CARESS Working Paper 97-13 An Equilibrium Model of Firm Growth and Industry Dynamics

We develop a model of ̄rm size in which ̄rms are unable to access as many consumers as they want. Newly arrived consumers match randomly with ̄rms. Subsequently, consumers must pay search costs to be able to switch ̄rms. This cost promotes an inertial tendency for consumers to remain with the ̄rm they currently buy from. Consequently, established ̄rms enjoy a proprietary relationship with respect to their old customers while new entrants only have access to ̄rst time consumers, who are as yet unattached to any ̄rm. As time goes on, ̄rms acquire successive generations of new consumers, and their stock of loyal customers grows gradually. Thus, more senior ̄rms command higher market shares. We construct an industry model based on this hypothesis and show that the aggregate implications of the model are consistent with empirical facts about industry dynamics (e.g., Dunne, Roberts and Samuelson, (1988, 1989) or Davis and Haltiwanger (1992)): Larger and older ̄rms are less likely to exit than younger and smaller ̄rms. In our model this results from the fact that the option value of remaining operative in the aftermath of a high cost-shock is greater for an older ̄rm than for a younger ̄rm because the value of a cost turnaround is greater for the former (which has already accumulated a large customer-base) than for the latter (which has yet to do so). This enables older (and larger) ̄rms to survive adverse cost-shocks which force the exit of younger (and smaller) ̄rms. For similar reasons, R&D expenditures are larger for larger ̄rms, as per the empirical ̄ndings surveyed by Cohen and Lewis (1989).