Advance sales and deterrence with heterogeneous firms

We examine the e?ects of ?rm heterogeneity when ?rms 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 ?rms may produce zero output in equilibrium if aggregate advance sales induce a price below their marginal cost. The endogenous number of active ?rms leads to the possibility of a deterrence equilibrium in which lower-cost ?rms act to deter the activity of higher-cost ?rms. In this case, the presence of inactive higher-cost ?rms in the market results in a lower price than would otherwise obtain. In addition, the advance sales equilibrium with heterogeneous ?rms has higher market shares for relatively e?cient ?rms compared to that in both the heterogeneous ?rm Cournot equilibrium and the homogeneous ?rm 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 e?ects of strategic advance sales even though the reallocation of market shares leads to higher measured concentration.