Ricardian Equilibrium with Stochastic Free Entry

The standard Ricardian model of competition has a fixed number of firms, each with limited capacity and differential exogenous costs or qualities. In this paper, we introduce a real entry process by formulating a multistage Ricardian equilibrium model with free entry and stochastic product qualities and costs. The set of active firms and their qualities and costs are determined by an equilibrium dynamic entry process in which an unlimited number of potential entrants face identical investment costs and prospects. In the first stage, each firm sequentially chooses whether or not to undertake a risky investment that determines its quality and cost. The process continues until no more firms wish to invest. In the second stage, the firms compete to sell their limited capacity to a fixed number of identical buyers. The resulting Ricardian stochastic free entry equilibrium has a number of interesting properties. Firms invest as long as the "marginally active" (i.e., worst sold) seller's quality (or cost) does not meet a critical threshold that does not depend on the realizations of the other active sellers or the number of units demanded. There are two possible equilibrium market structures. One structure involves excess sellers in which prices are determined by the cost and quality of the "marginally inactive" (i.e., best unsold) seller. The other structure involves the number of investing potential entrants just equal to the number of units demanded, and sellers charging prices equal to the buyers' value. Regardless of the market structure, the entry process and equilibrium are socially optimal. Surprisingly, demand increases either have no effect on prices or, more generally, lead to lower prices. Restricting sales by active sellers similarly cannot lead to higher prices because such supply restrictions induce entry investment that continues until a new entrant replaces the unit that was withheld from the market. In fact, it generally leads to lower prices. However, "warehousing" the marginally inactive (best unsold) unit is a profitable method of raising prices because it does not induce entry. In the limiting case of a large number of small sellers, the model nicely illustrates the distinction between short and long run competitive equilibrium, and the expected price converges to a long run supply price