This paper develops a model of quality determination where the usual competitive equilibrium conditions hold. The explicit form of quality considered is the wait required to obtain the product. The analysis, however, is much more general, being valid for products that have a characteristic, z, such that (1) demand is a function of price and a measure defined on z, (2) costs are a function of output and the measure on z, and (3) z is a function of output and capacity. Expected profit-maximizing firms, in equilibrium, look like monopolistic competitors. Once constant quality is imposed, however, the perfect competitive results obtain.

Arthur S. De Vany, Wendy L. Gramm, Thomas R. Saving, Charles W. Smithson, Production in a Service Industry Using Customer Inputs: A Stochastic Model, The Review of Economics and Statistics, Vol. 65, No. 1 (Feb., 1983), pp. 149-153

What causes individual suppliers to allocate goods in such a way that the aggregate allocation satisfies the law of one price? A satisfactory answer to this question must confront two related problems: Equal net prices at all allocations provide no information to suppliers about the quantity to deliver to a specific location, and strategic uncertainty makes an observed violation of the law of one price an unreliable indicator of a profit opportunity. This paper develops a simple analytical framework to formalize these two problems, reviews some solutions found in the literature, and reports laboratory evidence on how people solve them. In addressing these issues, we focus on the role historical prices play in coordinating decentralized allocation decisions.

What causes individual suppliers to allocate goods in such a way that the aggregate allocation satisfies the law of one price? A satisfactory answer to this question must confront two related problems: Equal net prices at all allocations provide no information to suppliers about the quantity to deliver to a specific location, and strategic uncertainty makes an observed violation of the law of one price an unreliable indicator of a profit opportunity. This paper develops a simple analytical framework to formalize these two problems, reviews some solutions found in the literature, and reports laboratory evidence on how people solve them. In addressing these issues, we focus on the role historical prices play in coordinating decentralized allocation decisions.