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

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.

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:

$$\begin{aligned} \pi ^{mt}= & {}\; ax_{i}-F-v\left[P-\frac{\overline{E}}{n-m}\right]=\dfrac{a}{k}R-F-v\left(P-\dfrac{\overline{E}}{n-m}\right), \\ \pi ^{mm}= & {}\; ax_{i}-F-S=\dfrac{a}{k}R-F-S. \nonumber \end{aligned}$$

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

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

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

(7)

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

$$\begin{aligned} \pi ^{mm}=\frac{aL-k(F+S)+na\left(S-v\left(P-\dfrac{\overline{E}}{n-m}\right)\right)-ma\left(S-v\left(P-\dfrac{\overline{E}}{n-m}\right)\right)}{k-na}. \end{aligned}$$

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The profit of a clean monopolist is lower than the profit of a dirty monopolist as long as $S>v\left(P-\dfrac{\overline{E}}{n-m}\right).$ Conversely if $S < v\left(P-\dfrac{\overline{E}}{n-m}\right)$, 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 $\pi ^{mt}=\dfrac{a}{k}R-F-v\left(P-\dfrac{\overline{E}}{n-m}\right)$ with $R=\frac{L-nF-nv\left(P-\frac{\overline{E}}{n-m}\right)-m\left(S-v\left(P-\frac{\overline{E}}{n-m}\right)\right)}{1-\frac{na}{k}}.$ 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 $\pi ^{mt}=\frac{aLn-Fkn-vPnk+v\overline{E}_{1}k}{\left( k-an\right) n}$ equal to zero and solving for n allows us to derive $n_{1}^{*}$. It is equal to:

$$\begin{aligned} n_{1}^{*}=\frac{v\overline{E}}{vP-\dfrac{aL}{k}+F}. \end{aligned}$$

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Fig. 6

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

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 $\overline{n} < n < n_{1}^{*}$.

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

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$$\begin{aligned} \dfrac{d\pi ^{mt}}{dn}<\frac{v\overline{E}\left[ -k^{2}+2kna-n^{2}a\right] }{n^{2}(-k+na)^{2}}. \end{aligned}$$

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$$\begin{aligned} \dfrac{d\pi ^{mt}}{dn}<\frac{-v\overline{E}\left[ (k-na)^{2}-n^{2}a^{2}+n^{2}a\right] }{n^{2}(-k+na)^{2}}=\frac{-v\overline{E}\left[ (k-na)^{2}+n^{2}a(-a+1)\right] }{n^{2}(-k+na)^{2}}<0. \end{aligned}$$

(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:

$$\begin{aligned} \pi ^{mt}=\frac{aL-k(F+v(P-\frac{\overline{E}}{n-m})-ma(S-v(P-\frac{\overline{E}}{n-m}))}{k-na}, \end{aligned}$$

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$$\begin{aligned} \pi ^{mm}=\frac{aL-k(F+S)+na(S-v(P-\frac{\overline{E}}{n-m}))-ma(S-v(P-\frac{\overline{E}}{n-m}))}{k-na}. \end{aligned}$$

(14)

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 tax-subsidy scheme is profitable for both the dirty modern and clean modern sectors:

$$\begin{aligned} \pi ^{mt}(\overline{E},n_{1}^{*})\le & {}\; \pi ^{mt}(\overline{E},n_{1}^{*},t) \\\Leftrightarrow & {}\; v(P-\frac{\overline{E}}{n_{1}^{*}-m})+t\frac{\overline{E}}{n_{1}^{*}-m}\le v(P-\frac{\overline{E}}{n_{1}^{*}}), \nonumber \\ \pi ^{mm}(\overline{E},n_{1}^{*})\le & {}\; \pi ^{mm}(\overline{E},n_{1}^{*},t) \nonumber \\\Leftrightarrow & {}\; S-t\frac{\overline{E}}{m}\le v(P-\frac{\overline{E}}{n_{1}^{*}}). \nonumber \end{aligned}$$

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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 $\left( a-v\beta \right)$, 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 $(\pi ^{mt}=0):$ 

$$\begin{aligned} \pi ^{mt}= & {}\; \frac{a}{k}R-F-v(\frac{\beta R}{k}-\frac{\overline{E}}{n_{1}^{*}})=\frac{a-v\beta }{k}R-F+\frac{v\overline{E}}{n_{1}^{*}}=0, \\ \text {with }R= & {}\; \frac{L+v\overline{E}-n_{1}^{*}F}{1-\dfrac{n_{1}^{*}(a-v\beta )}{k}}\text {.} \nonumber \end{aligned}$$

(16)

Solving for Eq. 16 leads to: $n_{1}^{*}=\frac{v\overline{E}}{F-L\frac{a-v\beta }{k}}{}$.

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 $v^{\prime }\left(P-\frac{\overline{E}}{n}\right)$ 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, $aL-kF>0$, and Assumption 2’, $S<(v-v^{\prime })P$, there are three types of equilibrium:

• a) Incomplete and dirty modernization defined by:

  $$\begin{aligned}&aL\le k\left(v\left(P-\frac{\overline{E}}{k}\right)+F\right)\;(\mathrm{Condition\;1})\\&S>(v-v^{\prime })\left(P-\frac{\overline{E}}{k}\right)\;(\mathrm{Condition\;2'}).\end{aligned}$$

• b) Full and dirty modernization defined by :

  $$\begin{aligned}&aL>k\left(v\left(P-\frac{\overline{E}}{k}\right)+F\right)\;(\mathrm{Condition\;3})\\&S>(v-v^{\prime })\left(P-\frac{\overline{E}}{k}\right)\;(\mathrm{Condition\;2'}).\end{aligned}$$

• c) Full and clean modernization defined by :

  $$\begin{aligned}&aL>k(S+v^{\prime }\left(P-\frac{\overline{E}}{k}\right)+F)\;(\mathrm{Condition\; 4'})\\&S<(v-v^{\prime })\left(P-\frac{\overline{E}}{k}\right)\;(\mathrm{Condition\; 5'})\end{aligned}$$

The proof follows. We have $\pi ^{mt}=\frac{aL-k(F+v(P-\frac{\overline{E}}{n})-am(S-(v-v^{\prime })(P-\frac{\overline{E}}{n}))}{k-an}$ (Equation E1), and $\pi ^{mm}=\frac{aL-k(F+S+v^{\prime }(P-\frac{\overline{E}}{n}))+a(n-m)(S-(v-v^{\prime })(P-\frac{\overline{E}}{n}))}{k-an}$ (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, [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 (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, $2P>\overline{E}{}$.

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 $\pi ^{mm}=\frac{aL-3((1+r)F+S)}{3-2a}.$ 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.