Entry regulation and social welfare with an integer problem

This paper elaborates on Salop (1979) who showed that the number of firms at free-entry equilibrium is excessive from the viewpoint of social welfare (excess-entry theorem). This paper considers an integer problem of the number of firms entering the market. We find that the excess-entry theorem does not hold true if the marginal production cost is increasing, while it holds true if the marginal production cost is constant. This result warns against the use of the excess-entry theorem for rationalizing entry regulation such as the notorious Japanese Large-Scaled Retail Act restricting the new entry of retailers.     

COMPETITION‐ACCELERATING PUBLIC INVESTMENTS*

We investigate the effects of infrastructure investments that reduce transport costs. We use a spatial model of Salop (1979). It is well known that the number of firms is excessive at free‐entry equilibrium (excess entry theorem). We find that the optimal investment level exceeds the ex post cost‐minimising level because investments accelerate competition and reduce the number of entering firms; resulting in the improvement of welfare. We also show that, in cases where the excess‐entry theorem is true, the desirable policy is the one accelerating, rather than restricting, competition.     

Imperfect price discrimination, market structure, and efficiency

Abstract.  We introduce a flexible third‐degree price discrimination framework by modeling the information firms possess about consumers' locations (preferences) on the Salop circle as a partition. Higher information quality is translated into a partition refinement. In the limit, we obtain the perfect price discrimination paradigm. We show that the free‐entry equilibrium number of firms exhibits a U‐shape as a function of the quality of information. This implies that imperfect price discrimination generates the most efficient free‐entry outcome. JEL classification: D43, L11, L43     

Rationing rule, imperfect information and equilibrium

Summary. The impact of imperfect information on the price setting behaviour of firms is analysed. Specifically, consumers support an information cost to become informed about prices. Firms are endowed with U-shaped average cost curves. If a firm does not supply more than its competitive supply as determined by its marginal cost schedule, then we show that the existence of a pure strategy equilibrium is conditional on the rationing rule employed. If uninformed consumers are served first then the monopoly price is the sole equilibrium whenever consumers' information costs are high enough. Otherwise, a pure strategy equilibrium fails to exist contrary to the results of Salop and Stiglitz (1977) or Braverman (1980) who implicitly suppose that firms supply all the demand at a given price. Received: May 17, 1999; revised version: September 15, 2000     

Free and second-best entry in oligopolies with network effects

We compare the number of firms in equilibrium in a Cournot industry with positive network effects and complete compatibility, under free and second-best entry. Under free entry, the firms decide whether to enter the market or not; in the second-best problem, the number of firms is established by the regulator to maximize social welfare (the regulator controls entry but not production). We show that when individual equilibrium output decreases with entry (business-stealing competition), free entry may lead to more or less firms than the second-best problem. This contrasts with the standard (nonnetwork) Cournot oligopoly model, wherein with business-stealing competition, free entry leads to an excessive number of firms compared with the second-best solution.     

INSUFFICIENT ENTRY OF EMPLOYEE‐CONTROLLED FIRMS IN A FREE‐ENTRY OLIGOPOLY

This study is a theoretical examination of whether employee‐controlled firms (ECFs) enter a free‐entry oligopolistic market excessively or insufficiently, from the viewpoint of welfare maximization. The excess entry theorem is well known in oligopoly theory. According to this theorem, a greater number of profit‐maximizing firms enter a free‐entry oligopolistic market than is optimal for welfare maximization. We demonstrate the possibility that insufficient entry arises when ECFs compete in a free‐entry market. In particular, we show that if both the demand and cost functions are convex, insufficient ECF entry necessarily occurs. Our results suggest that competition among firms seeking purposes other than profit might lead to insufficient entry because differences in competing firms’ objectives affect the intensity of market competition.     

Coalition-proof Bertrand equilibria

Summary. This paper examines the coalition-proof Nash equilibria of a Bertrand model of price competition where firms supply all demand. When firms are asymmetric we prove existence and provide a sufficient condition for uniqueness. For symmetric firms, we show that an equilibrium is necessarily unique. We also examine whether this unique equilibrium outcome is implementable through a sequential move game where the firms take turns at announcing prices. Finally we examine the limiting property of such equilibria as the number of firms go to infinity.Received: 20 March 2002, Revised: 5 August 2003JEL Classification Numbers: D43, D41, L13.Correspondence to: Kunal SenguptaWe are deeply indebted to an anonymous referee for very helpful and incisive comments that led to substantial improvements in the paper. We also gratefully acknowledge the hospitality of the Department of Finance, Hong Kong University of Science and Technology where much of the work on this paper was carried out.     

Lack of commitment to future privatization policies may lead to worst welfare outcome

We investigate the welfare consequences of a lack of commitment to future privatization policies. The government implements a privatization policy after the competition structure is determined by the entry of private firms. We find that in an equilibrium, the government fully privatizes (nationalizes) a public firm if private firms expect that the government fully privatizes (nationalizes) the public firm. This is because an increase in the number of firms entering a market increases the government's incentive to privatize the public firm, which mitigates future competition and stimulates entries. The full-privatization equilibrium is the worst privatization policy among all possible (either equilibrium or non-equilibrium) privatization policies for welfare because it causes excessive market entry of private firms. Partial commitment of a minimal public ownership share may mitigate this problem.     

Edgeworth's taxation paradox when firms engage in cost-reducing investment

This study examines whether and when Edgeworth's taxation paradox, that taxation decreases the equilibrium price, occurs in a free-entry Cournot oligopoly with cost-reducing investment. In contrast to the fact that no paradox occurs in the short-run equilibrium, the paradox can occur in the long-run equilibrium, in which the number of firms is endogenous. However, the conditions under which the paradox occurs are restrictive when there is no investment. By incorporating cost-reducing investments into the model, we demonstrate that the paradox is likely to occur under less restrictive conditions, irrespective of whether the tax is specific or ad valorem.     

Preemptive entry in differentiated product markets

Summary. Models of spatial competition are typically static, and exhibit multiple free-entry equilibria. Incumbent firms can earn rents in equilibrium because any potential entrant expects a significantly lower market share (since it must fit into a niche between incumbent firms) along with fiercer price competition. Previous research has usually concentrated on the zero-profit equilibrium, at which there is normally excessive entry, and so an entry tax would improve the allocation of resources. At the other extreme, the equilibrium with the greatest rent per firm normally entails insufficient entry, so an entry subsidy should be prescribed. A model of sequential firm entry (with an exogenous order of moves) resolves the multiplicity problem but raises a new difficulty: firms that enter earlier can expect higher spatial rents, and so firms prefer to be earlier in the entry order. This tension disappears when firms can compete for entry positions. We therefore suppose that firms can commit capital early to the market in order to lay claim to a particular location. This temporal competition dissipates spatial rents in equilibrium and justifies the sequential move structure. However, the policy implications are quite different once time is introduced. An atemporal analysis of the sequential entry process would prescribe an entry subsidy, but once proper account is taken of the entry dynamics, a tax may be preferable. Received: April 26, 1999; revised version: September 22, 1999     

产品差异、转移成本和市场竞争

文章通过在豪泰林空间差异模型的基础上结合转移成本构建的博弈模型,主要研究转移成本和产品差异的存在对于企业价格竞争和策略性行为的影响。文章发现纯策略价格均衡是否存在以及在位企业容纳还是遏制竞争对手的潜在进入,都依赖于转移成本相对于产品差异程度的大小。     

R&D networks and absorptive capacity in a Salop model

The paper investigates the incentives of Salop-type oligopolistic firms to cooperate and the architecture of the resulting collaboration networks. We find that when spillovers are exogenous, firm profits are not affected by the network structure. On the contrary, with endogenous spillovers (absorptive capacity) firms tend to form less dense networks. We also seek out the architecture of socially efficient networks, showing that social welfare is maximised in the complete network. Also, given the network structure we conclude that a Salop industry could be characterized by a general tendency to under-connection.     

Mixed Oligopoly at Free Entry Markets

We investigate the optimal behavior of a public firm in a mixed market involving private firms and one public firm. Existing works show that welfare-maximizing behavior by the public firm is suboptimal when the number of firms is given exogenously. We allow free entry of private firms and find that, in contrast to the case with the fixed number of firms, welfare-maximizing behavior by the public firm is always optimal in mixed markets. Furthermore, we find that mixed markets are better than pure markets involving no public firm if and only if the public firm earns nonnegative profits.     

Tacit Coordination in a Decentralized Market Entry Game with Fixed Capacity

We focus on a class of market entry games in which a newly emergent market opportunity may be fruitfully exploited by no more than a commonly known, exogenously determined number of firms. Our results show significant effects of the parameters manipulated in the study, namely, the market capacity, entry fee, and method of subject assignment to groups (fixed vs. random). In contrast to previous market entry games with linear payoff functions, we find no evidence of convergence to equilibrium play on the aggregate level. Shifting the focus of the analysis from the aggregate to the individual level, four clusters of subjects are identified. The patterns are: (1) choice of the same action that is independent of the parameters of the game or the outcome of previous presentations of the same game; (2) random choices with probabilities prescribed by the equilibrium solution for risk-neutral players; (3) random choices with probabilities equal to the individual observed overall proportion of entry; and (4) sequential dependencies that violate any model that assumes randomization. Subjects in the fourth and largest category are shown to adjust their choices in accordance with a simple principle of strategic reasoning.     

Horizontal mergers and product quality

We study the effects of a horizontal merger when firms compete on price and quality. In a Salop framework with three symmetric firms, several striking results appear. First, the merging firms reduce quality but possibly also price, whereas the outside firm increases both price and quality. As a result, the average price in the market increases, but also the average quality. Second, the outside firm benefits more than the merging firms from the merger, and the merger can be unprofitable for the merger partners, i.e., the “merger paradox” may appear. Third, the merger always reduces total consumer utility (though some consumers may benefit), but total welfare can increase due to endogenous quality cost savings. In a generalized framework with n firms, we identify two key factors for the merger effects: (i) the magnitude of marginal variable quality costs, which determines the nature of strategic interaction and (ii) the cross‐quality and cross‐price demand effects, which determines the intensity of price relative to quality competition. These findings have implications for antitrust policy in industries where quality is a key strategic variable for the firms.     

FREE VERSUS SECOND‐BEST ENTRY IN COURNOT OLIGOPOLIES WITH FIRM‐SPECIFIC NETWORKS

This paper endogenizes the number of firms in an industry with positive network effects, complete incompatibility, and firms that compete in quantity. To this end, we compare two possibilities: free entry and second‐best number of firms (the one that maximizes social welfare). We show that with business‐stealing competition, free entry yields, in general, more firms than the socially optimal solution. In addition, we find that by the nature of the industry with firm‐specific networks, total production may be greater or lower under free entry than with a regulator; moreover, some industries attain their maximum social welfare with a monopoly.     

Long-run industry equilibrium with uncertainty

In this paper we consider the effects of uncertainty on industry equilibrium when firms must commit themselves to production before prices are revealed. We show that (a) an increase in demand uncertainty will (i) not affect the equilibrium number and size of firms if they are risk neutral, (ii) reduce the equilibrium number of firms if they are risk averse, but will have an ambiguous effect on their size. (b) In equilibrium, firms operate at capacity if they are risk neutral, but at excess capacity if they are risk averse.     

The effects of mergers and acquisitions on the firm size distribution

This paper provides new empirical evidence on the effects of mergers and acquisitions (M&As) on the shape of the firm size distribution, by using data of the population of manufacturing firms in the Netherlands. Our analysis shows that M&As do not affect the size distribution when we consider the entire population of firms. When we focus on the firms involved in an M&A event, we observe a shift of the firm size distribution towards larger sizes. Firm size distribution becomes more concentrated around the mean, less skewed to the right hand side, and thinner at the tails as a whole. The shift toward higher sizes due to M&A is not uniform but affects firms of different sizes in different ways. While the number of firms in the lower tail decreased, the number of firms in the central size classes increased substantially and outweighed the increase in the number (and mean size) of firms in the upper tail of the distribution (consequently the overall market concentration measured by the Herfindahl index declines). M&As lead to a departure from log-normality of the firm size distribution, suggesting that external growth does not follow Gibrat’s law. Our counterfactual analysis highlights that only internal growth does not affect the shape of the size distribution of firms. On the contrary, it suggests that the change in the size distribution is almost entirely due to the external growth of the firms.

Free Entry under Uncertainty

When focusing on firm’s risk-aversion in industry equilibrium, the number of firms may be either larger or smaller when comparing market equilibrium with and without price uncertainty. In this paper, we introduce risk-averse firms under cost uncertainty in a model of spatial differentiation and show that the impact of uncertainty will increase the number of firms in an industry. With increased uncertainty, the risk premium of the marginal buyer increases by more than the risk premium of the average buyer, so that the price increases by more than the risk premium. When turning to the free entry game, we find that the market generates too many firms.     

Free entry and stability in a cournot model

In a Cournot model for a single homogeneous good, we study simultaneously two stability properties of a Cournot equilibrium: the stability of a continuous quantity adjustment process with a fixed number of firms and the stability relative to entry. Under usual assumptions, we show that these two properties are consistent—i.e., there exists an equilibrium that is stable in both senses—and determine quite sharply the number of active firms.