Abstract
A critical issue in designing a system of tradable emission permits concerns the distribution of the initial pollution rights. The purpose of this paper is to investigate how the initial rights should be optimally set, when the determination of the number of tradable permits is subject to the influence of interest groups. According to the Coase theorem, in the case where there are low transaction costs, the assignment of the initial rights does not affect the efficiency of the final resource allocation. In the presence of political pressure, we show that the distribution of the initial rights has a significant effect on social welfare. In contrast to the conventional results, we find that grandfathered permits may be more efficient than auctioned permits, even after taking into consideration the revenue-recycling effect.
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The author is grateful to two anonymous reviewers and the editor Professor Gregory Poe for helpful comments. The remaining errors are the author’s sole responsibility.
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Appendix
Appendix
(A) The derivation of Equation (14)
Differentiating Π i with respect to E yields
According to Equations (2) and (3), the first term of the above equation will equal zero, and the second term and the fifth term will cancel out. Thus the MWTC of industry i can be reduced to
(B) The Proof of Lemma 1
Proof. Differentiating Equation (11) with respect to E yields: ∂W/∂E = τ − D′(E). The optimal E that maximizes the social welfare function requires that ∂W(E*)/∂E = τ* − D′(E*) = 0. The comparative-static result shows that dE*/dλ = − (∂W2/∂E ∂λ)/ (∂2W/∂E2). The denominator is equal to dτ/dE = D′′ < 0, whereas the numerator is equal to zero. Therefore, E* is independent of λ. Furthermore, the effect of changing λ on the social welfare is given by:
Clearly, the second term on the right-hand side of the above equation is equal to zero. Rearranging Equation (11) yields \(\sum_i f_i -w\sum_i x_i -<$> <$>\sum_i A_i + n_c y_c + n_g y_g - D(E)\), so ∂W/∂λ is equal to zero. Thus we prove that the maximum of social welfare is also independent of λ. □
(C) The Proof of Lemma 2
Proof. We will prove this by contradiction. Suppose not, i.e. when τ° < D′(E°), E° ≤ E* and τ° ≥ τ*. Since D′′ > 0, according to E° ≤ E*, we know that D′(E°) ≤ D′(E*). When E = E*, the marginal damage from pollution will be equal to the socially optimal permit price, that is D′(E*) = τ*. By combining this equation with the inequality D′(E°) ≤ D′(E*) and τ° ≥ τ*, we obtain D′(E°) ≤ τ* ≤ τ°. Clearly, this contradicts the premise τ° < D′(E°), and thus we can prove that τ° < D′(E°) implies that E° > E* and τ° < τ*. The other case can be proved in a similar way. □
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Lai, YB. The Optimal Distribution of Pollution Rights in the Presence of Political Distortions. Environ Resource Econ 36, 367–388 (2007). https://doi.org/10.1007/s10640-006-9020-4
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DOI: https://doi.org/10.1007/s10640-006-9020-4