Entry Bias and Product Substitutability

Economists have long been interested in the free entry equilibrium in imperfectly competitive markets. Entry biases have been well established in the literature. The papers by Guesnerie and Hart (1985), Mankiw and Whinston (1986), Suzumura and Kiyono (1987) and Cabral (2004) all study free entry from a social welfare point of view. They establish that entry biases exist if firms are not behaving as perfect competitors. A common assumption that has been made in the literature is that firms are identical. For example, Mankiw and Whinston (1986) consider a homogeneous good market with identical firms that engage in Cournot output competition. They show that free entry entails excessive entry from a social welfare point of view. Cabral (2004) considers a homogenous product industry and answers the question whether free entry leads to the socially optimal number of firms in the market. He discovers that entry costs affect entry biases. When entry costs are low, he examines market competition. Tough competition in the market implies insufficient entry whereas soft competition in the market implies excessive entry. On the other hand, when entry costs are high, entry bias depends on the entry game being played in the market.

Recently, Gotz (2005) and Ohkawa et al. (2005) examine market selection of production technologies under Cournot competition and free entry. They establish that only one type of technologies (or firms) can survive in a free entry homogenous good Cournot market. Ohkawa et al. (2005) find a second kind of entry bias. Namely, free entry may lead to the wrong type of firm (technology) being selected by the market in the sense that surviving technology under free entry is different from that required by the social optimum.

The present paper extends the existing literature on free entry under imperfect competition by examining a differentiated goods market. We focus on a market with two imperfectly substituting goods each of which can be produced by multiple technologies (types of firm). Our main finding is that there is a third kind of entry bias. More specifically, it is shown that, in a Cournot market with asymmetric firms and imperfectly substituting goods, free entry may lead to a wrong product mix. This bias can take three forms: free entry can lead to over-provision of goods, under-provision of goods, or a wrong good, compared to the social optimum. We also establish that, in the free entry equilibrium, each good is produced by only one type of firm. This generalizes the market selection result by Gotz (2005) and Ohkawa et al. (2005) to a differentiated goods setting.

We use a symmetric linear demand system so as to have a mathematically easily tractable model. Symmetric demands for the goods help highlight that under-provision or over-provision of goods is not caused by lack of demand but rather due to the effect of entry and the presence of asymmetry in production technology.