Optimal allocation of tradable emission permits under upstream-downstream strategic interaction

In this paper we analyze environmental regulation based on tradable emission permits in the presence of strategic interaction in an output market with differentiated products. We characterize firms' equilibrium behavior in the permits and in the output market and we show that both firms adopt "rival's cost-rising strategies". Then, we study the problem of the regulator that aims to maximize social welfare, proposing an efficient criterion to allocate permits between firms. We find that the optimal allocation criterion requires a perfect balance between the difference on firms' price-cost margins in the permits and the difference on firms' markups in the output market. In light of the previous result, we use a simulation to obtain the optimal allocation of permits between firms as a function of output market characteristics, in particular as a function of goods substitutability.