Selective Penalization Of Polluters: An Inf-Convolution Approach

In this paper, we consider an asymmetric polluting oligopoly: firms have different production costs, and their pollution characteristics may also be different. We will demonstrate that, in this case, optimal tax rates per unit of emission are not the same for all firms. We call this property ``selective penalization'', or ``favoritism in penalties.'' Thus, the ``efficiency'' objective may be served only at the expense of ``fairness'. One of our main results is the Optimal Distortion Theorem.. We show that even in the case w here the rates of emission per unit of output are identical for all firms, the efficient tax structure requires that high cost firms pay a higher tax rate on emissions. Our result implies that the efficient tax structure favors the efficient firms, but the magnitude of the favors is a decreasing function of the marginal cost of public fund. Another characterization of optimal tax structure is our Pro-concentration Motive Theorem. Optimal taxes penalize the inefficient firms more, and thus increases the concentration of the industry, as measured by the Herfindahl index. In fact, we show that the variance of the distribution of the firms' tax-inclusive marginal costs after the imposition of efficient taxes exceeds the variance that would be obtained if there were no taxes. We call this the Magnification Effect: the variance of marginal costs is magnified by a factor which depends on the marginal cost of public fund. On modélise un oligopole hétérogène : les firmes ont des coûts différents et des paramètres de pollution différents. On montre que les taux de taxes optimales imposées sur les émissions ne sont pas les mêmes. On appelle cette propriété la pénalisation sélective. Il existe donc un conflit entre l'équité et l'efficacité. Le résultat principal de notre article est Le Théorème de la Distorsion Optimale. La structure des taxes optimales exige que les firmes aux coûts les plus élevés paient les taxes les plus élevées. Un autre résultat s'appelle le Théorème sur le motif pro-concentration.