José M. Usategui

The Shapley value and average convex games

In this paper we reformulate the necessary and sufficient conditions for the Shapley value to lie in the core of the game. Two new classes of games, which strictly include convex games, are introduced: average convex games and partially average convex games. Partially average convex games, which need not be superadditive, include average convex games. The Shapley value of a game for both classes is in the core. Some Cobb Douglas production games with increasing returns to scale turn out to be average convex games. The paper concludes with a comparison between the new classes of games introduced and some previous extensions of the convexity notion.

NON-STATIONARY DEMAND IN A DURABLE GOODS MONOPOLY

In a context where demand for the services of a durable good changes over time, and this change may be uncertain, we show in this paper that social welfare may be higher when the monopolist seller can commit to any future price level he wishes than when he cannot. Moreover, the equilibrium under a monopolist with commitment power may Pareto-dominate the equilibrium under a monopolist without commitment ability. These results affect the desired regulation of a durable goods monopolist in this context.

Time Structure of Emissions and Comparison Between the Optimal Emission Taxes Under Selling and Under Renting in Durable Goods Oligopolies: Time Structure of Emissions and Comparison between Optimal Emission Taxes

We compare the optimal emission taxes on selling firms and on renting firms in a model of a durable†goods oligopoly considering three types of emissions: emissions at production, emissions during use and emissions at disposal. We find that the optimal emission tax in the present may be lower when firms sell their output than when they rent their output if emissions are during use or at the disposal of the good. When emissions occur at production that optimal emission tax is higher on selling firms than on renting firms. Moreover, the total expected optimal emission tax per unit produced in the present is higher on selling firms than on renting firms for any of the three types of emissions considered. We provide intuition for these results.

Timing of Emissions and Effects of Emission Taxes in Durable-Goods Oligopolies

Abstract Given an oligopoly of firms that produce and sell a durable good that causes pollution at production, during use or at disposal, the effects of present and future emission taxes on quantities, emissions, consumer surplus, producer surplus and the sum of consumer and producer surpluses and the revenue from emission taxes for each type of emission are analyzed. Among other results, it is proved that producers may support an increase in the emission tax in the future or in the present, that emissions in the present may be increasing in the emission tax in the future and that the timing of emissions may affect the directions of some effects of a change in an emission tax on welfare variables. The results obtained are based on the interaction between present and future emission taxes, the intertemporal effects of such taxes, imperfect competition, the strategic behavior of each firm in stealing sales from its rivals in the present and in the future, the type of emission and the producers’ commitment problem. The analysis is extended to the cases of monopoly and perfect competition.