Limit Pricing and Uncertain Entry - Kamien, Morton I.; Schwartz, Nancy L. (Econometrica, 1971)
The situation in which a seller is aware that his pricing policy will affect the probability of entry of competing suppliers is studied. The seller's optimal policy is developed under the assumption that the entry probability is a non-decreasing function of product and that the objective is present value maximization. It is shown that the optimal pre-entry tends to fall as the discount rate drops, the market growth rate rises, the post-entry profit possibilities decline, or certain non-price barriers to entry fall. ECONOMISTS HAVE LONG known that maximizing immediate profits is often not the optimal strategy for a firm to pursue if its planning horizon extends beyond the present. A policy for achieving the highest overall reward may dictate the sacrifice of some current gain. This point has played a central role in the development of the theory of a The theory deals with determination of the entrypreventing by a supplier of a market when potential entrants exist. The supplier in question may be a firm or a group of (tacitly) cooperating firms. The high short term profits associated with the pursuit of monopoly pricing must be balanced against the loss of long term profits upon entry of additional suppliers attracted by the high price. In an early paper formalizing the problem, Bain [2] defined the price as the highest that the established sellers can set without inducing entry. Modigliani [9] developed a graphical derivation of the limit and analyzed a number of its determinants. Fisher [6] related these results to Cournot's duopoly model. Recent contributors include Pashigian [10] and Dewey [5]. On the other side of the Atlantic, Harrod [7], in an attack on the doctrine of excess capacity, argued that a long-run profit maximizing firm would set to preclude entry. According to Hicks' [8] formalization of Harrod's argument, the firm seeks maximization of a weighted sum of short-run and long-run profits, with the relative weights reflecting the firm's attitudes regarding these periods. It follows from this that the firm may not set at its entry preventing level. Explicit criticism of the limit concept has not been lacking. Williamson [13], while extending the concept of a limit to a limit price-selling cost frontier, suggested that the deterministic framework be modified to a probabilistic one. In proposing a stochastic approach, he noted that the limit theory is highly rigid, with a single point or curve dividing certain entry from no entry. Williamson also observed that the assumed optimality of the limit implied that the firm would be willing to prevent entry at any cost. Stigler [12, p. 227] has pointed out that the attractiveness of entry will depend not only upon the current rate of return to the industry, but also upon the anticipated rate of growth of industry demand. If the latter is large, then the present value of future profits may be sufficiently large