1. Introduction
Being aware of the (probably) most serious threat to the sustainability of human being and society, Global Warming and Climate Change, many scientists and policy makers make enormous efforts to find the reason of, and remedy for, the threat. All in all, they agree that the explosive increase in greenhouse gas emissions from the consumption of fossil energy that fueled the growth engine of the world economy over the past several centuries poses a serious threat to sustainable growth. (According to the U.S. Environmental Protection Agency, fossil fuel-related carbon dioxide (CO
2) emissions contributed approximately 65 percent of the greenhouse gas emissions worldwide in 2010. In the United States, fossil energy combustion alone accounted for approximately 76 percent of total GWP-weighted emissions in 2014. The IPCC [
1] attributes approximately 78 percent of the explosive increase in greenhouse gas emissions from 1970 to 2010 to fossil energy consumption.) The limited and inelastic supply of fossil energy, (Krichene [
2] provides empirical evidence of the inelasticity of the supply of crude oil and natural gas.) coupled with each country’s competitive eagernesss for economic growth, gives us an irrefutable warning that the threat cannot be resolved without international cooperative efforts.
After the largest greenhouse gas trading program, the European Union Emission Trading Scheme (EU ETS) was implemented as an important turning point in the history of the actual and effective international cooperation for environmental regulations, so called “cap-and-trade” schemes have been widely spread out. (A plot phase of EU ETS was implemented from 2005, the year Japan’s Voluntary Emissions Trading Scheme (JVETS) was launched in 2008. The Korea Emission Trading Scheme (KETS) was begun in 2015. In addition, ten north-eastern states in the United States implemented the Regional Greenhouse Gas Initiative in 2015. The California Greenhouse Gas Solutions Act was signed into law in 2006, and adopted the cap-and-trade program to set the upper limit on statewide greenhouse gas emissions starting in 2010. To see more about EU ETS and US ETS, refer to Hintermann [
3] and Stavins [
4].)
However, no theoretical studies of what enables emission trading schemes to outperform Pigouvian taxation without administrative failure have thus far been undertaken. This paper attempts to close the gap between “theory” and “reality” by showing the former to be superior to the latter in terms of domestic and global surplus in a globalized setting with international trade of inputs and outputs. It also examines under what conditions international linkage of tradable permit markets improves global welfare as well as the domestic welfare of participating countries.
In the wake of seminal work by Pigou [
5], Pigouvian taxation was promulgated as a canonical approach to various environmental issues. The insightful theory implies that requiring polluting agents to internalize negative externalities enables the decentralized equilibrium to achieve the first best outcome. So-called Pigouvian taxation does not work properly, however, in the globalized situation in which an environmental policy of one government has heterogenous effects on domestic and foreign firms competing for inelastic supply of common input (e.g., fossil energy). In particular, we consider an international trade model in which both countries import fossil energy (input) and sell their final products (output) through the international market a la Cournot fashion. (Kiyono and Ishikawa [
6] assumes a perfectly competitive final goods market to explain why developed countries adopt emission trading, whereas developing countries prefer direct taxation.)
Consuming fossil fuels during the production process inevitably generates pollutants (greenhouse gas), which creates environmental damage and lowers domestic consumer surplus. This market failure justifies government intervention, which can be implemented either using Pigouvian taxation or cap-and-trade schemes. Suppose that both governments adopt the former scheme. A unilateral environmental tax cut by one major country that implements Pigouvian taxation in its own territory increases its demand for fossil energy and consequently the fossil energy price. Thus, it raises the marginal costs of foreign firms and discourages production of the other countries. As a result, each government competitively lowers its environmental tax rate below the globally efficient level. Motivated by the failure of Pigouvian taxation, this paper develops a simple three-stage decision game between two symmetric non oil-producing countries to evaluate the relative performance of the alternative scheme, “cap-and-trade” together. (We borrow the basic structure of the game from Sim and Lin [
7], who analyze a similar issue in the presence of cross border pollution.)
Each government chooses its environmental policy instrument, Pigouvian taxation or cap-and-trade, in the first stage, and, after observing the other’s choice, adjusts the strength of regulation (the tax rate if it adopted the former, or cap if the latter) in the second stage. Inputs are purchased and outputs produced by the firms in each country in the third stage. Reflecting recent discussions of the linkage of permit markets, this paper also examines the welfare implications of the permit market linkage that allows free international trade of those permits, no matter where they were originally issued. (The discussions can be found in Helm [
8], Copeland and Taylor [
9], Carbone, Helm, and Rutherford [
10], Flanchsland, Marschinski, and Edenhofer [
11], Ranson and Stavins [
12], and Doda and Taschini [
13].)
In the decentralized setting in which only Pigouvian taxation is implemented, each government competitively lowers its environmental tax rate to increase the marginal cost of and discourage production by foreign firms. In the decentralized setting in which cap-and-trade as well as Pigouvian taxation may be implemented, adopting the former scheme and announcing the cap (domestic production) without knowing the other country’s tax rate or cap preemptively neutralizes the adverse influence of the other country’s raising the rivals’ marginal cost strategy. It protects domestic production at the pre-committed level. Cap-and-trade outperforms Pigouvian taxation in terms of both global and domestic welfare because the associated “shield effect” expands each government’s control over domestic production.
Whereas the strategy of “raising the rival’s marginal cost,” which Sartzetakis [
14] mentioned, is competitively abused under the Pigouvian taxation, the aggressive effect of the strategy is simply nullified under the cap-and-trade scheme. However, neither of them reaches the first best outcome because the adverse influence exerted through the adjustment channel of the fossil energy price is not considered to lower domestic production for both countries as in the efficiency benchmark. As permit markets are linked such that permits are freely traded and used across borders, the marginal costs of all firms, regardless of location, respond to either country’s environmental policy in the same direction. If one country issues more permits, all firms’ marginal costs decline together. This synchronization leads each government to take into account foreign firms’ marginal costs, even though the linkage elicits competition between government for greater revenue. When the energy supply is sufficiently inelastic, linking permit markets improve both domestic and global welfare.
After Weitzman [
15], many studies have attempted to assess the relative advantages of Pigouvian taxation and emission trading in terms of “price control” versus “quantity control”. However, most, assuming complete regulation that maintains all polluting agents within a target (or direct treatment) set, conclude that the schemes provide equivalent incentives to reduce emissions. A concise, insightful survey of the literature is provided by Goulder and Schein [
16]. Relaxing the complete regulation assumption, Fowlie [
17] and Baylis, Fullerton and Karney [
18] examine the issue of “carbon leakage” consequent to incomplete regulation applied to only a subset of polluting agents. Assessing relative performance being an objective of neither study, however, both presume Pigouvian taxation and emission trading to work equivalently. In the study by Sim and Lin [
7], the competitive dominance of the emission trading scheme is derived by the commitment on cross border pollution to the neighboring country, which can be made by the government adopting the emission trading scheme. (Similarly, Hoel [
19] analyzes the transboundary pollution case with no explicit consideration of fossil fuel input. He concludes that each country choosing emission trading scheme holds as one of the Nash equilibria, while the present paper shows that it is a strictly dominant strategy unless the supply of fossil energy is perfectly elastic). The authors emphasize, on the basis of this setting, the significance of international cooperation and coordination in slowing down “global warming”.
An extensive literature considering fossil fuel, e.g., Liski and Tahvonen [
20], and Strand [
21], focused on the optimal emission(or fossil fuel) taxation rule by analyzing non-cooperative Nash Equilibrium between importer and exporter, assuming that there is no unilateral deviation by one importing country. The present paper contributes to the literature by allowing unilateral deviation of an individual country and providing a detailed analysis of each (fossil fuel) importing country’s strategy. It is because the latter scheme neutralizes the negative influence of raising the rival country’s marginal cost strategy through the international price of fossil energy, which improves domestic welfare in a globalized setting.
The paper proceeds as follows. In
Section 2, we introduce the theoretical framework, in
Section 3, we perform efficiency analyses on each pair of environmental policies. The dominant strategy equilibrium is presented in
Section 4, and the linkage issue is discussed in
Section 5.
Section 6 concludes the paper.
3. Efficiency Analysis
We first settle the efficiency benchmark by denoting as
the socially efficient allocation by the social planner, who maximizes the global surplus of the economy
by directing the quantity of final goods
to individual firms in each country. The planner’s decisions regarding output in country
, and, in the entire global economy, are denoted by
and
, respectively. The planner chooses
to maximize
Alternatively, consider the problem of the “constrained” planner who, taking (global) imperfect competition among firms as given, maximizes the global welfare by imposing taxes
. Rewriting (
3) yields
Plugging the first best allocation
by the unconstrained planner into (
12) yields
, which implies that the constrained planner can implement the first best outcome by imposing
. In other words, the potential efficiency loss from international imperfect competition can be controlled by allowing the constrained planner two policy tools,
. To implement the cap-and-trade scheme in country
, the constrained planner can issue
number of permits, such that
solves the market clearing condition in (
7), given
. Lemma 2 concludes that decentralizing the production decision and introducing Cournot competition among individual firms causes no efficiency loss, whether the constrained planner implements “price control” or “quantity control.”
Lemma 2. There exists a unique solution of in the unconstrained planner’s problem. The constrained planner can also achieve the first best allocation of , whether price control or quantity control is implemented.
The unconstrained as well as constrained planner implements the pair,
, such that
In Equation (
13), the left-hand side captures the sum, in each country, of the marginal consumer’s willingness to pay. The right-hand side captures both countries’ marginal social costs, marginal production cost, and environmental damage. The last term captures an increase in foreign firms’ cost consequent to one country’s increase in domestic production, and input price, which typically cannot be considered in a decentralized equilibrium. (An exception, described later, is the case in which permit markets are linked internationally.) Note that
, which renders the right-hand side of (
13) greater than that of (
10) for any
. The left-hand side of (
13) being strictly decreasing in
, the right-hand side is strictly increasing and the optimal allocation of
well defined.
We now decentralize the second stage decision by each government. When both countries implement Pigouvian taxation, total output
should solve for
When country
A implements cap-and-trade and country
B Pigouvian taxation, total output
should solve for
In Equations (
10) and (
13)–(
15), the left-hand sides are the same and strictly decreasing in
, the right-hand sides different and strictly increasing in
. (Without loss of generality, we can obtain
by restricting attention to the symmetric solution. We can then, with a small abuse of notation, define
instead of
.) The intersection points can be ordered thus:
. The equality holds only when
.
Figure 1, by restricting attention to the symmetric solution, such that
, summarizes the output price, quantity, and global welfare for each case. (The second order sufficient condition globally holds, which implies that there exists a unique optimum. It also predicts that “the closer (to the optimum point), the better welfare”.) The second order sufficient condition of the social planner being globally satisfied, the following welfare implication is obtained.
Lemma 3. Unless the supply of fossil energy is perfectly elastic , In the special case with perfectly elastic supply of fossil energy , 4. Decentralized Equilibrium
We show in this section that adopting the cap-and-trade scheme in the first stage is the strict dominant strategy for each country. We do so by examining which policy instrument accrues greater domestic surplus to one country when the other country adopts Pigouvian taxation first and the cap-and-trade scheme later. We focus in this section on the nontrivial case with . (One can readily infer that if , both policy instruments yield the same outcome.)
Without loss of generality, suppose that country
B adopts the Pigouvian taxation scheme. If country
A adopts Pigouvian taxation as well, both countries competitively lower their tax rates. That a decrease in one country’s tax rate, by increasing the input price (Sartzetakis [
14] analyzes the welfare implication of “raising rivals’ cost strategies” in the permit market of an autarky economy. Dertwinkel-Kalt, Haucap, and Wey [
24] recently applied “raising rivals’ cost strategies” to the input price discrimination issue in an autarky setting), encourages domestic production and discourages foreign production, leading each government to maintain its tax rate at an inefficiently low level.
Country A, if it adopts instead the cap-and-trade scheme, nullifies the negative influence from the foreign environmental policy and protects the domestic production through direct “quantity control.” Country B optimally adjusts its tax rate by putting more weights on domestic environmental damage. The cap-and-trade scheme gives an effective “shield” to the adopting country, which discourages the other country’s aggressive policy. Lemma 4 shows the cap-and-trade scheme by country A to accrue a larger domestic surplus to the adopting country than to the other country adopting Pigouvian taxation, and to perform better than the Pigouvian taxation scheme, although whether remains ambiguous.
Lemma 4. Suppose, without loss of generality, that country B implements the Pigouvian taxation scheme. When country A adopts the cap-and-trade scheme, Greater domestic surplus accrues to country A when it adopts cap-and-trade than when it adopts Pigouvian taxation .
Suppose that country B adopts the cap-and-trade scheme. It makes a commitment on the amounts of input to purchase and output to produce. The government in country A realizes that its raising the rival’s marginal cost strategy does not work and that its adoption of the cap-and-trade scheme induces country B to strengthen its environmental regulation in response to the same consideration. The “shield effect" of cap-and-trade scheme, by nullifying the raising rival’s marginal cost strategy of the opponent, encourages the opponent government to put more weights on its environmental damages and raise their emission price. Lemma 5 shows that, when country B adopts the cap-and-trade scheme, country A can expand its domestic surplus by implementing the cap-and-trade rather than the Pigouvian taxation scheme.
Lemma 5. Suppose, without loss of generality, that country B implements the cap-and-trade scheme. When country A implements the cap-and-trade scheme as well, a unique symmetric outcome is obtained, and country A’s surplus is greater when it chooses the cap-and-trade over the Pigouvian taxation scheme .
Lemmas 4 and 5 jointly imply that adopting the cap-and-trade scheme is the strict dominant strategy of each country, and, together with Lemma 3, imply that global surplus is maximized when both countries adopt the cap-and-trade scheme. In particular, Lemma 5 proves the existence and uniqueness of the decentralized equilibrium. Proposition 1 summarizes this result.
Proposition 1. Unless the supply of fossil fuels is perfectly elastic, it is the strictly dominant strategy for each country to implement the cap-and-trade scheme. Global surplus is maximized when all countries choose their own strict dominant strategy.
Proof. This is straightforward from Lemmas 3–5. □
Although the cap-and-trade scheme has been widely adopted, many countries still rely on Pigouvian taxation. The novel point of Lemma 3 and Proposition 1 is that global surplus can improve without technological innovation. (One aspect we leave to future research is to extend our model to a dynamic setting with technological innovation. See Biglaiser, Horowitz, and Quiggin [
25], Fischer [
26], Weber and Neuhoff [
27], Kim and Lee [
28], D’Amato and Dijkstra [
29], and Sim and Hong [
30] for various issues regarding technological innovation.) This point raises one more relevant question, “whether the market equilibrium can achieve the first best outcome”. It is discussed in the following section.