as the resulting eviction legal price $p^L$ around USD 98, and the resulting relative increase in the extensive margin of consumption *post-legalization* – which depends on the values of price elasticities of demand – in columns 5 to 8.

Rows 2 to 7 of table A7 present several scenarios regarding the marginal cost of operating on the black market. In the first scenario, the marginal cost for illegal production and distribution of cannabis drops to 15$ per ounce. This captures a situation in which controls are very lax and hence are not inflating the marginal cost of operation for illegal suppliers, which comes close to the estimates given by Caulkins (2010). We then present other cases where increasing and enforcing the sanctions against illegal producers and retailers raises the marginal cost of production on the black market up to 250$.

Another parameter whose evolution is hard to predict is $b$. Indeed, when retail sales for cannabis are legal, certified products appear, which is likely to increase $b$. Moreover, legalization decreases search costs, which also contributes to raising $b$. Meanwhile, being challenged by a newly legalized market, black market producers and retailers may decide to invest in better products and services. For instance, some consumers may not want to be seen coming in person to a dispensary, due to social stigma or professional constraints that strictly forbid them to consume cannabis (in the case of truck drivers for example), and may turn to a black market delivery service. This may reduce the relative value of legal cannabis. Starting from our benchmark value, $b = 1.58$, rows 8 to 12 consider alternative cases, for $b$ increasing to 3.00 or falling to 0.50.<fnref n="52" />

Rows 13 to 18 vary the probability of being caught on the black market, $q$. Once a legal market is established, it may become more costly to detect consumers of illegal cannabis than it was under strict prohibition, such that $q$ may decrease. On the other hand, it may be politically more feasible to be tough on consumers of illegal cannabis, such that $q$ may increase. Rows 19 to 23 allow for several values of fines, $F$. For similar reasons, it may or may not be easier to implement higher fines with legalization, which is captured by the range of values chosen for the sensitivity analysis. In particular, it might be politically easier to implement higher fines when a legal alternative exists.

**Response to the policy mix** To illustrate how governments may use a combination of policy instruments to regulate the market for cannabis *post-legalization*, table A8 exploits

<footnote n="52">⁵²Appendix H.4 discusses the case with $b < 1$.</footnote>
<table><caption>Table A7: Sensitivity of legalization price (in USD per ounce) and change in post-legalization demand (in percentage)</caption><thead><tr><th colspan="4">Policy parameters</th><th colspan="1">Eviction price</th><th colspan="4">Increase in demand</th></tr><tr><th>c</th><th>b</th><th>q</th><th>F</th><th>p<sup>L</sup></th><th>ε = -0.5</th><th>ε = -0.6</th><th>ε = -0.7</th><th>ε = -0.8</th></tr></thead><tbody><tr><td>50</td><td>1.58</td><td>0.1%</td><td>1000</td><td>97.79</td><td>53%</td><td>65%</td><td>78%</td><td>92%</td></tr><tr><td>15</td><td>1.58</td><td>0.1%</td><td>1000</td><td>41.86</td><td>64%</td><td>79%</td><td>95%</td><td>111%</td></tr><tr><td>25</td><td>1.58</td><td>0.1%</td><td>1000</td><td>57.84</td><td>61%</td><td>75%</td><td>90%</td><td>105%</td></tr><tr><td>75</td><td>1.58</td><td>0.1%</td><td>1000</td><td>137.74</td><td>46%</td><td>56%</td><td>67%</td><td>78%</td></tr><tr><td>100</td><td>1.58</td><td>0.1%</td><td>1000</td><td>177.68</td><td>38%</td><td>47%</td><td>56%</td><td>65%</td></tr><tr><td>150</td><td>1.58</td><td>0.1%</td><td>1000</td><td>257.58</td><td>25%</td><td>30%</td><td>35%</td><td>41%</td></tr><tr><td>250</td><td>1.58</td><td>0.1%</td><td>1000</td><td>417.37</td><td>0%</td><td>-1%</td><td>-1%</td><td>-1%</td></tr><tr><td>50</td><td>0.50</td><td>0.1%</td><td>1000</td><td>30.95</td><td>66%</td><td>82%</td><td>98%</td><td>115%</td></tr><tr><td>50</td><td>0.75</td><td>0.1%</td><td>1000</td><td>46.42</td><td>63%</td><td>78%</td><td>93%</td><td>109%</td></tr><tr><td>50</td><td>1.00</td><td>0.1%</td><td>1000</td><td>61.89</td><td>60%</td><td>74%</td><td>89%</td><td>104%</td></tr><tr><td>50</td><td>2.00</td><td>0.1%</td><td>1000</td><td>123.78</td><td>48%</td><td>59%</td><td>71%</td><td>83%</td></tr><tr><td>50</td><td>3.00</td><td>0.1%</td><td>1000</td><td>185.68</td><td>37%</td><td>45%</td><td>54%</td><td>63%</td></tr><tr><td>50</td><td>1.58</td><td>0.0%</td><td>-</td><td>79.0</td><td>57%</td><td>70%</td><td>84%</td><td>98%</td></tr><tr><td>50</td><td>1.58</td><td>0.01%</td><td>1000</td><td>82.06</td><td>56%</td><td>69%</td><td>83%</td><td>97%</td></tr><tr><td>50</td><td>1.58</td><td>0.2%</td><td>1000</td><td>111.56</td><td>51%</td><td>62%</td><td>74%</td><td>87%</td></tr><tr><td>50</td><td>1.58</td><td>0.5%</td><td>1000</td><td>146.68</td><td>44%</td><td>54%</td><td>64%</td><td>75%</td></tr><tr><td>50</td><td>1.58</td><td>1.0%</td><td>1000</td><td>197.33</td><td>35%</td><td>43%</td><td>51%</td><td>59%</td></tr><tr><td>50</td><td>1.58</td><td>2.0%</td><td>1000</td><td>287.37</td><td>20%</td><td>24%</td><td>28%</td><td>33%</td></tr><tr><td>50</td><td>1.58</td><td>0.1%</td><td>500</td><td>88.84</td><td>55%</td><td>68%</td><td>81%</td><td>95%</td></tr><tr><td>50</td><td>1.58</td><td>0.1%</td><td>1500</td><td>106.74</td><td>52%</td><td>63%</td><td>76%</td><td>88%</td></tr><tr><td>50</td><td>1.58</td><td>0.1%</td><td>2000</td><td>115.68</td><td>50%</td><td>61%</td><td>73%</td><td>85%</td></tr><tr><td>50</td><td>1.58</td><td>0.1%</td><td>3000</td><td>133.58</td><td>46%</td><td>57%</td><td>68%</td><td>79%</td></tr><tr><td>50</td><td>1.58</td><td>0.1%</td><td>5000</td><td>169.37</td><td>40%</td><td>49%</td><td>58%</td><td>68%</td></tr></tbody></table>

Notes: Behavioral parameters are set at $\lambda = 2.25$, $\alpha = 0.88$, $\gamma^+ = 0.61$, and $\gamma^- = 0.69$ as estimated by Tversky and Kahneman (1992). Variation in demand relies on the baseline estimates for the parameters of the distribution of $\theta$ corresponding to different price elasticities of demand, as described in table A2.
<table><caption>Table A7: Sensitivity of legalization price (in USD per ounce) and change in post-legalization demand (in percentage)</caption><thead><tr><th colspan="4">Policy parameters</th><th colspan="1">Eviction price</th><th colspan="4">Increase in demand</th></tr><tr><th>c</th><th>b</th><th>q</th><th>F</th><th>p<sup>L</sup></th><th>ε = -0.5</th><th>ε = -0.6</th><th>ε = -0.7</th><th>ε = -0.8</th></tr></thead><tbody><tr><td>50</td><td>1.58</td><td>0.1%</td><td>1000</td><td>97.79</td><td>53%</td><td>65%</td><td>78%</td><td>92%</td></tr><tr><td>15</td><td>1.58</td><td>0.1%</td><td>1000</td><td>41.86</td><td>64%</td><td>79%</td><td>95%</td><td>111%</td></tr><tr><td>25</td><td>1.58</td><td>0.1%</td><td>1000</td><td>57.84</td><td>61%</td><td>75%</td><td>90%</td><td>105%</td></tr><tr><td>75</td><td>1.58</td><td>0.1%</td><td>1000</td><td>137.74</td><td>46%</td><td>56%</td><td>67%</td><td>78%</td></tr><tr><td>100</td><td>1.58</td><td>0.1%</td><td>1000</td><td>177.68</td><td>38%</td><td>47%</td><td>56%</td><td>65%</td></tr><tr><td>150</td><td>1.58</td><td>0.1%</td><td>1000</td><td>257.58</td><td>25%</td><td>30%</td><td>35%</td><td>41%</td></tr><tr><td>250</td><td>1.58</td><td>0.1%</td><td>1000</td><td>417.37</td><td>0%</td><td>-1%</td><td>-1%</td><td>-1%</td></tr><tr><td>50</td><td>0.50</td><td>0.1%</td><td>1000</td><td>30.95</td><td>66%</td><td>82%</td><td>98%</td><td>115%</td></tr><tr><td>50</td><td>0.75</td><td>0.1%</td><td>1000</td><td>46.42</td><td>63%</td><td>78%</td><td>93%</td><td>109%</td></tr><tr><td>50</td><td>1.00</td><td>0.1%</td><td>1000</td><td>61.89</td><td>60%</td><td>74%</td><td>89%</td><td>104%</td></tr><tr><td>50</td><td>2.00</td><td>0.1%</td><td>1000</td><td>123.78</td><td>48%</td><td>59%</td><td>71%</td><td>83%</td></tr><tr><td>50</td><td>3.00</td><td>0.1%</td><td>1000</td><td>185.68</td><td>37%</td><td>45%</td><td>54%</td><td>63%</td></tr><tr><td>50</td><td>1.58</td><td>0.0%</td><td>-</td><td>79.0</td><td>57%</td><td>70%</td><td>84%</td><td>98%</td></tr><tr><td>50</td><td>1.58</td><td>0.01%</td><td>1000</td><td>82.06</td><td>56%</td><td>69%</td><td>83%</td><td>97%</td></tr><tr><td>50</td><td>1.58</td><td>0.2%</td><td>1000</td><td>111.56</td><td>51%</td><td>62%</td><td>74%</td><td>87%</td></tr><tr><td>50</td><td>1.58</td><td>0.5%</td><td>1000</td><td>146.68</td><td>44%</td><td>54%</td><td>64%</td><td>75%</td></tr><tr><td>50</td><td>1.58</td><td>1.0%</td><td>1000</td><td>197.33</td><td>35%</td><td>43%</td><td>51%</td><td>59%</td></tr><tr><td>50</td><td>1.58</td><td>2.0%</td><td>1000</td><td>287.37</td><td>20%</td><td>24%</td><td>28%</td><td>33%</td></tr><tr><td>50</td><td>1.58</td><td>0.1%</td><td>500</td><td>88.84</td><td>55%</td><td>68%</td><td>81%</td><td>95%</td></tr><tr><td>50</td><td>1.58</td><td>0.1%</td><td>1500</td><td>106.74</td><td>52%</td><td>63%</td><td>76%</td><td>88%</td></tr><tr><td>50</td><td>1.58</td><td>0.1%</td><td>2000</td><td>115.68</td><td>50%</td><td>61%</td><td>73%</td><td>85%</td></tr><tr><td>50</td><td>1.58</td><td>0.1%</td><td>3000</td><td>133.58</td><td>46%</td><td>57%</td><td>68%</td><td>79%</td></tr><tr><td>50</td><td>1.58</td><td>0.1%</td><td>5000</td><td>169.37</td><td>40%</td><td>49%</td><td>58%</td><td>68%</td></tr></tbody></table>

Notes: Behavioral parameters are set at $\lambda = 2.25$, $\alpha = 0.88$, $\gamma^+ = 0.61$, and $\gamma^- = 0.69$ as estimated by Tversky and Kahneman (1992). Variation in demand relies on the baseline estimates for the parameters of the distribution of $\theta$ corresponding to different price elasticities of demand, as described in table A2.
combined variations in several policy parameters.

The first row presents the current benchmark values for the different policy parameters, the recommended legal price $p^L$ and the *post-legalization* increase in the extensive margin of consumption.

Rows 2 to 5 present scenarios in which the government certifies the quality of legal cannabis, such that $b$ goes up to 2, and does not invest a lot in detecting illegal purchases, such that the probability of arrest $q$ is half the benchmark value, but doubles the fines for illegal purchase ($F=2000$). At the same time it may choose or not to enforce repression against illegal providers, the marginal cost $c$ varying from 15 – i.e. less than a third of the benchmark value – to 200 – i.e. four times the benchmark value. Simulations show that the government is able to contain consumption at the *pre-legalization* level when the marginal cost is four times the benchmark value ($c = 200$).

Rows 6 to 11 show that investing in quality differentiation (increasing $b$) is effective at reducing cannabis consumption. Even with lax enforcement of arrest of illegal users ($q = 0.05\%$), row 11 shows that limiting the consumption increase *post-legalization* can be achieved by investing in quality differentiation and certification of legal cannabis, such that $b = 4$.

Rows 12 to 16 show simulations of policies which increase repression on the demand side through various intensities of arrests $q$ and fine amounts $F$, while the other parameters are kept at benchmark values. While increasing the level of fines seems to be an effective way to limit *post-legalization* consumption, high fines may be neither cost-effective nor fair, especially to low income users. Similarly, increased enforcement of arrests combined with statistical discrimination may also result in an uneven burden on some populations.

The fourth part of the table (rows 17 to 25) presents results where the *post-legalization* consumption is contained around the *pre-legalization* level. They highlight that a government aiming at controlling cannabis consumption through legalization would have to invest in strict repression of either the supply or the demand side, as well as in product differentiation, certification and information campaigns. For instance, a legalization policy combined with significant investments in quality differentiation of legal cannabis ($b = 2$) and increased fines for illegal consumption up to USD 4000 would lead to the eviction price of USD 430 per ounce, decreasing cannabis consumption by 2.35% to 3.75%.

The last exercise illustrates an extreme case of no differentiation between legal and illegal products in a liberal state without repression on the demand and supply sides of the market, thus pricing legal cannabis at the marginal cost of production, which is the same on the illegal market. The absence of regulation results in large increases in *post-legalization* consumption, larger than 50% in most scenarios and more than 100% with large price elasticities of demand or low production costs.
combined variations in several policy parameters.

The first row presents the current benchmark values for the different policy parameters, the recommended legal price $p^L$ and the *post-legalization* increase in the extensive margin of consumption.

Rows 2 to 5 present scenarios in which the government certifies the quality of legal cannabis, such that $b$ goes up to 2, and does not invest a lot in detecting illegal purchases, such that the probability of arrest $q$ is half the benchmark value, but doubles the fines for illegal purchase ($F=2000$). At the same time it may choose or not to enforce repression against illegal providers, the marginal cost $c$ varying from 15 – i.e. less than a third of the benchmark value – to 200 – i.e. four times the benchmark value. Simulations show that the government is able to contain consumption at the *pre-legalization* level when the marginal cost is four times the benchmark value ($c = 200$).

Rows 6 to 11 show that investing in quality differentiation (increasing $b$) is effective at reducing cannabis consumption. Even with lax enforcement of arrest of illegal users ($q = 0.05\%$), row 11 shows that limiting the consumption increase *post-legalization* can be achieved by investing in quality differentiation and certification of legal cannabis, such that $b = 4$.

Rows 12 to 16 show simulations of policies which increase repression on the demand side through various intensities of arrests $q$ and fine amounts $F$, while the other parameters are kept at benchmark values. While increasing the level of fines seems to be an effective way to limit *post-legalization* consumption, high fines may be neither cost-effective nor fair, especially to low income users. Similarly, increased enforcement of arrests combined with statistical discrimination may also result in an uneven burden on some populations.

The fourth part of the table (rows 17 to 25) presents results where the *post-legalization* consumption is contained around the *pre-legalization* level. They highlight that a government aiming at controlling cannabis consumption through legalization would have to invest in strict repression of either the supply or the demand side, as well as in product differentiation, certification and information campaigns. For instance, a legalization policy combined with significant investments in quality differentiation of legal cannabis ($b = 2$) and increased fines for illegal consumption up to USD 4000 would lead to the eviction price of USD 430 per ounce, decreasing cannabis consumption by 2.35% to 3.75%.

The last exercise illustrates an extreme case of no differentiation between legal and illegal products in a liberal state without repression on the demand and supply sides of the market, thus pricing legal cannabis at the marginal cost of production, which is the same on the illegal market. The absence of regulation results in large increases in *post-legalization* consumption, larger than 50% in most scenarios and more than 100% with large price elasticities of demand or low production costs.
<table><caption>Table A8: Sensitivity analysis of eviction price and post-legalization demand</caption><thead><tr><th rowspan="2">c</th><th colspan="3">Policy parameters</th><th colspan="1">Eviction Price</th><th colspan="4">Increase in Demand</th></tr><tr><th>b</th><th>q</th><th>F</th><th>p<sup>L</sup></th><th>ε = -0.5</th><th>ε = -0.6</th><th>ε = -0.7</th><th>ε = -0.8</th></tr></thead><tbody><tr><td>50</td><td>1.58</td><td>0.1%</td><td>1000.0</td><td>97.79</td><td>53%</td><td>65%</td><td>78%</td><td>91%</td></tr><tr><td>15</td><td>2.00</td><td>0.05%</td><td>2000.0</td><td>56.39</td><td>61%</td><td>75%</td><td>90%</td><td>106%</td></tr><tr><td>25</td><td>2.00</td><td>0.05%</td><td>2000.0</td><td>76.52</td><td>57%</td><td>71%</td><td>84%</td><td>99%</td></tr><tr><td>100</td><td>2.00</td><td>0.05%</td><td>2000.0</td><td>227.5</td><td>30%</td><td>36%</td><td>43%</td><td>50%</td></tr><tr><td>200</td><td>2.00</td><td>0.05%</td><td>2000.0</td><td>428.81</td><td>-2%</td><td>-3%</td><td>-3%</td><td>-3%</td></tr><tr><td>50</td><td>1.00</td><td>0.05%</td><td>1000.0</td><td>56.88</td><td>61%</td><td>75%</td><td>90%</td><td>106%</td></tr><tr><td>50</td><td>1.25</td><td>0.05%</td><td>1000.0</td><td>71.09</td><td>58%</td><td>72%</td><td>86%</td><td>101%</td></tr><tr><td>50</td><td>1.58</td><td>0.05%</td><td>1000.0</td><td>89.86</td><td>55%</td><td>67%</td><td>81%</td><td>94%</td></tr><tr><td>50</td><td>2.00</td><td>0.05%</td><td>1000.0</td><td>113.75</td><td>50%</td><td>62%</td><td>74%</td><td>86%</td></tr><tr><td>50</td><td>3.00</td><td>0.05%</td><td>1000.0</td><td>170.63</td><td>40%</td><td>49%</td><td>58%</td><td>67%</td></tr><tr><td>50</td><td>4.00</td><td>0.05%</td><td>1000.0</td><td>227.5</td><td>30%</td><td>36%</td><td>43%</td><td>50%</td></tr><tr><td>50</td><td>1.58</td><td>0.05%</td><td>1000.0</td><td>89.86</td><td>55%</td><td>67%</td><td>81%</td><td>94%</td></tr><tr><td>50</td><td>1.58</td><td>0.1%</td><td>2000.0</td><td>115.68</td><td>50%</td><td>61%</td><td>73%</td><td>85%</td></tr><tr><td>50</td><td>1.58</td><td>0.05%</td><td>3000.0</td><td>110.55</td><td>51%</td><td>62%</td><td>75%</td><td>87%</td></tr><tr><td>50</td><td>1.58</td><td>0.2%</td><td>500.0</td><td>96.06</td><td>54%</td><td>66%</td><td>79%</td><td>92%</td></tr><tr><td>50</td><td>1.58</td><td>0.5%</td><td>5000.0</td><td>404.51</td><td>1%</td><td>2%</td><td>2%</td><td>2%</td></tr><tr><td>50</td><td>2.00</td><td>1.0%</td><td>2000.0</td><td>392.45</td><td>3%</td><td>4%</td><td>5%</td><td>5%</td></tr><tr><td>100</td><td>1.58</td><td>1.5%</td><td>1500.0</td><td>408.79</td><td>1%</td><td>1%</td><td>1%</td><td>1%</td></tr><tr><td>50</td><td>2.00</td><td>0.5%</td><td>4000.0</td><td>430.44</td><td>-2%</td><td>-3%</td><td>-3%</td><td>-4%</td></tr><tr><td>100</td><td>2.25</td><td>1.0%</td><td>1000.0</td><td>401.54</td><td>2%</td><td>2%</td><td>3%</td><td>3%</td></tr><tr><td>15</td><td>2.50</td><td>1.0%</td><td>2000.0</td><td>396.82</td><td>3%</td><td>3%</td><td>4%</td><td>4%</td></tr><tr><td>15</td><td>1.58</td><td>0.5%</td><td>6000.0</td><td>411.41</td><td>0%</td><td>0%</td><td>1%</td><td>1%</td></tr><tr><td>25</td><td>1.25</td><td>2.0%</td><td>2500.0</td><td>427.67</td><td>-2%</td><td>-2%</td><td>-3%</td><td>-3%</td></tr><tr><td>50</td><td>1.58</td><td>2.0%</td><td>1500.0</td><td>386.59</td><td>4%</td><td>5%</td><td>6%</td><td>7%</td></tr><tr><td>50</td><td>3.00</td><td>1.0%</td><td>1000.0</td><td>374.68</td><td>6%</td><td>7%</td><td>8%</td><td>9%</td></tr><tr><td>15</td><td>1.00</td><td>0%</td><td>-</td><td>15.0</td><td>69%</td><td>86%</td><td>103%</td><td>121%</td></tr><tr><td>25</td><td>1.00</td><td>0%</td><td>-</td><td>25.0</td><td>67%</td><td>83%</td><td>100%</td><td>117%</td></tr><tr><td>50</td><td>1.00</td><td>0%</td><td>-</td><td>50.0</td><td>62%</td><td>77%</td><td>92%</td><td>108%</td></tr><tr><td>75</td><td>1.00</td><td>0%</td><td>-</td><td>75.0</td><td>58%</td><td>71%</td><td>85%</td><td>99%</td></tr><tr><td>100</td><td>1.00</td><td>0%</td><td>-</td><td>100.0</td><td>53%</td><td>65%</td><td>78%</td><td>91%</td></tr><tr><td>125</td><td>1.00</td><td>0%</td><td>-</td><td>125.0</td><td>48%</td><td>59%</td><td>70%</td><td>82%</td></tr></tbody></table>

Notes: Behavioral parameters are set at values calibrated by Tversky and Kahneman (1992): $\lambda = 2.25$, $\alpha = 0.88$, $\gamma^+ = 0.61$, and $\gamma^- = 0.69$. Variation in demand relies on the baseline estimates for the parameters of the distribution of $\theta$ corresponding to different price elasticities of demand, as described in table A2.
<table><caption>Table A8: Sensitivity analysis of eviction price and post-legalization demand</caption><thead><tr><th rowspan="2">c</th><th colspan="3">Policy parameters</th><th colspan="1">Eviction Price</th><th colspan="4">Increase in Demand</th></tr><tr><th>b</th><th>q</th><th>F</th><th>p<sup>L</sup></th><th>ε = -0.5</th><th>ε = -0.6</th><th>ε = -0.7</th><th>ε = -0.8</th></tr></thead><tbody><tr><td>50</td><td>1.58</td><td>0.1%</td><td>1000.0</td><td>97.79</td><td>53%</td><td>65%</td><td>78%</td><td>91%</td></tr><tr><td>15</td><td>2.00</td><td>0.05%</td><td>2000.0</td><td>56.39</td><td>61%</td><td>75%</td><td>90%</td><td>106%</td></tr><tr><td>25</td><td>2.00</td><td>0.05%</td><td>2000.0</td><td>76.52</td><td>57%</td><td>71%</td><td>84%</td><td>99%</td></tr><tr><td>100</td><td>2.00</td><td>0.05%</td><td>2000.0</td><td>227.5</td><td>30%</td><td>36%</td><td>43%</td><td>50%</td></tr><tr><td>200</td><td>2.00</td><td>0.05%</td><td>2000.0</td><td>428.81</td><td>-2%</td><td>-3%</td><td>-3%</td><td>-3%</td></tr><tr><td>50</td><td>1.00</td><td>0.05%</td><td>1000.0</td><td>56.88</td><td>61%</td><td>75%</td><td>90%</td><td>106%</td></tr><tr><td>50</td><td>1.25</td><td>0.05%</td><td>1000.0</td><td>71.09</td><td>58%</td><td>72%</td><td>86%</td><td>101%</td></tr><tr><td>50</td><td>1.58</td><td>0.05%</td><td>1000.0</td><td>89.86</td><td>55%</td><td>67%</td><td>81%</td><td>94%</td></tr><tr><td>50</td><td>2.00</td><td>0.05%</td><td>1000.0</td><td>113.75</td><td>50%</td><td>62%</td><td>74%</td><td>86%</td></tr><tr><td>50</td><td>3.00</td><td>0.05%</td><td>1000.0</td><td>170.63</td><td>40%</td><td>49%</td><td>58%</td><td>67%</td></tr><tr><td>50</td><td>4.00</td><td>0.05%</td><td>1000.0</td><td>227.5</td><td>30%</td><td>36%</td><td>43%</td><td>50%</td></tr><tr><td>50</td><td>1.58</td><td>0.05%</td><td>1000.0</td><td>89.86</td><td>55%</td><td>67%</td><td>81%</td><td>94%</td></tr><tr><td>50</td><td>1.58</td><td>0.1%</td><td>2000.0</td><td>115.68</td><td>50%</td><td>61%</td><td>73%</td><td>85%</td></tr><tr><td>50</td><td>1.58</td><td>0.05%</td><td>3000.0</td><td>110.55</td><td>51%</td><td>62%</td><td>75%</td><td>87%</td></tr><tr><td>50</td><td>1.58</td><td>0.2%</td><td>500.0</td><td>96.06</td><td>54%</td><td>66%</td><td>79%</td><td>92%</td></tr><tr><td>50</td><td>1.58</td><td>0.5%</td><td>5000.0</td><td>404.51</td><td>1%</td><td>2%</td><td>2%</td><td>2%</td></tr><tr><td>50</td><td>2.00</td><td>1.0%</td><td>2000.0</td><td>392.45</td><td>3%</td><td>4%</td><td>5%</td><td>5%</td></tr><tr><td>100</td><td>1.58</td><td>1.5%</td><td>1500.0</td><td>408.79</td><td>1%</td><td>1%</td><td>1%</td><td>1%</td></tr><tr><td>50</td><td>2.00</td><td>0.5%</td><td>4000.0</td><td>430.44</td><td>-2%</td><td>-3%</td><td>-3%</td><td>-4%</td></tr><tr><td>100</td><td>2.25</td><td>1.0%</td><td>1000.0</td><td>401.54</td><td>2%</td><td>2%</td><td>3%</td><td>3%</td></tr><tr><td>15</td><td>2.50</td><td>1.0%</td><td>2000.0</td><td>396.82</td><td>3%</td><td>3%</td><td>4%</td><td>4%</td></tr><tr><td>15</td><td>1.58</td><td>0.5%</td><td>6000.0</td><td>411.41</td><td>0%</td><td>0%</td><td>1%</td><td>1%</td></tr><tr><td>25</td><td>1.25</td><td>2.0%</td><td>2500.0</td><td>427.67</td><td>-2%</td><td>-2%</td><td>-3%</td><td>-3%</td></tr><tr><td>50</td><td>1.58</td><td>2.0%</td><td>1500.0</td><td>386.59</td><td>4%</td><td>5%</td><td>6%</td><td>7%</td></tr><tr><td>50</td><td>3.00</td><td>1.0%</td><td>1000.0</td><td>374.68</td><td>6%</td><td>7%</td><td>8%</td><td>9%</td></tr><tr><td>15</td><td>1.00</td><td>0%</td><td>-</td><td>15.0</td><td>69%</td><td>86%</td><td>103%</td><td>121%</td></tr><tr><td>25</td><td>1.00</td><td>0%</td><td>-</td><td>25.0</td><td>67%</td><td>83%</td><td>100%</td><td>117%</td></tr><tr><td>50</td><td>1.00</td><td>0%</td><td>-</td><td>50.0</td><td>62%</td><td>77%</td><td>92%</td><td>108%</td></tr><tr><td>75</td><td>1.00</td><td>0%</td><td>-</td><td>75.0</td><td>58%</td><td>71%</td><td>85%</td><td>99%</td></tr><tr><td>100</td><td>1.00</td><td>0%</td><td>-</td><td>100.0</td><td>53%</td><td>65%</td><td>78%</td><td>91%</td></tr><tr><td>125</td><td>1.00</td><td>0%</td><td>-</td><td>125.0</td><td>48%</td><td>59%</td><td>70%</td><td>82%</td></tr></tbody></table>

Notes: Behavioral parameters are set at values calibrated by Tversky and Kahneman (1992): $\lambda = 2.25$, $\alpha = 0.88$, $\gamma^+ = 0.61$, and $\gamma^- = 0.69$. Variation in demand relies on the baseline estimates for the parameters of the distribution of $\theta$ corresponding to different price elasticities of demand, as described in table A2.
## H.4 On the existence of $\theta^L$ when $b < 1$

In the theory, for the sake of simplicity, we prove the existence and uniqueness of $\theta^L$ under the sufficient condition $b \ge 1$. However, this condition is not necessary.

Take the weighting and value functions calibrated in Tversky and Kahneman (1992), as well as $v = 1$. In this case,

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

while

$$ \theta^L = \left[ \left( \lambda \frac{w^-(q)}{w^+(1-q)} \right)^{\frac{1}{\alpha}} b + b - 1 \right]^{-1} \left[ \left( \lambda \frac{w^-(q)}{w^+(1-q)} \right)^{\frac{1}{\alpha}} (p^L - p - F) + p^L - p \right]; $$

which does not require that $b \ge 1$. For instance, when $c = 50$, $b = 0.5$, $q = 0.1\%$ and $F = 1000$, the legal price threshold $\underline{p}^L$ is around 31$ and $\theta^L(c, \underline{p}^L)$ exists and is unique – it is approximately equal to 61.89.

# I Maximizing tax revenues: a numerical application

This section provides detail on the tax policy application discussed in section 5. It also presents the results for the other values of the price demand elasticity, as well as other examples, where there is very lax enforcement on the demand side of the market, leading to a probability of arrest close to zero, $q = 0$.

The methodology of this numerical exercise relies on the calibration results of table A2 and follows the same principle as in section 6 and appendix H. We use an iterative solver on the system of equations (15) and (10) with $p^L = (1 + \tau)c^L$.

Table A9 explores different scenarios in terms of enforcement and quality. The first column presents the *post-legalization* concentration on the illegal market. Using the Cournot optimality condition with the benchmark black market price of USD 97.79 computed in appendix H and marginal costs valued at USD 320 and USD 50 respectively, yields a concentration on the black market under prohibition of between 0.42 and 0.68, when the price demand elasticity varies between 0.5 and 0.8. We therefore chose 0.55 as a benchmark value for this parameter. Although the concentration on the black market is not a policy parameter *per se*, the legalization may generate changes in the concentration on the black market, which is why we study scenarios where this parameter varies from 0.10 to 1.00.

Columns 2 to 5 describe the values of the other policy parameters, whose notations are unchanged. Columns 6 and 7 provide the equilibrium prices on the black market and on
## H.4 On the existence of $\theta^L$ when $b < 1$

In the theory, for the sake of simplicity, we prove the existence and uniqueness of $\theta^L$ under the sufficient condition $b \ge 1$. However, this condition is not necessary.

Take the weighting and value functions calibrated in Tversky and Kahneman (1992), as well as $v = 1$. In this case,

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

while

$$ \theta^L = \left[ \left( \lambda \frac{w^-(q)}{w^+(1-q)} \right)^{\frac{1}{\alpha}} b + b - 1 \right]^{-1} \left[ \left( \lambda \frac{w^-(q)}{w^+(1-q)} \right)^{\frac{1}{\alpha}} (p^L - p - F) + p^L - p \right]; $$

which does not require that $b \ge 1$. For instance, when $c = 50$, $b = 0.5$, $q = 0.1\%$ and $F = 1000$, the legal price threshold $\underline{p}^L$ is around 31$ and $\theta^L(c, \underline{p}^L)$ exists and is unique – it is approximately equal to 61.89.

# I Maximizing tax revenues: a numerical application

This section provides detail on the tax policy application discussed in section 5. It also presents the results for the other values of the price demand elasticity, as well as other examples, where there is very lax enforcement on the demand side of the market, leading to a probability of arrest close to zero, $q = 0$.

The methodology of this numerical exercise relies on the calibration results of table A2 and follows the same principle as in section 6 and appendix H. We use an iterative solver on the system of equations (15) and (10) with $p^L = (1 + \tau)c^L$.

Table A9 explores different scenarios in terms of enforcement and quality. The first column presents the *post-legalization* concentration on the illegal market. Using the Cournot optimality condition with the benchmark black market price of USD 97.79 computed in appendix H and marginal costs valued at USD 320 and USD 50 respectively, yields a concentration on the black market under prohibition of between 0.42 and 0.68, when the price demand elasticity varies between 0.5 and 0.8. We therefore chose 0.55 as a benchmark value for this parameter. Although the concentration on the black market is not a policy parameter *per se*, the legalization may generate changes in the concentration on the black market, which is why we study scenarios where this parameter varies from 0.10 to 1.00.

Columns 2 to 5 describe the values of the other policy parameters, whose notations are unchanged. Columns 6 and 7 provide the equilibrium prices on the black market and on
the legal market, while columns 8 and 9 give the overall increase in demand $\Delta D(p, p^L)$, as well as the share of the black market in the total demand, $\%D^I$. Column 10 describes the tax revenue $R$ in USD per capita and per annum derived from state cannabis sales for the specified price and demand on the legal market. The last three columns provide the eviction price, as well as the corresponding increase in demand and tax revenue in USD per capita and per annum.

We present, in tables A10 to A12, the results of the numerical exercise from section 5 for higher values of the demand price elasticity (-0.5, -0.6 and -0.7). As expected, the more inelastic the demand, the higher the equilibrium prices and the government revenue. Again we find that the price maximizing tax revenue is generally well above the eviction price (except when the quality is the same on both markets) and the corresponding extensive margins of consumption are of the same magnitude.

## Results with $q = 0$

We detail in tables A13 to A16 scenarios where consumers going to the illegal market are not arrested. Since the case where $b = 1$ and $q = 0$ yields perfect competition between the legal and the illegal markets, we prefer to present a case where there is very little quality differentiation ($b = 1.01$), rather than no differentiation. When there are no arrests on the demand side, individuals are all the more sensitive to quality. For a government maximizing tax revenue, quality has a large influence on the optimal price: when the quality differential is 1.01, the equilibrium price on the legal market, $p^L$, is between USD 54 and 57 per ounce, depending on the elasticity; when $b = 1.80$, this price rises up to USD 387 to 549 per ounce.
the legal market, while columns 8 and 9 give the overall increase in demand $\Delta D(p, p^L)$, as well as the share of the black market in the total demand, $\%D^I$. Column 10 describes the tax revenue $R$ in USD per capita and per annum derived from state cannabis sales for the specified price and demand on the legal market. The last three columns provide the eviction price, as well as the corresponding increase in demand and tax revenue in USD per capita and per annum.

We present, in tables A10 to A12, the results of the numerical exercise from section 5 for higher values of the demand price elasticity (-0.5, -0.6 and -0.7). As expected, the more inelastic the demand, the higher the equilibrium prices and the government revenue. Again we find that the price maximizing tax revenue is generally well above the eviction price (except when the quality is the same on both markets) and the corresponding extensive margins of consumption are of the same magnitude.

## Results with $q = 0$

We detail in tables A13 to A16 scenarios where consumers going to the illegal market are not arrested. Since the case where $b = 1$ and $q = 0$ yields perfect competition between the legal and the illegal markets, we prefer to present a case where there is very little quality differentiation ($b = 1.01$), rather than no differentiation. When there are no arrests on the demand side, individuals are all the more sensitive to quality. For a government maximizing tax revenue, quality has a large influence on the optimal price: when the quality differential is 1.01, the equilibrium price on the legal market, $p^L$, is between USD 54 and 57 per ounce, depending on the elasticity; when $b = 1.80$, this price rises up to USD 387 to 549 per ounce.
<table><caption>Table A9: Legalization price and resulting demand when the government maximizes tax revenue ($\epsilon = -0.8$)</caption><thead><tr><th rowspan="2">1/N</th><th colspan="4">Policy parameters</th><th colspan="2">Equilibrium prices</th><th colspan="3">Demand and revenue</th><th colspan="3">Eviction scenario</th></tr><tr><th>c</th><th>b</th><th>q</th><th>F</th><th>p</th><th>p<sup>L</sup></th><th>ΔD(p, p<sup>L</sup>)</th><th>s<sup>I</sup>(p, p<sup>L</sup>)</th><th>R</th><th>p<sup>L</sup></th><th>ΔD(p<sup>L</sup>)</th><th>R</th></tr></thead><tbody><tr><td>0.55</td><td>50</td><td>1.58</td><td>0.1%</td><td>1000</td><td>95.33</td><td>297.47</td><td>33%</td><td>35%</td><td>341</td><td>97.79</td><td>104%</td><td>151</td></tr><tr><td>0.55</td><td>25</td><td>1.58</td><td>0.1%</td><td>1000</td><td>78.60</td><td>292.94</td><td>29%</td><td>39%</td><td>320</td><td>57.84</td><td>113%</td><td>71</td></tr><tr><td>0.55</td><td>125</td><td>1.58</td><td>0.1%</td><td>1000</td><td>146.13</td><td>311.84</td><td>45%</td><td>18%</td><td>409</td><td>217.63</td><td>78%</td><td>350</td></tr><tr><td>0.55</td><td>200</td><td>1.58</td><td>0.1%</td><td>1000</td><td>200.42</td><td>338.15</td><td>54%</td><td>0%</td><td>491</td><td>337.47</td><td>54%</td><td>490</td></tr><tr><td>0.10</td><td>50</td><td>1.58</td><td>0.1%</td><td>1000</td><td>61.33</td><td>288.35</td><td>25%</td><td>44%</td><td>300</td><td>97.79</td><td>104%</td><td>151</td></tr><tr><td>0.25</td><td>50</td><td>1.58</td><td>0.1%</td><td>1000</td><td>75.15</td><td>292.01</td><td>28%</td><td>40%</td><td>316</td><td>97.79</td><td>104%</td><td>151</td></tr><tr><td>0.75</td><td>50</td><td>1.58</td><td>0.1%</td><td>1000</td><td>105.23</td><td>300.20</td><td>35%</td><td>32%</td><td>353</td><td>97.79</td><td>104%</td><td>151</td></tr><tr><td>1.00</td><td>50</td><td>1.58</td><td>0.1%</td><td>1000</td><td>115.05</td><td>302.94</td><td>37%</td><td>29%</td><td>366</td><td>97.79</td><td>104%</td><td>151</td></tr><tr><td>0.55</td><td>50</td><td>1.00</td><td>0.1%</td><td>1000</td><td>56.11</td><td>67.85</td><td>102%</td><td>0%</td><td>88</td><td>61.89</td><td>104%</td><td>77</td></tr><tr><td>0.55</td><td>50</td><td>1.10</td><td>0.1%</td><td>1000</td><td>55.20</td><td>84.04</td><td>76%</td><td>15%</td><td>103</td><td>68.08</td><td>104%</td><td>90</td></tr><tr><td>0.55</td><td>50</td><td>1.30</td><td>0.1%</td><td>1000</td><td>76.13</td><td>173.87</td><td>44%</td><td>31%</td><td>205</td><td>80.46</td><td>104%</td><td>115</td></tr><tr><td>0.55</td><td>50</td><td>1.80</td><td>0.1%</td><td>1000</td><td>105.56</td><td>393.40</td><td>28%</td><td>36%</td><td>443</td><td>111.41</td><td>104%</td><td>180</td></tr><tr><td>0.55</td><td>50</td><td>1.58</td><td>0.2%</td><td>1000</td><td>92.88</td><td>302.42</td><td>33%</td><td>33%</td><td>351</td><td>111.56</td><td>101%</td><td>177</td></tr><tr><td>0.55</td><td>50</td><td>1.58</td><td>0.5%</td><td>1000</td><td>86.81</td><td>314.70</td><td>36%</td><td>29%</td><td>377</td><td>146.68</td><td>93%</td><td>240</td></tr><tr><td>0.55</td><td>50</td><td>1.58</td><td>1.0%</td><td>1000</td><td>78.42</td><td>331.60</td><td>38%</td><td>23%</td><td>413</td><td>197.33</td><td>82%</td><td>320</td></tr><tr><td>0.55</td><td>50</td><td>1.58</td><td>0.0%</td><td>1000</td><td>98.73</td><td>290.60</td><td>31%</td><td>37%</td><td>327</td><td>79.00</td><td>108%</td><td>115</td></tr><tr><td>0.55</td><td>50</td><td>1.58</td><td>0.1%</td><td>100</td><td>98.65</td><td>295.63</td><td>31%</td><td>37%</td><td>333</td><td>81.68</td><td>108%</td><td>120</td></tr><tr><td>0.55</td><td>50</td><td>1.58</td><td>0.1%</td><td>500</td><td>97.17</td><td>296.45</td><td>32%</td><td>36%</td><td>336</td><td>88.84</td><td>106%</td><td>134</td></tr><tr><td>0.55</td><td>50</td><td>1.58</td><td>0.1%</td><td>1500</td><td>93.49</td><td>298.51</td><td>33%</td><td>34%</td><td>346</td><td>106.74</td><td>102%</td><td>168</td></tr><tr><td>0.55</td><td>50</td><td>1.58</td><td>0.1%</td><td>2000</td><td>91.66</td><td>299.55</td><td>34%</td><td>32%</td><td>350</td><td>115.68</td><td>100%</td><td>185</td></tr></tbody></table>

<footnote>Notes: The above results are based on a price demand elasticity of 0.8 and the corresponding distribution parameters (see table A2). The marginal cost on the legal market, $c^L$, is USD 25 per ounce. The tax revenue in USD *per capita* and *per annum* is given as the product of the difference $p^L - c^L$ with the extensive and intensive margins of consumption. The intensive margin is approximated using Orens et al. (2018) estimates for consumption in Colorado in 2017.</footnote>