Mixed oligopoly and spatial agglomeration

Abstract We investigate a mixed market where a state‐owned welfare‐maximizing public firm competes against profit‐maximizing private firms. We use a circular city model with quantity‐setting competition. In contrast to a pure market case discussed by Pal (1998a) , spatial agglomeration of private firms always appears in equilibrium. All private firms locate at the same point, and the public firm locates at the opposite side. We also find that this equilibrium pattern of the location is second best provided that output of each private firm cannot be controlled by the social planner. JEL Classification: H42, L13
Oligopole mixte et agglomération spatiale Les auteurs examinent un marché mixte où une entreprise publique possédée par l'État et cherchant à maximiser le niveau de bien‐être est en concurrence avec des entreprises privées qui cherchent à maximiser leurs profits. On utilise un modèle de cité circulaire où la concurrence se fait en choisissant la quantité produite. En contraste avec le cas du marché parfait discuté par Pal (1998a), l'agglomération spatiale des entreprises privées paraît être en équilibre. Toutes les entreprises privées se localisent au même point, et l'entreprise publique se localise du côté opposé. Il appert que ce pattern d'équilibre de localisation est un équilibre de second ordre compte tenu du fait que la production de chaque entreprise privée ne peut être contrôlée par le planificateur social.     

Mixed pricing in oligopoly with limited monopoly

We analyze price competition between two brands. Buyers consist of switchers and two segments of customers with limited brand loyalty. We identify a unique symmetric mixed-strategy price equilibrium and find that competition is most relaxed when there exists some switchers.     

QUALITY AND WELFARE IN MIXED DUOPOLY: EFFECTS OF CAPACITY REDUCTION*

Under rationing of a public service due to its lower price and higher quality, the “privatization” could be regarded as a reduction in the capacity of the public service. We develop a model of mixed duopoly in which the service is vertically differentiated, a public firm is in a Stackelberg leader position, rationing happens, and the market is not covered. In one of two possible cases, it is shown that any reduction in the capacity of a public service will lower total surplus unless the price of the public service is too low and its quality is too high.     

Quality and Welfare in a Mixed Duopoly with Regulated Prices: The Case of a Public and a Private Hospital

Abstract. Hospital markets are often characterized by price regulation and the existence of different ownership types. Using a Hotelling framework, this paper analyses the effect of heterogeneous objectives of hospitals on quality differentiation, profits and overall welfare in a price‐regulated duopoly with exogenous symmetric locations. In contrast to other studies on mixed duopolies, this paper shows that, in this framework, privatization of the public hospital may increase overall welfare. This holds if the public hospital is similar to the private hospital or less efficient and competition is low. The main driving force is the single‐regulated price which induces under‐provision (over‐provision) of quality of the more (less) efficient hospital compared with the first best. However, if the public hospital is sufficiently more efficient and competition is fierce, a mixed duopoly outperforms both a private and a public duopoly due to an equilibrium price below (above) the price of the private (public) duopoly. This medium price discourages over‐provision of quality of the less efficient hospital and – together with the non‐profit objective – encourages an increase in quality of the more efficient public hospital.     

A public firm in a model of spatial duopoly with price discrimination

We visit the role of privatization in the location decision of firms in an industry where no firm can produce all varieties demanded. We demonstrate that the Nash equilibrium locations are socially optimal, in the presence of a publicly owned firm, notwithstanding the degree of privatization.     

R&D competition between public and private sectors

We investigate a mixed market where a welfare-maximizing public research institute competes against profit-maximizing private firms. We investigate R&D competition by using a standard model of patent races where each firm chooses both its innovation size and R&D expenditure. We find that the innovation size (R&D expenditure) chosen by the public institute is too small (too large) from the viewpoint of social welfare, respectively, and so the government should control the public institute appropriately. We also discuss the welfare implications of privatization of public research institutes.     

Mixed duopoly,privatization, and subsidization with excess burden of taxation

We investigate optimal tax‐subsidy policies in mixed and private oligopolies with excess burden of taxation. We compare the optimal subsidies and the resulting welfare levels among four regimes: mixed and private Cournot duopolies and Stackelberg competition with public and private leaderships. We show that, in contrast to the existing works on the privatization neutrality theorem, privatization affects resulting welfare.     

Comparative statics for oligopoly: A generalized result

We perform comparative statics for a general model of asymmetric oligopoly and derive a concise formula for the response of one firm to a marginal change in its rival’s strategic variable, taking into account the responses of all other firms. We obtain the conditions under which the sign of this response coincides with that of the mixed second-order partial derivative of the firm’s payoff function. We then propose a distinction between gross and net strategic relationships (i.e., strategic substitute and complement).     

Equilibrium locations in a mixed duopoly with sequential entry in real time

We investigate a mixed duopoly model where a public firm and a private firm enter a market sequentially over an infinite time horizon, with and without uncertainty over the follower's entry date. We assume that there is a unit-length linear city and show that, if the public firm moves first, equilibrium location falls inside the second and third quartiles. The later the follower is expected to enter, the closer the two firms are. However, if the private firm acts first, it moves aggressively to locate at the middle point (one-half), forcing the public firm to locate nearer the periphery (one-sixth), to minimize consumers' transportation cost. In addition, social welfare is strictly greater when the public firm moves as the leader.     

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.     

Second-best trade policies in Cournot oligopoly

In this paper we study the optimal import policy in an oligopolistic market with a given number of quantity-setting firms. In the absence of fixed costs, we show that if the policy instrument is an import quota, the optimal policy is either free trade or autarky, while if the instrument is a tariff the optimal policy is neither free trade nor autarky. In the case of fixed costs, we show that contrary to the traditional protectionist argument, a restrictive import policy might increase domestic welfare by increasing domestic consumers' surplus, instead of increasing domestic profits.     

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, optimal privatization, and foreign penetration

This paper examines the impact of foreign penetration on privatization in a mixed oligopolistic market. In contrast to the simple framework of single domestic market with foreign entry by entry mode of foreign direct investment (FDI) or exports, our result shows that government should increase the degree of privatization along with increasing proportion of domestic ownership of multinational firms. Furthermore, we show that an increase in domestic ownership of multinational firms raises all domestic private firms' profit and social welfare, while it may either increase or decrease public firm's profit. With the aid of numerical example, intensive competition from private firms in general will enhance the degree of privatization gradually; in particular, the degree of privatization is lower in the presence of multinational firms.     

Competition and waiting times in hospital markets

This paper studies the impact of hospital competition on waiting times. We use a Salop-type model, with hospitals that differ in (geographical) location and, potentially, waiting time, and two types of patients: high-benefit patients who choose between neighbouring hospitals (competitive segment), and low-benefit patients who decide whether or not to demand treatment from the closest hospital (monopoly segment). Compared with a benchmark case of monopoly, we find that hospital competition leads to longer waiting times in equilibrium if the competitive segment is sufficiently large. Given a policy regime of hospital competition, the effect of increased competition depends on the parameter of measurement: Lower travelling costs increase waiting times, higher hospital density reduces waiting times, while the effect of a larger competitive segment is ambiguous. We also show that, if the competitive segment is large, hospital competition is socially preferable to monopoly only if the (regulated) treatment price is sufficiently high.     

Welfare effects of competitive lobbying efforts in international oligopoly markets

Conventionally, rent-seeking activities have been considered to deteriorate social welfare and to distort resource allocation. This paper examines whether rent-seeking behavior can improve social welfare by focusing on the welfare effects of firms’ competitive lobbying efforts when governments can impose market entry regulation against foreign firms. We demonstrate that competitive lobbying efforts can improve social welfare when such lobbying efforts are directed to reduce market entry barriers. In addition, social welfare can be maximized when the government shows the maximum sensitivity to the foreign firm's political contributions while maintaining competitive market structure. Moreover, it is shown that the dominant strategy for a domestic firm is to allocate more resources to R&D sectors while it is optimal for foreign firms is to exert more efforts in lobbying to reduce the market entry barriers when a government makes political economic approach in market entry regulations.     

On intrabrand and interbrand competition: The strategic role of fees and royalties

We examine oligopolistic markets with both intrabrand and interbrand competition. We characterize equilibrium contracts involving a royalty (or wholesale price) and a fee when each upstream firm contracts with multiple downstream firms. Royalties control competition between own downstream firms at the expense of making them passive against rivals. When the number of downstream firms is endogenous, each upstream firm chooses to have only one downstream firm. This result is in sharp contrast to previous literature where competitors benefit by having a larger number of independent downstream firms under only fixed fee payments. We discuss why allowing upstream firms to charge per-unit payments in addition to fixed fees dramatically alters their strategic incentives.     

Leadership and Privatisation in a Mixed Multi‐product Oligopoly: An Endogenous Timing Model

This paper examines both leadership choice and welfare consequences of privatisation in an endogenous timing mixed multi‐product oligopoly. It shows that a multi‐product firm undermines the welfare‐maximising efforts of a public firm by cross‐subsidising. The paper demonstrates that a unique subgame perfect Nash equilibrium emerges in a multi‐product market, in contrast to the multiple equilibria of a single‐product market. This unique equilibrium indicates that profit‐maximising private firms retain leadership while a welfare‐maximising public firm acts as a follower. Even on the off‐equilibrium path where the public firm acts as a leader, it rarely generates maximum social welfare. However, privatising the public firm usually harms social welfare and results in a different timing structure in equilibrium.     

Mixed Competition and Patent Licensing

This paper studies the patent licensing decision of an insider patentee when two firms engage in a mixed (Cournot–Bertrand or Bertrand–Cournot) competition where one firm adopts the quantity strategy while the other uses the price strategy and vice versa. If either the fixed fee or royalty is applied, then the licensor prefers the fixed fee when the licensor takes the quantity strategy, while the licensee uses the price strategy (Cournot–Bertrand). If the two‐part tariff is applied, then the two‐part tariff is more likely to be adopted by the licensor under Cournot–Bertrand than under Bertrand–Cournot competition.     

Endogenous vertical restraints in international trade

This paper examines interbrand competition between a domestic and a foreign manufacturer who market their products through intermediaries. The contracts manufacturers offer these intermediaries are endogenous. In equilibrium contracts may specify exclusive territories (ET), depending on the degree of substitutability between products and the level and degree of transparency of trade barriers. Trade liberalization, through lower or more transparent barriers, may lead manufacturers to use ET, thereby substituting private anti-competitive arrangements for government-imposed barriers. This substitution may decrease competition and welfare, and thus create a role for competition policy in a freer trade environment.     

Strategic spin-offs of input divisions

When a downstream producer enters backward into the input market, a “helping the rivals effect” exists: Such entry hurts the firm's downstream business as it increases upstream competition and thus benefits its rival downstream firms. This negative externality prevents the newly-created upstream unit from expanding. A spin-off enables the firm to credibly expand in the input market, thereby forcing its upstream competitors to behave less aggressively. Spin-offs occur in equilibrium if and only if the number of downstream firms exceeds a threshold level. When there is more than one integrated firm, a spin-off by a firm can trigger spin-offs by others that would not occur otherwise.