Learning and Capacity Expansion under Demand Uncertainty

Abstract

A competitive, dynamic model of entry into a new industry is set up and both its positive and normative aspects are studied. The main assumptions are that entry is sequential, that it occurs under imperfect information on the size of the market and that better information becomes available as goes on. The gradual improvement in information is due to the fact that later waves of entrants are able to observe the profitability of earlier entrants. The major results reported here (under suitable restrictions) are that the equilibrium rate of entry is monotonically decreasing over time, and that-at any given point in time-it is smaller than the socially optimal one. When a new market opens (as a result of a product being newly invented, for instance) or when an existing market starts to expand, uncertainty with respect to its size is likely to prevail. As a result of this uncertainty, entry of firms into such markets typically will occur in waves: some firms will enter initially, while others will wait to see the consequences of that initial entry. If the experience of early entrants is favourable, entry will continue; otherwise entry will cease. Hence, with the introduction of a new product, two phases are associated: the phase, typified by positive operating profits for existing firms and expansion of productive capacity due to entry of new firms, and the mature phase, typified by erosion of profits and fixed total productive capacity. Empiricists estimating the time-pattern of investments during the growth phase have found an S-shaped diffusion curve (see Mansfield (1986), and Gort and Klepper (1982)). The purpose of the present paper is to theoretically characterize these time-patterns and to investigate their welfare properties. Any attempt to model the type of entry described above, must account for differences in both entry dates and resultant earnings. In other words, the theory must explain why the realized earnings of different cohorts of firms are not equal. Often such ex post differences are reconciled by assuming heterogeneity with respect to some latent underlying characteristic (managerial ability, for instance) and attributing differences in earnings to differences in that characteristic. In this paper, instead, earning differentials are attributable to luck only: ex ante all firms are technologically identical and equally capable of forecasting market prospects and rationally acting upon those forecasts. Ex post, some firms turn out to have entered at the right time and are-for that reason-more profitable. The model developed in this paper analyzes a parametric example of a sequential entry problem in which the uncertainty over market size is gradually resolved over in a Bayesian setting. In an environment of perfect competition and constant returns-toscale, a free-entry equilibrium concept is introduced and the aggregate implications of the time-path of investments are derived. I then compare this (actual) time-path to the optimum. This comparison is interesting because the equilibrium is analysed under the