Advance sales and deterrence with heterogeneous firms, with Sébastien Mitraille.
We examine the effects of firm heterogeneity when firms can compete in advance for future demand by either entering forward contracts or by selling to agents that store the good to meet future demand. Firms' sales in the second period are reduced by aggregate advance sales, so high-cost firms may produce zero output in equilibrium if aggregate advance sales induce a price below their marginal cost. The endogenous number of active firms leads to the possibility of a deterrence equilibrium in which lower-cost firms act to deter the activity of higher-cost firms. In this case, the presence of inactive higher-cost firms in the market results in a lower price than would otherwise obtain. In addition, the advance sales equilibrium with heterogeneous firms has higher market shares for relatively efficient firms compared to that in both the heterogeneous firm Cournot equilibrium and the homogeneous firm advance sales equilibrium. Consequently, the equilibrium outcome results in industry output produced at a lower average cost, which represents an additional welfare gain associated with the pro-competitive effects of strategic advance sales even though the reallocation of market shares leads to higher measured concentration.