Optimal profits under environmental regulation: the benefits from emission intensity averaging

Abstract

In this paper we analyze the economic effects of implementing EPA’s newly proposed regulations for carbon dioxide ($\hbox {CO}_2$) on existing U.S. coal-fired power plants using nonparametric methods on a sample of 144 electricity generating units. Moreover, we develop an approach for evaluating the economic gains from averaging emission intensities among the utilities’ generating units, compared to implementing unit-specific performance standards. Our results show that the implementation of flexible standards leads to up to 2.7 billion dollars larger profits compared to the uniform standards. Moreover, we find that by adopting best practices, current profits can be maintained even if an intensity standard of 0.88 tons of $\hbox {CO}_2$ per MWh is implemented. However, our results also indicate a trade-off between environmental and profit gains, since aggregate $\hbox {CO}_2$ emissions are higher with emission intensity averaging than with uniform standards.

Appendix

Proof of the equivalence of the JP and the MB model:

To start consider the profit optimization subject to the non-convex JP model:

(4.1)

In the optimum $x^P=\sum _{j=1}^n x_j^{P} \lambda _j$ and $y = \sum _{j=1}^n y_j \lambda _j\theta$ hold since $x^P$ and y can be freely chosen and $b=\sum _{j=1}^n b_j \lambda _j\theta$ by construction. Moreover, $\theta$ can be set equal to one since y and b can be freely chosen. Replacing the modified equalities in the objective function and the regulatory constraint leads to:

(4.2)

The optimization problem under the non-convex MB model is given by:

(4.3)

In this formulation the slack on the good output $\epsilon _y$ is removed and the equality replaced by an inequality since the output in our analysis (electricity) does not contain any materials. In the optimum $\epsilon _x=\epsilon _b=0$ since $x^P$ and b can be freely chosen. Hence, $x^P=\sum _{j=1}^n x_j^{P} \lambda _j$ and $b=\sum _{j=1}^n b_j \lambda _j$. Moreover, $y=\sum _{j=1}^n y_j \lambda _j$ since y can be freely chosen. Replacing these equalities in the objective function and the regulatory constraint leads to:

(4.4)

Therefore, the JP and the MB model lead to the same results for the profit maximization.