Two Remarks on Cournot Equilibria

Making the weak assumption that the left-hand side of this equation is downward sloping, there will be a unique Y that solves this equation, which depends only on the sum of the marginal costs, not on their distribution across the firms. The observation that output and price in a Cournot industry is independent of the distribution of marginal costs has undoubtably been noted and used several times in the literature. See for example, Dixit and Stern (1982) Katz (1984) Loury (1983) or Bergstrom and Varian (n.d.). Note that the same independence result holds in any conjectural variations model, as long as all firms have the same conjectural variation and we consider only interior equilibria. The latter condition becomes increasingly important as the market equilibrium approaches a competitive structure, since in that case only the low cost producer will produce a positive amount. Here we consider an application of this result to a taxation problem. Suppose that each of the n firms in the industry faces a quantity tax t,. Then this tax is just the same as a marginal cost, so we can apply the above result to show that the equilibrium output and price is independent of the distribution of taxes across the firms. Furthermore, if we make a tax change (At,) that preserves the sum of the taxes, we must satisfy the first-order condition