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 taxsubsidy 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.
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Notes
Our 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.
As 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.
The 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.
When (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: \(R(n)=\frac{k(LnF)}{kna}\).
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.
In Appendix 5, we relax this assumption to consider endogenous emissions proportional to production. We discuss this extension in section 5 (Concluding remarks).
This 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 [10]. Thus, we exclude learning or imitation possibilities across sectors.
Here 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 \(v\prime\) less than v, we obtain similar results but based on more complex calculation (see Appendix 6).
\((F+S)\) represents the cost of investment in a cleaner (e.g., a more energy efficient) production technology.
The equilibria presented are Nash equilibria: No firm has any interest in deviating from them. These equilibria resemble “coupled constraint Nash equilibria” à la Rosen [24] and applied to an environmental compliance problem by Krawczyk [25], 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.
Middle 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).
The World Bank classifies Argentina as an uppermiddle/high income country, Tunisia as a lowermiddle/uppermiddleincome country, and India as a low/lowermiddleincome country based on gross national income per capita (https://datatopics.worldbank.org/worlddevelopmentindicators/stories/theclassificationofcountriesbyincome.html).
The budget constraint is balanced because the collection of the tax is equal to \(T=(n_{1}^{*}m)\left( t\dfrac{\overline{E}}{n_{1}^{*}m}\right) =t\overline{E},\) and the revenue from the tax is redistributed equally in the form of a subsidy \(\sigma\) to each clean sector: \(\sigma =\dfrac{T}{m}=\dfrac{t\overline{E}}{m}{}\).
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Acknowledgements
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 (JuneJuly 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”.
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Appendices
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:
Recall that the profit of the competitive fringe in the market is zero.
By replacing \(R=\frac{LnFnv\left(P\frac{\overline{E}}{nm}\right)m\left(Sv\left(P\frac{\overline{E}}{nm}\right)\right)}{1\frac{na}{k}}\) in \(\pi ^{mt}\) , we obtain the profit of a dirty monopolist for any n > m:
By replacing \(R=\frac{LnFnv\left(P\frac{\overline{E}}{nm}\right)m\left(Sv\left(P\frac{\overline{E}}{nm}\right)\right)}{1\frac{na}{k}}\) in \(\pi ^{mm}\), we obtain the profit of a clean monopolist for any n > m:
The profit of a clean monopolist is lower than the profit of a dirty monopolist as long as \(S>v\left(P\dfrac{\overline{E}}{nm}\right).\) Conversely if \(S < v\left(P\dfrac{\overline{E}}{nm}\right)\), 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 \(\pi ^{mt}=\dfrac{a}{k}RFv\left(P\dfrac{\overline{E}}{nm}\right)\) with \(R=\frac{LnFnv\left(P\frac{\overline{E}}{nm}\right)m\left(Sv\left(P\frac{\overline{E}}{nm}\right)\right)}{1\frac{na}{k}}.\) R is increasing with m given Assumption 2, S < vP. Consequently, \(\dfrac{\partial \pi ^{mt}}{\partial m}>0\) given Assumption 2.
Appendix 2: Incomplete and Dirty Modernization
The number of modern sectors \(n_{1}^{*}{}\) is defined (see Fig. 6) as when the profit of the marginal modern and dirty firm nullifies \((\pi _{mt}=0).\) Setting the numerator of \(\pi ^{mt}=\frac{aLnFknvPnk+v\overline{E}_{1}k}{\left( kan\right) n}\) equal to zero and solving for n allows us to derive \(n_{1}^{*}\). It is equal to:
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, \(aL\le k\left(v\left(P\frac{\overline{E}}{k}\right)+F\right)\).
Remark 2
The profit of a dirty modern sector \(\pi ^{mt}{}\) is a decreasing function of the number of modern sectors n (with \(\overline{n} < n < n_{1}^{*}\)), if Condition 1, \(aL\le k\left(v\left(P\frac{\overline{E}}{k}\right)+F\right)\) holds.
Proof
Here, we ask the question whether \(\dfrac{d\pi ^{mt}}{dn}<0\) for \(\overline{n} < n < n_{1}^{*}\).
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:
For a) and b), we set m = 0 in Eq. 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 \(\left( n_{1}^{*}m\right)\) dirty modern sectors at level \(\left( t\dfrac{\overline{E}}{n_{1}^{*}m}\right)\) and subsidy m clean modern sectors at level \(\left( \sigma =t\dfrac{\overline{E}}{m}\right)\) such that the taxsubsidy scheme is profitable for both the dirty modern and clean modern sectors:
We can show that such t and \(\sigma\) exist. The first inequality in Eq. 15 is equivalent to \(\dfrac{t}{m}\le \dfrac{v}{n_{1}^{*}}.\) If we take the equality \(\dfrac{t}{m}=\dfrac{v}{n_{1}^{*}},\) 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 \(\left( av\beta \right)\), 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 \((\pi ^{mt}=0):\)
Solving for Eq. 16 leads to: \(n_{1}^{*}=\frac{v\overline{E}}{FL\frac{av\beta }{k}}{}\).
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 \(v^{\prime }\left(P\frac{\overline{E}}{n}\right)\) with \(v^{\prime }< v\). 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 \(\overline{E}\) must be abated by all of the (n) firms in a uniform way. In this case, proposition 1 reads as follows.
Under Assumption 1, \(aLkF>0\), and Assumption 2’, \(S<(vv^{\prime })P\), there are three types of equilibrium:

a)
Incomplete and dirty modernization defined by:
$$\begin{aligned}&aL\le k\left(v\left(P\frac{\overline{E}}{k}\right)+F\right)\;(\mathrm{Condition\;1})\\&S>(vv^{\prime })\left(P\frac{\overline{E}}{k}\right)\;(\mathrm{Condition\;2'}).\end{aligned}$$ 
b)
Full and dirty modernization defined by :
$$\begin{aligned}&aL>k\left(v\left(P\frac{\overline{E}}{k}\right)+F\right)\;(\mathrm{Condition\;3})\\&S>(vv^{\prime })\left(P\frac{\overline{E}}{k}\right)\;(\mathrm{Condition\;2'}).\end{aligned}$$ 
c)
Full and clean modernization defined by :
$$\begin{aligned}&aL>k(S+v^{\prime }\left(P\frac{\overline{E}}{k}\right)+F)\;(\mathrm{Condition\; 4'})\\&S<(vv^{\prime })\left(P\frac{\overline{E}}{k}\right)\;(\mathrm{Condition\; 5'})\end{aligned}$$
The proof follows. We have \(\pi ^{mt}=\frac{aLk(F+v(P\frac{\overline{E}}{n})am(S(vv^{\prime })(P\frac{\overline{E}}{n}))}{kan}\) (Equation E1), and \(\pi ^{mm}=\frac{aLk(F+S+v^{\prime }(P\frac{\overline{E}}{n}))+a(nm)(S(vv^{\prime })(P\frac{\overline{E}}{n}))}{kan}\) (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, [4]). 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 (oneperiod 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, \(2P>\overline{E}{}\).
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 \(\pi ^{mm}=\frac{aL3((1+r)F+S)}{32a}.\) 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.
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Bayramoglu, B., Jacques, JF. Is Clean Development Always Possible? The Role of Environmental Policy in Developing Countries in the Presence of Aggregate Demand Spillovers. Environ Model Assess 27, 139–153 (2022). https://doi.org/10.1007/s10666021097719
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DOI: https://doi.org/10.1007/s10666021097719