Agglomeration in a vertically-related oligopoly

This paper examines the location of three vertically-linked firms. In a spatial economy composed of two regions, a monopolist firm supplies an input to two consumer goods firms that compete in quantities. It is concluded that agglomeration is more likely to occur when the ratio between the transport cost of the intermediate good and the transport cost of the final good is higher. If this proportion is low, the likelihood of an agglomeration decreases with transport costs. If the ratio has an intermediate value, a non-monotonic pattern is obtained that is different from Krugman and Venables (1995).Received: October 2004, Accepted: March 2005, JEL Classification: C68, F12, F15, R12, R13This paper had the support of the Research Unit on Complexity in Economics (UECE). The author wishes to thank Masahisa Fujita, Armando Pires and an anonymous referee for helpful comments. The usual disclaimer applies.     

Cournot competition in a differentiated oligopoly

This paper studies product-quantity equilibria in an oligopoly. Products are interpreted as “qualities” and each firm chooses a quality-quantity pair, simultaneously. It is well known that a pure-strategy equilibrium in product-price pairs does not exist in this model, but a pure-strategy equilibrium in product-quantity pairs exists. Furthermore, in an example widely studied in the literature, the equilibrium has nice asymptotic properties.     

Optimal manipulation rules in a mixed oligopoly

We study the optimal manipulation rules of a public firm’s objective function in a mixed oligopoly with imperfect product substitutability. We start with a baseline duopoly model and compare the solutions under quantity and price competition, and the way they are affected by product substitutability. This allows us to show that partial privatization, strategic delegation and other specific government’s commitments on the objective function of the public management can be looked at as special cases of these optimal rules, and to evaluate the viability of these policies under the two modes of competition. In this framework, we also discuss the equivalence between manipulation of the objective function and Stackelberg leadership. Since optimal manipulation rules change as new dimensions are added, we also derive the optimal rules under oligopoly, quadratic costs, and competition of international firms. This fairly general unified framework allows to discuss the impact of these factors on the government’s implementation policies of the optimal manipulation rules.     

Comparative dynamics in a productive asset oligopoly

We build a subgame perfect Nash equilibrium of a common property productive asset oligopoly and analyze separately the impact of a change in the implicit growth rate of the asset and a change in the number of firms exploiting the asset. We show that the steady state level of asset can be a decreasing function of the asset's implicit growth rate. This phenomenon arises when the initial stock of asset is below a certain threshold. In the short-run we show that firms’ exploitation rate can be a decreasing function of the implicit growth rate. We study the impact of a change in the number of firms that share access to the asset. Reducing the number of firms can result, in the long-run, in higher industry production. In the short-run, it can result in an increase of the industry's exploitation and a decrease of the level of the asset's stock.     

Environmental policies in a differentiated oligopoly revisited

Constructing a model of polluting oligopoly with product differentiation, we consider how product differentiation, together with the presence and absence of free entry, affects optimal pollution tax/subsidy policies. The sign of the short- and long-run optimal pollution taxes are highly sensitive to the parameter measuring product differentiation as well as the presence of free entry. How they are affected by a change in product differentiation, which is not addressed in the existing literature, is also made clear.     

Product line pricing in a vertically differentiated oligopoly

Abstract This paper examines the joint pricing decision of products in a firm’s product line. When products are distinguished by a vertical characteristic, those with higher values of that characteristic will command higher prices. We investigate whether, holding the value of the characteristic constant, there is an additional price premium for products on the industry and/or the firm frontier, that is, for the products with the highest value of the characteristic in the market or in a firm’s product line. We also investigate the existence of price premia for lower‐ranked products and other product line pricing questions. Using personal computer price data, we show that prices decline with the distance from the industry and firm frontiers, even after holding absolute quality constant. We find evidence that consumer tastes for brands is stronger for the consumers of frontier products (and thus competition between firms weaker in the top end of the market). There is also evidence that a product’s price is higher if a firm offers products with the immediately faster and immediately slower computer chip (holding the total number of a firm’s offerings constant), possibly as an attempt to reduce cannibalization. Finally, a product’s price declines with the time it is offered by a firm, suggesting intertemporal price discrimination.     

Debt as a collusive device in an oligopoly supergame

This paper explores the impact of debt holdings on the output decisions of firms in an oligopoly supergame with stochastic demand fluctuations. It is demonstrated that when perfect collusion is not feasible then there exist circumstances in which increased debt holdings may facilitate tacit collusion. This occurs because higher debt levels act as a credible commitment device which lowers the payoffs accruing to a firm when it defects from the tacitly collusive equilibrium. It is further shown that in these circumstances firms may have an incentive to hold debt for strategic purposes which promote collusion.     

Endogenous timing in a mixed oligopoly under demand uncertainty

This paper analyzes a Hotelling-type game in a mixed oligopoly, where firms can either enter the market in period 1, facing demand uncertainty, or postpone their entry, in order to acquire complete information. It is shown that, for a high (low) level of uncertainty, there is a pure (mixed)-strategy equilibrium. Moreover, the standard result in the literature—that uncertainty is a differentiation force, is only possible when the degree of uncertainty is small. An increase in the degree of uncertainty could force firms to delay their entry and lead to a socially optimal outcome.     

On hierarchical competition in oligopoly

In this paper, we consider a hierarchical oligopoly model, in which firms compete on quantities of an homogeneous product. We provide a proof and an interpretation that under the three necessary and sufficient conditions of linear aggregate demand, constant and identical marginal costs, the strategy of leaders at any stage depends neither on the number of leaders who play after nor on the number of remaining stages. So, all firms behave as Cournotian oligopolists on the residual demand. We show that these three assumptions are not only sufficient but also necessary. Any departure from any of these assumptions rules out this property.     

New technology adoption in a Cournot oligopoly with spillovers

In a two-stage Cournot oligopoly where a subset of firms first make a choice between two alternative production technologies independently and then all firms compete in quantity, the effect of information spillovers is analyzed when the outcome of R&D is uncertain. It is shown that the range of parameter values that support heterogeneous firms in equilibrium will diminish as information spillovers become larger. Particularly, when the spillover effect is so strong that the investment by one firm is beneficial to its R&D active rivals, all active firms will choose the same technology. A similar result can be derived from a socially desirable point of view except that the cut-off magnitude of spillovers is different. By introducing a positive success probability to characterize the uncertainty of the R&D outcome, it is found that when information spillovers are not too small, there will be underinvestment in equilibrium relative to the social optimum.     

Endogenous timing in a mixed oligopoly with semipublic firms

An endogenous order of moves is analyzed in a mixed market where a firm jointly owned by the public sector and private domestic shareholders (a semipublic firm) competes with n private firms. We show that there is an equilibrium in which firms take production decisions simultaneously. This result is strikingly different from that obtained by Pal (Econ Lett 61:181–185, 1998), who shows that when a public firm competes with n private firms all firms producing simultaneously in the same period cannot be sustained as a Subgame Perfect Nash Equilibrium outcome. Our result differs from that of Pal (Econ Lett 61:181–185, 1998) for two reasons: firstly, we consider that there is a semipublic firm rather than a public firm. Secondly, Pal (Econ Lett 61:181–185, 1998) considers that the public firm is less efficient than private firms while in our paper all firms are equally efficient.     

Privatization and efficiency: a mixed oligopoly approach

While models of mixed oligopoly have been analyzed within a rapidly growing literature, little is known about the mechanism of efficiency improvement relating to partial privatization. In this paper, we endogenize efficiency improvement in relation to the level of privatization. We show that in the short run, an improvement in efficiency associated with a state-owned firm reduces the output substitution among firms, and that the reduction in output substitution effect is proportional to the strength of the improvement in efficiency. Specifically, if the effect of efficiency improvement is sufficiently small, the magnitude of the improvement of social welfare is reduced. In the literature, the optimal policy in the long run is full nationalization. However, we argue that the optimal policy for a state-owned firm is partial privatization. Moreover, efficiency improvement provides the impetus for indirect entry regulation of private entrants.     

Inferior factor in Cournot oligopoly

The condition for factor inferiority has been well known for a competitive firm facing perfect competition in both product and factor markets. Whether the factor inferiority is observable or not has been unknown for oligopoly facing perfect competition in factor market. We derive a general condition for the factor inferiority in Cournot oligopoly without product differentiation. We derive it on the basis of a novel technique for proving the existence of a unique Cournot equilibrium industry output.     

Merger profitability in mixed oligopoly

We analyse merger profitability in a mixed-oligopoy Cournot model. The “merger paradox” is qualified by showing that there are profitable gains for the firms participating in a horizontal merger that is not a merger to a monopoly. In particular, it is shown that merger sustainability depends on both, the privatization degree of the mixed firm and the number of non-merging firms.      

Coalition-proof supply function equilibria in oligopoly

In an industry where firms compete via supply functions, the set of equilibrium outcomes is large. If decreasing supply functions are ruled out, this set is reduced significantly, but remains large. Specifically, the set of prices that can be sustained by supply function equilibria is the interval between the competitive price and the Cournot price. In sharp contrast, when the number of firms is above a threshold we identify (e.g., three if demand is linear), only the Cournot outcome can be sustained by a coalition-proof supply function equilibrium.     

Mixed oligopoly and spatial agglomeration: a comment

Abstract.  This paper extends Matsushima and Matsumura (2003) by incorporating a large production cost difference between public and private firms in a quantity setting spatial mixed oligopoly. The public and private firms first choose their locations in a linear market and then compete in quantities. It is shown that for a significant inefficiency of the public firm, all firms (including both public and private firms) agglomerate at the market centre.     

Symmetric Cournot oligopoly and economic welfare: a synthesis

Summary Recently, Mankiw-Whinston (1986) and Suzumura-Kiyono (1987) have shown that socially excessive firm entry occurs in unregulated oligopoly. This paper extends this excess entry results by looking into strategic aspects of costreducing R&D investment that creates incentives towards socially excessive investments. In the first stage, firms decide whether or not to enter the market. In the second stage, firms make a commitment to cost-reducing R&D investment. In the third stage, firms compete in output quantities. It is shown that the excess entry holds even in the presence of strategic commitments.This is the synthesized version of the two earlier papers, Okuno-Fujiwara and Suzumura (1988) and Suzumura (1991). We are grateful to Professors J. Brander, D. Cass, M. Majumdar, A. Postlewaite, J. Richmond, A. Sandmo, B. Spencer and J. Vickers for their helpful comments and discussions on earlier drafts. Needless to say, they should not be held responsible for any remaining defects. Financial supports from the Japan Center for Economic Research, Tokyo Center for Economic Research, the Japanese Ministry of Education, and the Institute for Monetary and Economic Research, the Bank of Japan are gratefully acknowledged.