A Comparison of Two-Market Bertrand Duopoly and Two-Market Cournot Duopoly

In a two-market Bertrand duopoly,each of two firms chooses one of two markets and a price in that market. All four choices are made simultaneously. In a two-market Cournot duopoly, the firms choose quantities rather than prices.It is well known that in the one-market case the threat of price undercutting means that Bertrand equilibrium prices and profits will be lower and quantities higher than Cournot equilibrium prices, profits and quantities.We find a quite different consequence of price undercutting in two-market duopoly. In the two-market case the threat of price undercutting means that Bertrand equilibria are in continuous mixed strategies, while every Cournot duopoly has an equilibrium in pure strategies, or in strategies that are pure in each market.

Emissions Control and the Regulation of Product Markets: The Case of Automobiles

The paper investigates alternative policies to regulate emissions from polluting product markets, specifically considering the case of the automobiles market. The two policies we consider are: a quota that limits the quantity produced of the polluting model and a more flexible average efficiency standard that requires a minimum energy efficiency across all models produced by a firm, similar to the US Corporate Average Fuel Economy (CAFE) standards. We use a duopoly model of vertical differentiation where firms produce both an economy (i.e., low polluting) version and a luxury (i.e., high polluting) version of a given product. We show that while a quota can raise firm profit over a certain range, CAFE always reduces firm profit relative to the pre-regulation. We also show that while the quota reduces emissions, it is possible that emissions increase under CAFE. The optimal policy choice will depend on the magnitude of unit damages. We show that when unit damages are sufficiently high, the quota policy is more efficient than the average efficiency standard. This suggests that instead of tightening CAFE to limit damages from emissions, policy makers can shift to a quota policy which is both welfare enhancing and more profitable for firms.