Free entry and social efficiency under vertical oligopoly.

We analyze a successive vertical oligopoly model that incorporates vertical relationships between industries and demonstrate that free entry in an industry that produces a homogeneous product can lead to a socially insufficient number of firms. This is in contrast with the previous findings that, under Cournot oligopoly with fixed set-up costs, level of entry in the free-entry equilibrium is socially excessive. It has often been argued that this result can provide a justification for apparently anticompetitive entry regulations. Our finding yields an important policy implication that such a justification is not necessarily valid when vertical relationships are taken into account.

1. Introduction

* Is free entry desirable for social efficiency? We offer a new perspective on this important question through analyzing a model that explicitly incorporates vertical relationships between industries. Vertical relationships are common and important. For example, automobile manufacturers purchase steel, tires, and a number of parts produced by other firms, and general constructors purchase cement, steel, and other construction materials produced by other firms. We consider a successive vertical oligopoly model, in which downstream firms produce a final product using an intermediate product purchased from upstream firms. We demonstrate that free entry in an industry that produces a homogeneous product can lead to a socially insufficient, rather than excessive, number of firms when its vertical relationship to the other industry is explicitly taken into account.

Our insufficient entry result is in contrast with previous findings in the theoretical industrial-organization literature. Mankiw and Whinston (1986) and Suzumura and Kiyono (1987) showed that, in homogeneous product markets, (i) if firms must incur fixed set-up costs upon entry, (ii) if the post-entry game is characterized by quasi-Cournot conjectures and (iii) if output per firm falls as the number of firms in the industry increases (a "business-stealing" effect), then the level of entry in a free-entry equilibrium is socially excessive (see also von Weizsacker, 1980; Perry, 1984).

In our framework, this previous finding (often called "excess-entry theorem") arises as a special case when the downstream or upstream sector has no market power. However, except for this special case, we find that the number of firms entering in the free-entry equilibrium can be socially insufficient rather than excessive. In other words, we demonstrate that the previous excess-entry result can be overturned when vertical interactions are taken into account. It has often been argued that the excess-entry theorem can provide a justification for entry regulation as a way of improving social welfare. In contrast, our insufficient-entry result yields important policy implications by indicating that such a justification is not necessarily valid. We elaborate on this later in this section.

In our model, there exists a fixed number of downstream firms and a large number of potential entrants to the upstream sector, where each upstream firm must pay a fixed cost upon entry. In the presence of the business-stealing effect, a part of the postentry profit of the marginal upstream entrant is the business transferred (or "stolen") from other upstream firms. Because this transferred business does not contribute to the increase of total surplus but does contribute to the postentry profit of the marginal entrant, the business-stealing effect works in the direction of excessive private incentive for entry, as in the previous analyses in the literature. However, in our model, the increase of total surplus due to the marginal upstream entry is in part captured as the profit of the downstream sector. The marginal upstream entrant cannot capture this as its own profit and so ignores this socially positive consequence of its own entry. This effect, which we call a "business-creation effect" to the downstream sector, has not been considered in the previous analyses. We find that, if the business-creation effect to the downstream sector dominates the business-stealing effect in the upstream sector, then the number of upstream firms in the free-entry equilibrium becomes socially insufficient rather than excessive. We then show that insufficient entry actually occurs under a range of parameterizations. (1)

We are not the first to point out that the level of entry in the free-entry equilibrium might be socially insufficient. It is well known that, under the presence of product diversity where consumers prefer variety, free entry can result in a socially insufficient number of firms (see Spence, 1976; Dixit and Stiglitz, 1977). (2) Our contribution is to demonstrate that insufficient entry can occur even in homogeneous product markets, when firms' interactions with other firms in vertically related industries are taken into account. We believe that this finding yields important policy implications, as discussed below.

Apparently anticompetitive industrial policy, such as entry regulation, has been employed in a number of countries. For example, throughout the postwar period, a guiding principle of Japanese industrial policy has been the regulation of so-called "excessive competition" (Suzumura and Kiyono, 1987). Komiya (1975) pointed out that excessive competition tended to develop in industries such as iron and steel, petroleum refining, petrochemicals, certain other chemicals, cement, paper and pulp and sugar refining, which are characterized by heavy overhead capital, homogeneous products, and oligopoly. Because these three features are key driving forces of the previous excess-entry results, it appears that the excess-entry theorem could provide a justification for such an anticompetitive policy. (3,4)

Our contribution here is to demonstrate that such a justification is not necessarily valid. To see our argument, note importantly that all industries mentioned above share another important feature; that is, they produce intermediate products. The excess-entry theorem could provide a justification for entry regulation in such an industry if the final-product industries served by the intermediate-product industry cannot capture any rents due to the lack of market power. This, however, is not always the case and just a special case in our framework. For instance, main customers of steel manufacturers include automobile manufacturers and general constructors, who seem to have substantial market power. Our analysis indicates that free entry in such an intermediate-product industry can lead to a socially insufficient, rather than excessive, number of firms, and hence entry regulation may not be welfare enhancing.

The rest of the paper is organized as follows. Section 2 presents a model of successive vertical oligopoly. In Section 3, we first demonstrate the possibility of insufficient entry under general demand functions, and then show that insufficient entry actually occurs in a range of parameterizations. Section 4 concludes.

2. The model

* Consider an industry with two sectors of production, upstream and downstream. In the upstream sector, a homogeneous intermediate product is produced with a constant marginal cost, c > 0. In the downstream sector, the intermediate product is transformed into a homogeneous final product with a constant marginal cost, ca, which is normalized to zero. (5) Production of one unit of the final product requires one unit of the intermediate product. There is a fixed number (denoted M [greater than or equal to] 1) of downstream firms, while there is free entry in the upstream sector. The downstream firms face the inverse demand given by P(Q), where Q ([greater than or equal to] 0) denotes the aggregate output in the downstream sector. We assume that (i) P(Q) is continuously differentiable as often as is required and P'(Q) < 0 for all Q and (ii) [P.sub.0] > c > [P.sub.[infinity]] = 0, where [P.sub.0] [equivalent to] [lim.sub.Q[vector]0] P(Q) and [P.sub.[infinity]] [equivalent to] [lim.sub.Q[vector][infinity]] P(Q). Note that we allow [P.sub.0] [equivalent to] [infinity] as a possibility; in this case, P(Q) is not well defined at Q = 0.

We consider the three-stage game described below. In the first stage, a large number of identical potential entrants to the upstream sector exist, each of whom must decide whether or not to enter the upstream sector. Should an upstream firm decide to enter, it must incur a set-up cost of K. Stage 2 involves Cournot competition in the upstream sector in which profit-maximizing upstream firms commit to the quantities of the intermediate product, taking rival upstream firms' outputs as given. Stage 3 also involves a Cournot competition in the downstream sector in which profit-maximizing downstream firms commit to the quantities of the final product, taking the input price (denoted r) as given. The input price r is determined at the market-clearing level, which equates the demand of the downstream firms to the total amount of the intermediate product supplied by the upstream firms.

The downstream firms have no oligopsony power over the upstream sector and take the input price as given. This is a standard modeling choice in the literature on successive vertical oligopolies (see, e.g., Greenhut and Ohta, 1979; Salinger, 1988; Abiru et al., 1998; Ishikawa and Spencer, 1999) and a natural simplifying assumption when the number of downstream firms, M, is sufficiently large relative to the equilibrium number of upstream firms. (6)