# Is Clean Development Always Possible? The Role of Environmental Policy in Developing Countries in the Presence of Aggregate Demand Spillovers

Basak Bayramoglu, Jean-François Jacques

► To cite this version:

Basak Bayramoglu, Jean-François Jacques. Is Clean Development Always Possible? The Role of Environmental Policy in Developing Countries in the Presence of Aggregate Demand Spillovers. Environmental Modeling & Assessment, inPress, 27, pp.139-153. 10.1007/s10666-021-09771-9. hal-03279476

HAL Id: hal-03279476

https://hal.inrae.fr/hal-03279476v1

Submitted on 11 Sep 2025

HAL is a multi-disciplinary open access
archive for the deposit and dissemination of sci-
entific research documents, whether they are pub-
lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d'enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.

<figure><img src="image_1.png" /></figure>

Distributed under a Creative Commons Attribution 4.0 International License
# Is clean development always possible? The role of environmental policy in developing countries in the presence of aggregate demand spillovers

Basak BAYRAMOGLU\*, Jean-François JACQUES\d

April 12, 2021

## Abstract

This paper investigates whether economic development is impeded by binding national emission standards to control climate change. We develop a simple model to highlight the potential role of environmental policy for successful clean development in the presence of aggregate demand spillovers in line with the paper by Murphy, Shleifer and Vishny (1989). We consider emissions standards but also discuss the potential of a tax-subsidy scheme and international monetary transfers to achieve (or not) clean development. In theory, clean development depends on both the microeconomic conditions related to technology choice and the macroeconomic conditions related to satisfaction of aggregate demand effects. The model builds on two main assumptions: the presence of fixed costs which give rise to increasing returns to scale in production, and clean technology. We also discuss practical employment of these environmental policies by three middle income countries which experienced declining emissions to GDP ratios as their GDP increased.

*Keywords:* environmental policy, emission standard, emission tax, international aid, investment, technology adoption, development, demand spillovers.

<footnote>\*Université Paris-Saclay, INRAE, AgroParisTech, Economie Publique, 78850 Thiverval-Grignon, France. E-mail: Basak.Bayramoglu@inrae.fr</footnote>

<footnote>†Université Gustave Eiffel, ERUDITE (EA 437), UGE 77454 Marne la Vallée, France. E-mail: Jean-Francois.Jacques@univ-eiffel.fr</footnote>
# 1 Introduction

This paper develops a simple model to investigate whether economic development is impeded by binding national emission standards to control climate change. In December 2015, 195 countries signed the Paris Agreement (2015) on reducing greenhouse gas (GHG) emissions. In contrast to the Kyoto Protocol (1997), the Paris Agreement (2015) does not include internationally negotiated emission standards. The signatory countries are obliged only to communicate national objectives or Intended Nationally Determined Contributions (INDCs) related to their mitigation efforts. Although at the international level these targets are not binding, if the developing country aims to respect them they can be translated into binding national level emission standards.

The public good nature of efforts to reduce climate change requires that developing countries as well as the industrialized countries which historically are responsible for this problem, make efforts to cut their GHG emissions. The Bali Action Plan which was the outcome of the December 2008 United Nations climate change conference, marks the first time that developing countries recognized the need to contribute a fair share to what must be a global effort. It has been forecast that by 2020, the combined emissions from developing countries will exceed those of the industrialized economies. The U.S. Energy Information Administration (2014) predicted that by 2040 energy-related carbon dioxide emissions from developing countries will be 127% higher than those produced by the world's most developed economies.

This paper develops a simple model to highlight the potential role of environmental policy for successful clean development in the presence of aggregate demand spillovers. We consider emission standards and the potential of tax-subsidy schemes and international monetary transfers to achieve clean development. Clean development depends on satisfaction of both the microeconomic conditions related to the choice of technology and the macroeconomic conditions related to aggregate demand effects. The model builds on the assumption of presence of fixed costs which give rise to increasing returns to scale in production, and clean technology. Polluting firms have the possibility to invest in clean technology which is profitable above a high level of emissions abatement. This paper provides new insights into the role of environmental policy in relation to the adoption of clean technology in a developing country in the presence of aggregate demand effects.

To inform our theoretical investigation of the environmental policies analyzed, we examine the cases of three middle-income countries which experimented with these environmental policies and experienced declining emissions to GDP ratios as their GDP increased. Although many other countries have failed to change this ratio our model suggests that environmental policy could be effective in some contexts.
Our theoretical model builds on Murphy, Shleifer and Vishny (1989) (hereafter MSV, 1989). This general equilibrium model highlights large aggregate demand effects and the initial drive for development in a developing country context. Our model includes binding emission standards which add an environmental dimension to the model without changing the assumptions about consumer preferences and production technology. In line with MSV(1989), our model assumes large aggregate demand spillovers.<fnref n="1" /> The profit of each modern sector is redistributed to consumers which increases demand, and thus, increases the profit for other sectors. We ignore the debate over the relevance of the effects of demand externalities on the development process and assume that they are sufficiently important to justify adoption of this model which has the advantage that it is simple. We focus more on the existence of fixed costs which are the source of these demand externalities since environmental policies are linked to these fixed costs. In our view, environmental policies are relevant for a wider class of models which include fixed costs.

An important assumption made by MSV (1989) is the existence of increasing returns to scale from production technology (i.e. existence of fixed costs). This assumption applies also to endogenous growth models with pollution abatement (see among others Smulders and Gradus, 1996 and Xepapadeas, 1997), and overlapping generations models of growth and the environment (see among others John and Pecchenino, 1994). Andreoni and Levinson's (2001) static model to explain the empirical evidence on the environmental Kuznets curve depends on the same assumption (Grossman and Krueger, 1995).<fnref n="2" />

In an investigation of the poverty trap, Xepapadeas (1997) showed that poor countries with environmental problems can be caught in a poverty trap because their low levels of capital do not allow exploitation of the increasing returns from abatement. Prieur et al. (2013) in an overlapping generations model framework show that potential irreversibility of pollution can result in environmental and poverty traps. Fodha and Seegmuller (2014) employ a similar model and find that an environmental poverty trap can emerge in economies with initial low capital stock where environmental policies are financed by public debt. In contrast to work on endogenous growth theory and overlapping generations models, our model includes a large aggregate demand effect to account for the initial driver of development in the presence of binding emission standards.

Although not specific to the developing country case, the literature on the link between appropriate environmental regulation, innovation, and competitiveness deserves attention. Studies that assume a microeconomic perspective analyze how stringent environmental regulation affects competitiveness and environmental quality based on the development of an

<footnote n="1">¹For extensions of the MSV (1989) model see de Fontenay (2004) on the market power of firms and the quality of institutions, and Trindade (2005) on tradable intermediate goods for instance.</footnote>

<footnote n="2">²Our model as written is not comparable to an environmental Kuznets curve model since emissions do not exceed the emission standard at equilibrium i.e. any excess emissions are automatically abated.</footnote>
upstream pollution abatement sector (eco-industry) via a larger supply of new abatement equipment (Greaker, 2006), or increased entry to the eco-industry (David et al., 2011). Acemoglu et al. (2012) focus on both the microeconomic and macroeconomic conditions for the emergence and adoption of clean technology. However, we do not take the research activity into account but assume that both clean and dirty technologies already exist and are not improved by research. In our simple model, we consider both the microeconomic and macroeconomic aspects conditioning firms' adoption of a new production and abatement technology with fixed costs. In particular, in our model as in MSV (1989) the macroeconomic conditions relate to aggregate demand spillovers. In this context, policy matters not to make research profitable in order to develop a clean technology, as in Acemoglu et al. (2012) but to provide a favorable macroeconomic environment for the adoption of a clean technology.

The paper is organized as follows. Section 2 represents the full industrialization equilibrium with no environmental constraint. Section 3 presents the equilibria with an environmental constraint. Section 4 first presents the three environmental policies implemented in three middle income countries, and then analyzes theoretically the role of these environmental policies in clean development. Section 5 provides concluding remarks.

## 2 Equilibrium with no environmental constraint

In this section, we examine a developing economy whose sectors are not constrained by environmental regulation,<fnref n="3" /> and consider the transition from a clean agrarian economy to a polluting industrial economy. Modern sectors refer to those sectors which modernized their production such as the manufacturing sectors in developing countries. These modernized sectors are more polluting than traditional agrarian sectors (Arrow et al., 1995). At the beginning of the period, we assume that k traditional sectors do not pollute. After modernization which involves a payment of a fixed cost, each of these modern sectors emits P. In this section, we posit that the level of total pollution is not sufficiently high to warrant regulation.

Every sector whether traditional or modern, produces a different good. There is one price-taker consumer which supplies (L) units of labor inelastically and owns all the economic profit.

The utility function of the price-taker consumer is written as:

$$U = x_1x_2...x_k, \qquad (1)$$

where k goods are imperfect substitutes, and $x_i$ is the consumption of good i with

<footnote n="3">³Our presentation of Murphy, Shleifer and Vishny's (1989) model was inspired by Basu (2003, ch. 2).</footnote>
i = 1, 2, ..., k. Here, we focus only on national income effects not welfare effects.<fnref n="4" /> In line with MSV (1989), we stress the importance of aggregate revenue effects for the emergence of positive spillovers across sectors via market size effects.

Let (R) denote the aggregate income and ($p_i$) the price of good (i). Maximization of equation 1 subject to the budget constraint ($R = \sum_{i=1}^{k} p_i x_i$) gives the demand function for good (i):

$$x_i = \frac{R}{k p_i} \qquad (2)$$

Note that (k) is the number of sectors and imposes an upper bound on the number of modern sectors. We assume that the wage is the numeraire. The aggregate income is: $R = (\bar{\pi} + L)$ where $(\bar{\pi})$ represents the aggregate profit earned in the economy.

The competitive fringe of firms, called traditional firms, is able to convert 1 unit of labor into 1 unit of output (constant returns to scale production technology). We assume that these firms can enter and exit the industry at no cost. The zero profit condition of competitive firms implies that they have a perfectly elastic supply at price 1 ($p_i = 1$).

Moreover, in each sector, a monopolist (modern firm) can emerge if it pays a fixed cost. It can convert 1 unit of labor into $\alpha > 1$ units of output (so the marginal cost of production is $\frac{1}{\alpha} < 1$) if it incurs a fixed cost $F > 0$ (increasing returns to scale production technology). Sector industrialization occurs when a monopolist begins production in that sector. The price of the monopolist is also 1 due to potential competition from the competitive fringe of firms.<fnref n="5" /> Market demand then is equal to $x_i = \frac{R}{k}$. The monopolist's profit is given by:

$$\pi = \left(1 - \frac{1}{\alpha}\right)\left(\frac{R}{k}\right) - F = \frac{\alpha - 1}{\alpha}\frac{R}{k} - F \equiv \frac{aR}{k} - F, \qquad (3)$$

with $0 < a < 1$, which represents both the monopolist's mark-up and the measure of scale economies.

When (n) sectors have modernized, the profit of the monopolist in each sector is given by<fnref n="6" />:

$$\pi(n) = \frac{aL - kF}{k - na} \qquad (4)$$

<footnote n="4">⁴As will be shown later in the paper due to perfect competition, the price of the goods in the traditional and modern sectors is the same. Thus, substitution effects do not play a role.</footnote>

<footnote n="5">⁵The monopolist cannot fix its price but at equilibrium its profit is strictly positive which does not apply to the competitive firm. To maintain a competitive fringe of firms we assume a sector which cannot be modernized.</footnote>

<footnote n="6">⁶When (n) sectors industrialize, the profit of the monopolist is equal to $\pi = \frac{aR(n)}{k} - F$. The aggregate income when (n) sectors industrialize is given by $R(n) = n\left[\frac{aR(n)}{k} - F\right] + L$. The resolution of this equation leads to: $R(n) = \frac{k(L-nF)}{k-na}$.</footnote>
The denominator in this equation is always positive because $n \le k$ and $a < 1$. The sign of $\pi(n)$ is determined by the sign of $(aL - kF)$, which is independent of $(n)$, the number of modernized sectors. We assume that $(aL - kF)$ is positive so that it is in the interest for a firm to industrialize before it is constrained by an environmental regulation:

$$ \textbf{Assumption 1:} \quad (aL - kF) > 0. $$

This condition means that the potential monopoly rent generated by the labor resource from all sectors if all were modern, is greater than the total cost of modernization. Let $(n)$ sectors be modernized, and let us look at the incentive for a monopolist to enter production. Its profit will be: $\pi(n + 1) = \frac{aL-kF}{k-(n+1)a}$, which is positive because by assumption $(aL - kF)$ is positive. Consequently, with no environmental constraint, the only equilibrium is that all sectors modernize, $n = k$. In the next section, we show that with an environmental constraint development can slow meaning that the number of modern sectors $n$ could be less than $k$.

# 3 “Environmental” equilibria

## 3.1 Environmental constraint and abatement technology

We next present a simple theoretical example to express the idea that if a sufficient number of modern sectors invest in new abatement technology the increase in aggregate demand resulting from modernization could outweigh the cost of negative spillovers (pollution).

We consider a one-period model. At the beginning of the period, there are $k$ non-industrialized sectors. The firms in each sector have three choices: not to industrialize, to industrialize in a dirty way by paying the fixed cost of modernization ($F$) and a variable abatement cost associated to an old abatement technology, or to industrialize in a clean way by paying the fixed cost of modernization ($F$) and the fixed cost of investment in clean technology ($S$).$^7$

The developing country government sets an aggregate emission standard for its polluting sectors in the form of a maximum allowable level of emissions denoted $(\bar{E})$. In our model, there are both positive and negative spillovers between sectors. As in MSV (1989), there are positive aggregate demand spillovers among sectors based on market size effects. More extensive modernization of the industry increases the profits for all economic sectors via demand effects. However, a higher number of modern sectors implies more pollution. If

<footnote>$^7$Note that modifications to the model would be needed to account for a setting with some traditional and industrialized sectors coexisting at the beginning of the period, or a situation where some firms industrialize in two steps - first in a dirty way and later in a clean way – and some firms decide to industrialize directly using a clean technology.</footnote>
the aggregate emission standard is violated, then each modern sector abates a fraction of
the total pollution in excess of the emission standard (and hence pays an abatement cost)
such that $\bar{E}$ is met collectively. This is a negative spillover across sectors because the higher
the number of dirty modern sectors, the more each individual polluting sector has to pay.
Modern sectors have the option to invest in new abatement technology. For simplicity we
assume that this technology is so sophisticated that having invested in its fixed cost these
modern sectors no longer produce polluting emissions (i.e. the marginal abatement cost is
null). Thus, if a sufficiently high number of modern sectors invests in this technology, the
aggregate emission standard will be met collectively more easily. This is another channel of
positive spillovers across sectors.

We next propose an environmental counterpart of the model. For simplicity we assume
that each modern sector causes a fixed amount of emissions (P).<fnref n="8" /> If there are (n) sectors that
have industrialized, then two situations emerge: 1) the total level of emissions $E = n \times P$
is lower than the standard: $E = n \times P \le \bar{E}$, or 2) the total level of emissions exceeds the
standard $E = n \times P > \bar{E}$. We define $\bar{n}$ as the number of modern sectors for which the
environmental standard is just reached $\bar{n} = \frac{\bar{E}}{P}$. In the first case, the total level of emissions
in the economy is sufficiently low that it does not exceed the aggregate emission standard
which means that these modern sectors are not constrained by environmental regulation and
do not pay abatement costs. In the second case, the emission standard is violated because
a significantly high number of sectors which have modernized have not invested in new
abatement technology. The excess emissions compared to the aggregate emission standard
is equal to: $E - \bar{E} = n \times P - \bar{E}$. The emission standard requires each monopolist to pay the
following abatement cost: $v[\frac{n \times P - \bar{E}}{n}]$, where ($v > 0$) represents the marginal abatement
cost associated to the existing (traditional) abatement technology. All modern firms can
reduce pollution at cost $v$ per unit of abatement. We assume that the monopolist complies
fully with this emission standard. This requires the implicit assumption that government
is able to commit to strict imposition of a penalty on those sectors which do not respect
the emission standard. This policy is equivalent to a cap and trade policy where tradable
emission permits initially are distributed for free among firms. In this case, firms may need
to buy additional permits to allow them to emit more, and the price of a permit represents
the marginal cost of abatement.

Modern sectors have the possibility to invest in new (modern) abatement or clean tech-
nology. This investment requires payment of a fixed cost (S)<fnref n="9" />, but allows these modern

<footnote n="8">⁸In appendix 5 we relax this assumption to consider endogenous emissions proportional to production. We discuss this extension in section 5 (Concluding remarks).</footnote>

<footnote n="9">⁹This fixed investment cost does not depend on the number of sectors that have already invested in this technology which contrasts with the assumption in Greaker (2006). Thus, we exclude learning or imitation possibilities across sectors.</footnote>
sectors not to emit pollution P.<fnref n="10" /> The fixed cost of investment S would include acquisition of a new plant and new machines (setup costs). Thus, (F + S) represents the total cost of investment in modern production and modern abatement technology.<fnref n="11" />

Let us suppose now that m out of the n modern sectors invest in new abatement technology. Then the excess of emissions compared to the aggregate emission standard becomes $E - \bar{E} = (n - m) \times P - \bar{E}$. In deciding whether to invest in new abatement technology, the monopolist will compare its cost of investment S to the abatement cost associated to the old abatement technology $v[P - \frac{\bar{E}}{n - m}]$. It is clear that the more stringent the emission standard ($\bar{E}$ small) and/or the larger the number of polluting sectors ((n - m) large) the more willing the monopolist will be to invest. Furthermore, as the number of clean modern sectors (m) increases, the remaining dirty modern sectors have a smaller incentive to invest in new abatement technology (see Remark 1 in appendix 1). This effect is due to a more relaxed environmental constraint inducing higher profits both directly and indirectly through increased aggregate demand in the economy.

If $S = v(P - \frac{\bar{E}}{n - m})$ the monopolist will be indifferent between investing and non-investing in new abatement technology. This condition holds for a particular number of dirty modern sectors $N = (n - m)$ (see figure 1) above which it is in the interests of a modern sector to become clean but below this number it is not. To summarize, we have:

$$S = v(P - \frac{\bar{E}}{n - m}) \text{ if } (n - m) = N,$$

$$S < v(P - \frac{\bar{E}}{n - m}) \text{ if } (n - m) > N,$$

$$S > v(P - \frac{\bar{E}}{n - m}) \text{ if } (n - m) < N.$$

Moreover we assume that:

**Assumption 2: $S < vP$**.

This assumption requires that the fixed cost of investment in new abatement technology is sufficiently low for it to be adopted.

<footnote n="10">¹⁰Here we consider two extreme abatement technology cases: an old technology with no fixed cost only a variable abatement cost, and a modern technology with a fixed cost. A more realistic model would include both costs in the two cases, with a higher fixed cost for the new technology. Our extreme hypothesis simplifies the calculus but if we add a variable cost for the new abatement technology, with a marginal cost $v$ less than $v$, we obtain similar results but based on more complex calculation (see appendix 6).</footnote>

<footnote n="11">¹¹(F+S) represents the cost of investment in a cleaner (e.g. a more energy efficient) production technology.</footnote>
<figure><img src="image_2.png" /><figcaption>Figure 1: Threshold number of dirty modern sectors</figcaption></figure>
We next define dirty and clean modern firms.

**Definition 1** A *dirty modern sector*, denoted ‘mt’, is a monopolist which uses the traditional abatement technology. Its abatement cost is $v(P - \frac{\bar{E}}{n-m})$.

**Definition 2** A *clean modern sector*, denoted ‘mm’, is a monopolist which invests in and uses the modern abatement technology. Its abatement cost $S$ is fixed.

It is then possible to determine the profit of the firms in these different cases (see appendix 1) in order to classify the equilibria. It should be noted that if the number of dirty modern sectors ($n$) increases, the remaining sectors have a smaller incentive to modernize their production (see Remark 2 in appendix 2). It might seem that due to positive demand spillovers the profit of a modern sector using the old abatement technology will depend positively on the number of dirty modern sectors. However, the increased modernization is associated to higher levels of pollution. Hence the abatement cost of the dirty modern sector increases as the number of dirty modern sectors increases, and in turn, the individual profit drops.

## 3.2 Clean and dirty equilibria

In this section, we characterize different equilibria<fnref n="12" /> according to degree of industrialization and environmental efficiency. These equilibria are defined by two equations: one reflecting a macroeconomic condition and the other a microeconomic trade-off.

The macroeconomic condition indicates that aggregate profit is distributed among individuals as revenue which is consumed and then augments the profit. This virtuous circle ends when the abatement cost becomes so high that the profit cancels out for the marginal firm (the last to modernize). The microeconomic trade-off is related to the choice of abatement technology. The marginal cost of the old technology ($v$) is constant and the marginal cost of the modern technology is null. The old technology abates excess emissions up to the level compliant with the aggregate standard. However, the modern technology abates all the emissions of the firm which invests in it. This helps to relax the aggregate environmental constraint on the other firms: other traditional sectors can become modern. The modern sector adopts the modern abatement technology based on the abatement cost minimization: it is a microeconomic efficiency trade-off.

<footnote n="12">¹²The equilibria presented are Nash equilibria: no firm has any interest in deviating from them. These equilibria resemble “coupled constraint Nash equilibria” à la Rosen (1965) and applied to an environmental compliance problem by Krawczyk (2005), because the environmental constraint must be respected by all firms. However, in our work the firm’s strategies are discrete: stay traditional, or be modern and dirty, or be modern and clean.</footnote>
We next propose different equilibria depending on the value of the fundamental parameters. We show that three kinds of equilibrium related to the two conditions can emerge which is expressed in the following proposition.

**Proposition 1** Under Assumptions 1 and 2, there are three types of equilibrium:

a) Incomplete and dirty modernization defined by:

$$aL \leq k(v(P - \frac{\bar{E}}{k}) + F) \quad (\text{Condition 1})$$

$$S > v(P - \frac{\bar{E}}{k}) \quad (\text{Condition 2})$$

b) Full and dirty modernization defined by:

$$aL > k(v(P - \frac{\bar{E}}{k}) + F) \quad (\text{Condition 3})$$

$$S > v(P - \frac{\bar{E}}{k}) \quad (\text{Condition 2})$$

c) Full and clean modernization defined by:

$$aL > k(S + F) \quad (\text{Condition 4})$$

$$S < v(P - \frac{\bar{E}}{k}) \quad (\text{Condition 5})$$

**Proof.** See appendices 2 and 3.

Proposition 1 underlines that the three types of equilibrium are characterized according to their degree of industrialization and environmental efficiency. Each equilibrium is defined by two equations: one reflects a macroeconomic condition and the other a microeconomic trade-off.

Incomplete and dirty modernization are defined by Conditions 1 and 2. Condition 1 is related to the macroeconomic condition, Condition 2 is related to the microeconomic trade-off condition. The macroeconomic condition says that the profit of the modern firm ($aL - kF$) is not sufficient to cover the total abatement cost $kv(P - \frac{\bar{E}}{k})$ if all of the k firms were to abate. Parameter a is greater than 1, so ($aL$) indicates a multiplier effect from the demand spillovers. This condition says simply that if the marginal abatement cost $v$ or the level of the modern firm's emissions is too high (high $P$), a new monopoly can not emerge. In contrast, if the aggregate pollution cap $\bar{E}$ is high, the standard is not constraining so a new modern sector emerges as a monopoly. The microeconomic condition says that the modern abatement technology is too costly to be adopted. If the standard were more stringent (lower $\bar{E}$), this condition would be reversed, but the first condition can not be reversed because $kv(P - \frac{\bar{E}}{k})$ is decreasing with $\bar{E}$ (a low $\bar{E}$ implies a higher abatement cost): modernization remains incomplete and the clean technology cannot be implemented. To sum up, in this most pessimistic case aggregate demand spillovers are not
sufficiently high for firms to modernize their production and their abatement technology simultaneously. The standard is respected at the aggregate level but modern firms use the old abatement technology. As a result, other traditional sectors cannot be modernized because then the environmental constraint would become effective. Only a fraction of the sectors modernizes.

*Full and dirty modernization* are defined by Conditions 3 and 2. In contrast to Condition 1 in the previous case, Condition 3 indicates that the aggregate demand spillovers are sufficient to cover the abatement costs. The microeconomic condition (Condition 2) indicates that the environmental standard is not sufficiently stringent (low) to make the clean abatement technology profitable. To sum up, this second case reflects the situation where aggregate demand spillovers are sufficiently high as to give rise to complete industrialization where all firms pollute but where this collective pollution does not exceed the environmental standard.

*Full and clean modernization* are defined by Conditions 4 and 5. The macroeconomic condition (Condition 4) says that aggregate demand spillovers exceed the sum of the fixed cost of modernization and the fixed cost of the clean technology for all (k) firms. The microeconomic condition (Condition 5) indicates that the environmental standard is sufficiently stringent to make the modern abatement technology profitable. In this case, modern firms with the new abatement technology abate all their emissions. To sum up, in this most optimistic case, aggregate demand spillovers are sufficient for a complete and clean industrialization made possible by investment in modern abatement technology. The high revenue from profits generated by economic development renders the technology not too costly. For the full and clean modernization, the microeconomic condition for the technology choice taken is not sufficient on its own. Macroeconomic conditions are necessary because the large revenue effects allow consumption to sustain development based on the resulting high profits. Here, the revenue effect comes not from endogenous or exogenous technical progress but from the distribution of revenue. The increased revenue is triggered by the existence of increasing returns from the fixed costs and higher marginal labor productivity which increase the monopolist's profit. The microeconomic condition implies stability of this equilibrium because a clean monopolist has no incentive to switch to the old abatement technology.

# 4 Role of environmental policy

In this section we discuss the role of environmental policy for achieving clean development which is the central issue in this article. We address three policies successively: the environmental standard, a tax-subsidy scheme, and international monetary transfers.
As a motivation of the environmental policies that will be studied theoretically, we first discuss practical employment of these environmental policies by three middle income countries<fnref n="13" />: Argentina, Tunisia and India. These countries represent different continents and thus different socio-economic environments and different levels of development.<fnref n="14" /> More importantly, these three countries have seen their emissions/GDP ratios decline over time associated to positive growth rates of GDP. Figures 2, 3, 4 represent the respective evolutions of the GDP and emissions to GDP ratios for Argentina, Tunisia, and India in the period 1990-2019. While we stress the use of a specific environmental policy in a given country, we are aware that other types of policies may be employed simultaneously and may have a significant effect on the observed emissions/GDP ratio. However, these three countries have non-negligible experience of the environmental policy on which we focus. We then analyze theoretically the effects of these policies for each type of equilibria studied so far but taking account of the limitations linked to the specificity of the model we present.

# 4.1 More stringent environmental standard

## 4.1.1 Motivation

Figure 2 shows that Argentina experienced a declining CO2 emissions/GDP ratio (although there is small increase at the end of the period) associated to positive economic growth rates.

Several different reports and databases indicate good environmental performance by Argentina. We use the best available sources of data on climate policy (Kono et al., 2019): Steves and Teytelboym's (2013) Climate Laws, Institutions and Measures Index (CLIMI) and the Grantham Institute's Climate Change Laws of the World database.<fnref n="15" /> The CLIMI measures national climate policy in different countries and is based on policies reported to the United Nations Framework Convention on Climate Change (UNFCCC) between 2005 and 2011. Policies are scored depending on their proximity to worldwide best practice. The average final score ranges from 0 to 1, with higher values representing countries with more ambitious climate policy (Kono et al., 2019). Argentina has a score of 0.401 which positions it among the top-ten developing countries (Costa Rica is ranked 1st). The Grantham Institute's Climate Change Laws of the World database (hereafter Grantham database) among other information provides a count of each country's climate-related laws and policies. Argentina has a considerable number (18) of such policies. The 2020 environmental

<footnote n="13">¹³Middle income countries are defined as economies with gross national income per capita between US$1,026 and $12,475 (2011) (The World Bank, https://www.worldbank.org/en/country/mic).</footnote>

<footnote n="14">¹⁴The World Bank classifies Argentina as an upper-middle/high income country, Tunisia as a lower-middle/upper middle income country, and India as a low/lower middle income country based on gross national income per capita (https://datatopics.worldbank.org/world-development-indicators/stories/the-classification-of-countries-by-income.html).</footnote>

<footnote n="15">¹⁵https://climate-laws.org/.</footnote>
performance index (EPI) for climate change (Wendling et al., 2020) ranks 180 world countries and positions Argentina 54th with a positive improvement in the score over the 10 year period.

<figure><img src="image_3.png" /><figcaption>Figure 2: The case of Argentina</figcaption></figure>

The Grantham database lists the following climate policies for Argentina: Law 27191 on Renewable Energy passed in 2015 which builds on and updates the Regimen for the National Promotion for the Production and Use of Renewable Sources of Electric Energy established by Law 26190 in 2007, and extends the regime for the period 2018-2025. The 2007 law stipulates that 8% of all electricity consumed nationally must be generated from renewable energy sources by December 31, 2017. This policy was strengthened by the 2015 law which stipulates a progressive increase in the renewable energy ratio to achieve a minimum of 20% by December 31, 2025. The 2007 policy corresponds to the 15th year of our sample in figure 2 where we observe a clear decrease in the emissions/GDP ratio after this date.

4.1.2 Theory

The environmental standard can be related to the international climate negotiations. The INDCs in the Paris Agreement (2015) can be considered the national binding emission stan-
dard for a developing country motivated to respect its Paris Agreement (2015) obligation. Here, the environmental standard takes the form of a pollution standard and a maximum allowable emissions level, $\bar{E}$.

In the first type of equilibrium “the incomplete and dirty modernization” (conditions 1 and 2), if the pollution standard were more stringent (lower $\bar{E}$) this would increase the abatement cost and reduce the number of modern sectors. A more stringent standard would then reduce average productivity since there would be fewer modern sectors that were more productive than the traditional ones. This result rejects (the strong version of) the Porter hypothesis (PH) in this specific case. The PH predicts that well-designed environmental regulation will increase competitiveness by inducing more innovation (Porter and Van der Linde, 1995). There are two versions of the PH: the “weak” PH refers to the positive effect of well-designed environmental regulation on green innovation, and the “strong” PH refers to its positive effect on productivity and competitiveness.<fnref n="16" />

In the second type of equilibrium “the full but dirty modernization” (conditions 3 and 2), a more stringent pollution standard might increase the number of clean modern firms in order to reach the “full and clean modernization” equilibrium (conditions 4 and 5). In fact, adopting the modern abatement technology then becomes relatively less expensive than adopting the traditional abatement technology (inequality 2 can be reversed). However, the transition does not increase productivity because the modernization is already complete.

## 4.2 Tax-subsidy scheme

### 4.2.1 Motivation

Figure 3 shows that Tunisia also experienced a declining CO2 emissions/GDP ratio associated to positive economic growth rates.

Different reports and databases also indicate good environmental performance for Tunisia. The 2020 EPI of climate change ranks Tunisia 54th (equal to Argentina), with a positive improvement in the score over the 10 year period. The Grantham database shows that Tunisia has four climate law and policies. Sukhdev et al. (2010, p. 22) report that

> "A law establishing an 'energy conservation system' on energy management in 2005 was immediately followed with the creation of a funding mechanism – the National Fund for Energy Management – to support increased capacity in renewable energy technologies and also improved energy efficiency. The replenishment of this Fund is based on a duty levied on the first registration of private, petrol-powered and diesel powered cars and on import duty or

<footnote n="16">¹⁶See for instance Ambec et al. (2013) for a survey of the theoretical approaches proposed to explain the PH. The empirical evidence suggests that the weak PH is valid but the evidence for the strong PH is mixed (Rubashkina et al., 2015).</footnote>
local production duty of air-conditioning equipments with the exclusion of those produced for exports."

The National Fund for Energy Management is a taxation-subsidiary policy which taxes "dirty" production units and the revenue from this tax funds renewable energy developments, especially solar energy.

<figure><img src="image_4.png" /><figcaption>Figure 3: The case of Tunisia</figcaption></figure>

4.2.2 Theory

A tax-subsidy scheme would tax dirty modern firms and distribute the revenue from this tax in the form of subsidies for modern firms which invest in clean technology. A tax-subsidy policy would a priori affect the “incomplete and dirty modernization” and “the full but dirty modernization” equilibria.

In the second type of equilibrium - “the full but dirty modernization” - this policy would make development cleaner. The macroeconomic condition would not change (condition 3) but the microeconomic condition (condition 2) might be reversed if the cost of the clean technology S is reduced by a subsidy financed by the tax on dirty modern firms.
In the first type of equilibrium - “the incomplete and dirty modernization” - it is possible to improve development but not the environment because the level of pollution would remain at $\overline{E}$. We can study this case in more detail. Let us posit that the economy is in an incomplete and dirty industrialization equilibrium. It is possible to escape this equilibrium to reach an equilibrium with more modern firms. The logic is that since the new abatement technology is costly at the equilibrium, the government can tax the $(n - m)$ dirty modern sectors and subsidize new abatement technology for the $m$ clean modern sectors. This would decrease total emissions and reduce the economy’s total abatement costs: the aggregate revenue is higher and development can continue.

Formally, note that for all $m < n$, the following inequality is verified:

$$nv(P - \frac{\overline{E}}{n}) > mS + (n - m)v(P - \frac{\overline{E}}{n - m}), \quad (5)$$

given **Assumption 2**, $S < vP$. This means that the total abatement costs for the economy with $n$ dirty modern firms (left side of the inequality) are higher than the total abatement costs with $m$ clean modern sectors which invest in new abatement technology (right side of the inequality). This means that the tax on the polluting firms distributed to clean firms leads to a lower aggregate abatement cost: then the modernization can continue.

Now we present the policy which can implement this mechanism. Let us focus on the incomplete and dirty modernization equilibrium with $n = n_1^*$. We ask the following question. Is it possible to implement the following scheme: tax $(n_1^* - m)$ dirty modern sectors at level $(t \frac{\overline{E}}{n_1^* - m})$ and subsidy $m$ clean modern sectors at level $(\sigma = t \frac{\overline{E}}{m})$ such that<fnref n="17" /> the tax-subsidy scheme is profitable for both the dirty modern and clean modern sectors? If such $t$ and $\sigma$ exist, then the economy can escape from the “the incomplete and dirty modernization” equilibrium to reach a higher equilibrium with more modern firms.

**Proposition 2** There exists a tax-subsidy policy $(t, \sigma)$ which allows a low-income economy to escape from the incomplete and dirty modernization equilibrium to reach a higher equilibrium.

**Proof.** See appendix 4.

The tax-subsidy policy then could facilitate coordination of the investment decisions of modern sectors in order to converge towards a higher production equilibrium.

<footnote n="17">¹⁷The budget constraint is balanced because the collection of the tax is equal to $T = (n_1^* - m) \left(t \frac{\overline{E}}{n_1^* - m}\right) = t\overline{E}$, and the revenue from the tax is redistributed equally in the form of a subsidy $\sigma$ to each clean sector: $\sigma = \frac{T}{m} = \frac{t\overline{E}}{m}$.</footnote>
## 4.3 International monetary transfers

### 4.3.1 Motivation

Figure 4 shows that India also experienced a fairly continuously declining emissions/GDP ratio associated to positive economic growth rates.

<figure><img src="image_5.png" /><figcaption>Figure 4: The case of India</figcaption></figure>

Different reports and databases indicate a good environmental performance for India. The CLIMI gives India a score of 0.358 ranking it 43rd out of 95 countries while the Grantham database shows that India has a significant number (12) of climate laws and policies. The particularity of India is that it received the largest amount of international aid for mitigation purposes in the period 2002-2017, followed by Uzbekistan and Indonesia (figure 5). These data come from the OECD (2020) Bilateral Development Aid Database which gathers bilateral climate aid (for mitigation and adaptation separately) from the OECD Development Assistance Committee members. The projects are screened and their relevance relative to the Rio Markers for climate mitigation is evaluated as “principal”, “significant”, or “not targeted”. In the figure, we use the aggregate of principal and significant mitigation aid. As an emerging economy, India clearly benefits compared to other developing countries from international climate aid and its potential positive effect on “clean”
<figure><img src="image_6.png" /><figcaption>Figure 5: Top Ten Recipients of Mitigation Transfers (source: own calculations based on (OECD, 2020))</figcaption></figure>

investments.

4.3.2 Theory

International monetary transfers from developed to developing countries can take two forms: development aid for the acquisition of new production technology which contributes to reducing the fixed costs linked to modernization F, and climate aid (such as the “Green Fund”) for the acquisition of new abatement technology which reduces the fixed costs linked to clean environmental technology S.

We discuss these two international transfer policies in the context of the three types of equilibrium. In the first type of equilibrium “the incomplete and dirty modernization”, development aid which reduces the fixed cost *F* would modernize the economy to reach the second type of equilibrium of complete but dirty development. Due to the larger number of modern firms in the economy, average productivity would increase confirming (the strong version of) the PH in this specific case. To obtain the third type of equilibrium where development is complete and clean, it would be necessary to combine development aid and
environmental aid to simultaneously reduce *F* and *S*. It is clear that environmental aid alone is not enough to ensure modernization of the economy; an environmental transfer is necessary but not sufficient to achieve clean development. Kim and Krawczyk (2017) suggest using international aid to overcome the environmental constraint within a dynamic analysis framework in line with viability theory. This would make it possible to compensate for the country's low level of capital.

# 5 Concluding remarks

In this study, we developed a simple model to highlight the potential role of environmental policy in successful clean development in a developing country in the presence of aggregate demand spillovers. We incorporated an environmental counterpart in the general equilibrium model proposed by Murphy, Shleifer and Vishny (1989). We consider emission standards but also discuss the potential of a tax-subsidy scheme and international monetary transfers to achieve clean development.

The first implication of our model is that a binding emission standard does not necessarily impede national development (proposition 1 (c)) and can motivate some sectors to both modernize production and invest in new abatement technology. This is driven by spillovers across sectors channeled through the level of the aggregate emission standard and the implied level of the abatement cost if the standard is violated collectively. Moreover, investment in new abatement technology by a modern firm reduces the abatement burden on the other firms.

We theoretically analyzed the role of environmental policy to achieve clean development. We focused on three policies: an emission standard, a tax-subsidy scheme, and international monetary transfers. Clean development requires a coordinated effort from a group of pol-luting sectors to undertake costly investment in new abatement technology. It appears that depending on national objectives - either more significant development or cleaner development - and depending on the type of equilibrium which in turn depends on the economy's fundamental parameters, one or other of these policies will be effective. For example, in a large country (large *L*) a tax-subsidy scheme enables clean development without the need for international aid. A scheme which combines taxation of dirty modern sectors with a subsidy to clean modern sectors could help the economy converge towards an equilibrium with a higher number of modern and clean firms. In international climate negotiations, monetary transfers across countries could help. Under the Paris Agreement (2015), the developed countries agreed to maintain their existing collective goal to transfer USD 100 billion per year to developing countries up to 2025 when a new collective goal will be set
(European Commission, Climate Action<fnref n="18" />). This fund should help developing countries to respect their environmental commitments in the course of their economic development. We provided a theoretical analysis of the effects of three environmental policies inspired by the experience by three middle income countries: Argentina, Tunisia, and India.

Our results derive from a simple model which includes a developing country context. For instance, the model assumes that emissions are fixed with respect to production. In appendix 5 we relax this assumption in order to consider endogenous emissions proportional to production $P = \beta x_i$ with $\beta > 0$. This reduces the mark-up of the monopolist firm from $a$ to $(a-v\beta)$ in the first equilibrium without investment in clean technology, where $v$ represents the marginal abatement cost from use of traditional abatement technology. The conditions in this case are very similar to the conditions including exogenous emissions. However, one difference is that the number of dirty modern sectors ($n_1^*$) decreases because of the reduced mark-up, which makes aggregate demand spillovers less effective for counterbalancing the environmental costs. In the equilibria with investment in clean technology, the extension complicates the analysis although the basic mechanisms are the same.

For reasons of analytical framework simplicity and formal aspects, we considered a static model that does not account for the accumulation of capital stock or pollution stock over time. Accumulation of capital can take time in countries in an industrialization phase. Our static model can be considered a short-term model. Environmental policies can be a stimulus for clean development which would allow the country to embark on a clean development path. However, a poverty trap would be more likely in a dynamic model with capital accumulation (as shown in Xepapadeas, 1997). In this case, the conditions for clean development would be more restrictive (see appendix 7 for a simple extension of the model to capital accumulation).

Our results are based on a simple general equilibrium model with aggregate demand effects in line with Murphy, Shleifer and Vishny (1989). By assuming the existence of large aggregate demand effects, our model highlights the role of environmental policies when developing countries face large fixed costs of modernization and investment in new abatement technology. Future work could include both demand and supply-side effects in the models to analyze the relevance of environmental policies for developing countries.

# 6 Author Declarations

Funding: Not applicable.

Conflicts of interest/Competing interests: Not applicable.

Availability of data and material: Not applicable.

<footnote n="18">¹⁸http://ec.europa.eu/clima/index_en.htm.</footnote>
Code availability: Not applicable.

Authors' contributions: Not applicable.

Acknowledgments

The authors are grateful for very helpful comments and suggestions from the editor, the associate editor, and the reviewers. We would like to thank Anna Creti for her helpful comments and suggestions, and the participants of the EAERE Conference, Athens (June-July 2017), the EAAE Conference, Parma (September, 2017), and the FAERE Conference, Nancy (September 2017). A previous version of this paper has circulated as "Big Push, adoption of environmentally-friendly technology, and the Porter hypothesis".

References

[1] Acemoglu, D., Aghion, P., Bursztyn, L., Hemous, D. (2012): "The environment and directed technical change", American Economic Review, 102(1), 131-166.

[2] Ambec, S., Cohen, M. A., Elgie, S., Lanoie, P. (2013): "The Porter hypothesis at 20: can environmental regulation enhance innovation and competitiveness?", Review of Environmental Economics and Policy, 7(1), 2-22.

[3] Andreoni, J., Levinson, A. (2001): "The simple analytics of the environmental Kuznets curve", Journal of Public Economics, 80(2), 269-286.

[4] Arrow, K., Bolin, B., Costanza, R., Dasgupta, P., Folke, C., Holling, C., Jansson, B.O., Levin, S., Maler, K.G., Perrings, C., Pimentel, D. (1995): "Economic growth, carrying capacity, and the environment", Ecological Economics, 15(2), 91-95.

[5] Basu, K. (2003): Analytical Development Economics - The Less Developed Economy Revisited, MIT Press.

[6] David, M., Nimubona, A-D., Sinclair-Desgagné, B. (2011): "Emission taxes and the market for abatement goods and services", Resource and Energy Economics, 33 (1), 179-191.

[7] de Fontenay, C.C. (2004): "The dual role of market power in the Big Push: from evidence to theory", Journal of Development Economics, 75(1), 221-238.

[8] Fodha, M., Seegmuller, T. (2014): "Environmental quality, public debt and economic development", Environmental and Resource Economics, 57(4), 487-504.
[9] **Greaker, M.** (2006): "Spillovers in the development of new pollution abatement technology: a new look at the Porter-hypothesis", Journal of Environmental Economics and Management, 52(1), 411-420.

[10] **Grossman, G.M.**, **Krueger, A. B.** (1995): "Economic growth and the environment", The Quarterly Journal of Economics, 110(2), 353-377.

[11] **John, A.**, **Pecchenino, R.** (1994): "An overlapping generations model of growth and the environment", The Economic Journal, 104(427), 1393-1410.

[12] **Kim, K.**, **Krawczyk, J.B.** (2017): "Sustainable emission control policies", Seoul Journal of Economics, 30(3), 291-317.

[13] **Kono, D.Y.**, **Montinola, G.R.** (2019): "Foreign aid and climate change policy: what can ('t) the data tell us?", Politics and Governance, 7(2), 68-92.

[14] **Krawczyk, J.B.** (2005): "Coupled constraint Nash equilibria in environmental games", Resource and Energy Economics, 27(2), 157-181.

[15] **Murphy, K.M.**, **Shleifer, A.**, **Vishny, R.** (1989): "Industrialization and the Big Push", The Journal of Political Economy, 97(5), 1003-1026.

[16] **OECD** (2020), Creditor Reporting System : Aid activities targeting Global Environmental Objectives, OECD International Development Statistics (database), https://doi.org/10.1787/9c778247-en.

[17] **Porter, M.**, van der Linde, C. (1995): "Toward a new conception of the environment-competitiveness relationship", Journal of Economic Perspectives, 9(4), 97-118.

[18] **Prieur, F.**, **Jean-Marie., A.**, **Tidball, M.** (2013): "Growth and irreversible pollution: are emission permits a means of avoiding environmental and poverty traps?", Macroeconomic Dynamics, 17(2), 261-293.

[19] **Rosen, J.B.** (1965): "Existence and uniqueness of equilibrium points for concave n-person games", Econometrica: Journal of the Econometric Society, 520-534.

[20] **Rubashkina, Y.**, **Galeotti, M.**, **Verdolini, E.** (2015): "Environmental regulation and competitiveness: Empirical evidence on the Porter Hypothesis from European manufacturing sectors.", Energy Policy, 83: 288-300.

[21] **Smulders, S.**, **Gradus, R.** (1996): "Pollution abatement and long-term growth", European Journal of Political Economy, 12(3), 505-532.
[22] Steves, F., Teytelboym, A. (2013): “Political economy of climate change policy”, SSEE Working Paper, No.13-02. Oxford: SSEE. https://doi.org/10.2139/ssrn.2456538.

[23] Sukhdev, P., Stone, S., Nuttall, N. (2010): “Green economy, developing countries success stories”, St-Martin-Bellevue: United Nation Environment Programme (UNEP).

[24] Trindade, V. (2005): “The big push, industrialization and international trade: The role of exports”, Journal of Development Economics, 78.1, 22-48.

[25] U.S. Energy Information Administration (2014): International Energy Outlook 2014, September 2014.

[26] Wendling, Z. A., Emerson, J. W., de Sherbinin, A., Esty, D. C., et al. (2020). 2020 Environmental Performance Index. New Haven, CT: Yale Center for Environmental Law & Policy.

[27] Xepapadeas, A. (1997): “Economic development and environmental pollution: traps and growth”, Structural Change and Economic Dynamics, 8(3), 327-350.
# Appendix

## Appendix 1: the profit of firms and their properties

The respective profits of (n) modern sectors, (m) of which invest in the new abatement technology can be written as:

$$ \pi^{mt} = ax_i - F - v\left[P - \frac{\bar{E}}{n-m}\right] = \frac{a}{k}R - F - v\left(P - \frac{\bar{E}}{n-m}\right), \quad (6) $$

$$ \pi^{mm} = ax_i - F - S = \frac{a}{k}R - F - S. $$

Recall that the profit of the competitive fringe in the market is zero.

By replacing $R = \frac{L-nF-nv(P-\frac{\bar{E}}{n-m})-m(S-v(P-\frac{\bar{E}}{n-m}))}{1-\frac{na}{k}}$ in $\pi^{mt}$, we obtain the profit of a dirty monopolist for any $n > m$:

$$ \pi^{mt} = \frac{aL - k(F + v(P - \frac{\bar{E}}{n-m})) - ma(S - v(P - \frac{\bar{E}}{n-m}))}{k - na}. \quad (7) $$

By replacing $R = \frac{L-nF-nv(P-\frac{\bar{E}}{n-m})-m(S-v(P-\frac{\bar{E}}{n-m}))}{1-\frac{na}{k}}$ in $\pi^{mm}$, we obtain the profit of a clean monopolist for any $n > m$:

$$ \pi^{mm} = \frac{aL - k(F + S) + na(S - v(P - \frac{\bar{E}}{n-m})) - ma(S - v(P - \frac{\bar{E}}{n-m}))}{k - na}. \quad (8) $$

The profit of a clean monopolist is lower than the profit of a dirty monopolist as long as $S > v(P - \frac{\bar{E}}{n-m})$. Conversely if $S < v(P - \frac{\bar{E}}{n-m})$, investment in clean technology leads to a higher profit.

**Remark 1** The profit of a dirty modern sector $\pi^{mt}$ is increasing in the number of clean modern sectors m if Assumption 2 is satisfied.

**Proof.** The profit of a dirty monopolist is $\pi^{mt} = \frac{a}{k}R - F - v(P - \frac{\bar{E}}{n-m})$ with $R = \frac{L-nF-nv(P-\frac{\bar{E}}{n-m})-m(S-v(P-\frac{\bar{E}}{n-m}))}{1-\frac{na}{k}}$. R is increasing with m given **Assumption 2**, $S < vP$. Consequently, $\frac{\partial\pi^{mt}}{\partial m} > 0$ given **Assumption 2**.

## Appendix 2: Incomplete and dirty modernization

The number of modern sectors $n_1^*$ is defined (see Figure 6) as when the profit of the marginal modern and dirty firm nullifies ($\pi_{mt} = 0$). Setting the numerator of $\pi^{mt} =$
$\frac{aLn-Fkn-vPnk+v\overline{E}1k}{(k-an)n}$ equal to zero and solving for $n$ allows us to derive $n_1^*$. It is equal to:

$$n_1^* = \frac{v\overline{E}}{vP - \frac{aL}{k} + F} \qquad (9)$$

We obtain $n_1^* > 0$ if $aL < k(vP + F)$. This specific number of industrialized sectors decreases with the regulation stringency $\overline{E}$ (low $\overline{E}$), unit emissions $P$ (high $P$), the level of the fixed cost of investment in production $F$ (high $F$) and the marginal abatement cost of the traditional abatement technology (high $v$). In contrast, $n_1^*$ increases with the size of the economy $L$ and the coefficient $a$ which plays the role of a macroeconomic multiplier. Note that $n_1^* \le k$ thanks to **Condition 1**, $aL \le k(v(P - \frac{\overline{E}}{k}) + F)$.

**Remark 2** The profit of a dirty modern sector $\pi^{mt}$ is a decreasing function of the number of modern sectors $n$ (with $\bar{n} < n < n_1^*$), if Condition 1, $aL \le k(v(P - \frac{\overline{E}}{k}) + F)$ holds.

**Proof.** Here, we ask the question if $\frac{d\pi^{mt}}{dn} < 0$ for $\bar{n} < n < n_1^*$.

$$\begin{aligned} \frac{d\pi^{mt}}{dn} &= \frac{(-k^2v\overline{E} + 2kv\overline{E}na + n^2a^2L - n^2akF - n^2akvP)}{n^2(-k + na)^2} \qquad (10) \\ &= \frac{v\overline{E}(-k^2 + 2kna) + n^2a(aL - kF - kvP)}{n^2(-k + na)^2} < \\ &\frac{v\overline{E}(-k^2 + 2kna) + n^2a(-v\overline{E})}{n^2(-k + na)^2} \quad \text{if Condition 1 holds.} \end{aligned}$$

$$\frac{d\pi^{mt}}{dn} < \frac{v\overline{E}[-k^2 + 2kna - n^2a]}{n^2(-k + na)^2}. \qquad (11)$$

$$\frac{d\pi^{mt}}{dn} < \frac{-v\overline{E}[(k - na)^2 - n^2a^2 + n^2a]}{n^2(-k + na)^2} = \frac{-v\overline{E}[(k - na)^2 + n^2a(-a + 1)]}{n^2(-k + na)^2} < 0. \qquad (12)$$

Remark 2 ensures the stability of the equilibrium.

## Appendix 3: Proof of Proposition 1

The proofs are deduced from the expressions of the profits. Adoption of the clean abatement technology requires the profit of a dirty modern sector to be positive, and the profit of a clean monopoly to be positive.

The profits of the dirty monopolist and the clean monopolist are respectively:
Figure 6: Incomplete and dirty equilibrium. ($\bar{n}$) is the number of dirty modern firms for which the environmental standard is just reached. In the first region (from $n = 1$ to $n = \bar{n}$), the profit of a dirty modern firm increases because the standard is not binding. In the second region (from $n = \bar{n}$ to $n = n_1^*$), the profit decreases because of the abatement cost. The industrialization stops at $n = n_1^* < k$ (incomplete and dirty equilibrium).

<figure><img src="image_7.png" /></figure>
$$ \pi^{mt} = \frac{aL - k(F + v(P - \frac{\bar{E}}{n-m}) - ma(S - v(P - \frac{\bar{E}}{n-m})))}{k - na}, \quad (13) $$

$$ \pi^{mm} = \frac{aL - k(F + S) + na(S - v(P - \frac{\bar{E}}{n-m})) - ma(S - v(P - \frac{\bar{E}}{n-m}))}{k - na}. \quad (14) $$

For a) and b), we set $m = 0$ in Equation 13. In case a), **Condition 1** leads to $\pi^{mt} < 0$. In case b), **Condition 3** leads to $\pi^{mt} > 0$.

For c), $F$ is replaced by $S + F$ in **Assumption 1**, leading to **Condition 4**: $aL > k(S + F)$.

## Appendix 4: Proof of Proposition 2

We seek whether it is possible to implement the following scheme: tax ($n_1^* - m$) dirty modern sectors at level ($t \frac{\bar{E}}{n_1^* - m}$) and subsidy $m$ clean modern sectors at level ($\sigma = t \frac{\bar{E}}{m}$) such that the tax-subsidy scheme is profitable for both the dirty modern and clean modern sectors:

$$ \pi^{mt}(\bar{E}, n_1^*) \le \pi^{mt}(\bar{E}, n_1^*, t) \quad (15) $$

$$ \Leftrightarrow v(P - \frac{\bar{E}}{n_1^* - m}) + t \frac{\bar{E}}{n_1^* - m} \le v(P - \frac{\bar{E}}{n_1^*}), $$

$$ \pi^{mm}(\bar{E}, n_1^*) \le \pi^{mm}(\bar{E}, n_1^*, t) $$

$$ \Leftrightarrow S - t \frac{\bar{E}}{m} \le v(P - \frac{\bar{E}}{n_1^*}). $$

We can show that such $t$ and $\sigma$ exist. The first inequality in equation 15 is equivalent to $\frac{t}{m} \le \frac{v}{n_1^*}$. If we take the equality $\frac{t}{m} = \frac{v}{n_1^*}$, and put it into the second inequality, we obtain $S \le vP$ which is satisfied thanks to **Assumption 2**. So the two equations are not contradictory, and $t$ and $\sigma$ exist.

## Appendix 5: Endogenous Emissions

We consider endogenous emissions proportional to production $P = \beta x_i$ with $\beta > 0$. The change consists of replacing $a$ by $(a - v\beta)$, and setting $P$ equal to 0.

In the incomplete and dirty industrialization equilibrium, the number of modern sectors $n_1^*$ is defined when the profit of the marginal modern and dirty firm nullifies ($\pi^{mt} = 0$):
$$ \pi^{mt} = \frac{a}{k}R - F - v\left(\frac{\beta R}{k} - \frac{\bar{E}}{n_1^*}\right) = \frac{a - v\beta}{k}R - F + \frac{v\bar{E}}{n_1^*} = 0, \quad (16) $$

$$ \text{with } R = \frac{L + v\bar{E} - n_1^*F}{1 - \frac{n_1^*(a - v\beta)}{k}}. $$

Solving for Equation 16 leads to: $n_1^* = \frac{v\bar{E}}{F - L\frac{a - v\beta}{k}}$.

## Appendix 6: Variable cost of the new abatement technology

We consider a clean abatement technology whose investment requires payment of a fixed cost (S) and a variable abatement cost $v'(P - \frac{\bar{E}}{n})$ with $v' < v$. This relationship means that the marginal abatement cost of a modern clean firm is lower than that of a modern dirty firm thanks to investment in the modern abatement technology. We assume that all modern firms emit pollution P, and the total pollution in excess of the emission standard $\bar{E}$ must be abated by all of the (n) firms in a uniform way. In this case, proposition 1 reads as follows.

Under **Assumption 1**, $aL - kF > 0$, and **Assumption 2'**, $S < (v - v')P$, there are three types of equilibrium:

a) Incomplete and dirty modernization defined by:

$$ aL \le k\left(v\left(P - \frac{\bar{E}}{k}\right) + F\right) \quad (\text{Condition 1}) $$

$$ S > (v - v')(P - \frac{\bar{E}}{k}) \quad (\text{Condition 2}). $$

b) Full and dirty modernization defined by:

$$ aL > k\left(v\left(P - \frac{\bar{E}}{k}\right) + F\right) \quad (\text{Condition 3}) $$

$$ S > (v - v')(P - \frac{\bar{E}}{k}) \quad (\text{Condition 2}). $$

c) Full and clean modernization defined by:

$$ aL > k\left(S + v'(P - \frac{\bar{E}}{k}) + F\right) \quad (\text{Condition 4}) $$

$$ S < (v - v')(P - \frac{\bar{E}}{k}) \quad (\text{Condition 5}) $$

The proof follows. We have $\pi^{mt} = \frac{aL - k(F + v(P - \frac{\bar{E}}{n}) - am(S - (v - v')(P - \frac{\bar{E}}{n}))}{k - an}$ (Equation E1), and $\pi^{mm} = \frac{aL - k(F + S + v'(P - \frac{\bar{E}}{n})) + a(n - m)(S - (v - v')(P - \frac{\bar{E}}{n}))}{k - an}$ (Equation E2).

For Proposition 1, a) and b), we set $m = 0$ in equation E1. In case a), **Condition 1** leads to $\pi^{mt} < 0$. In case b), **Condition 3** leads to $\pi^{mt} > 0$.

Proposition 1, c), in order to obtain $m = n$ and $\pi^{mm} > 0$, **Condition 4'** gives us a sufficient condition.
# Appendix 7: Dynamic case with capital accumulation

We provide a simple example to show that the conditions for clean development would be more restrictive in a dynamic model. A dynamic model would take account of the capital accumulation and/or pollution stock dynamics. Here, let us consider only the dynamics of capital accumulation to show that the analysis would be richer. Indeed a poverty trap would be more likely to appear in this case (as shown in Xepapadeas, 1997). We consider now a model with two stages and three sectors ($k = 3$), one of which remains traditional in order to guarantee a competitive fringe. Suppose that Assumptions 1 and 2 and Conditions 4 and 5 are satisfied so that clean development would be possible were the model static (one-period model). The timing of the game is as follows:

**Stage 1:** Decision of each of the two sectors to modernize their production or to remain in traditional production.

Assume that a monopoly in both sectors wants to emerge, then it borrows at an interest rate $r$ to invest in period 1 an amount $F$ in capital for the following period. In the first period, its profit is then equal to 0 because the capital investment will not be productive until the following period. Suppose that both sectors modernize and the sum of their emissions exceeds the emission standard, $2P > \bar{E}$.

**Stage 2:** Decision of each of the two modern sectors to modernize their abatement technology or not.

In the second period, the modern sectors have the choice either to abate using traditional technology or to abate using modern technology. The profit of each firm in the second period would then be equal to $\pi^{mm} = \frac{aL-3((1+r)F+S)}{3-2a}$. Then, this profit would be negative if the discount rate (interest rate $r$) was too high (a high interest rate can come either from a low capital endowment or from a high risk premium for the foreign lender). In that case neither of the two firms in the duopoly will have an interest in emerging. Then the economy would remain in a poverty trap while in the static model we would see clean development.