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.     

Mixed oligopoly and the choice of capacity

We analyze the capacity choice of firms under different time structures in a mixed oligopoly market, in which firms decide not only production quantities but also capacity scales. We show that the public firm never chooses excess capacity, while the private firm never chooses under capacity under all possible strategic environments.     

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.     

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.     

Cooperative oligopoly equilibrium

Oligopoly cooperation is investigated in an industry with N firms: each firm selects its own output. We show that such oligopoly problems have the same structure as problems of allocating public goods since each firm views its own output as a private good while viewing the outputs of others as public bads. This leads to ‘cooperative oligopoly equilibria’ which are the Lindahl equilibria of the oligopoly model. Agreements are modeled by the selection of a mechanism or ‘game form’ which obeys certain axioms. Under the postulated axioms we show the equivalence of agreed allocations with the set of oligopoly equilibria.It is argued that the principle of ‘Lindahl agreements’ may have wider applications.     

Exchange rates and bertrand oligopoly

The impact of exchange-rate changes on industrial prices seems ambiguous. Incomplete and even perverse pass-through has been observed: the import prices in the depreciating country decrease while those in the appreciating country increase. To explain these counterintuitive price reactions we consider a situation of international Bertrand competition: two firms, based in different countries, are selling in both countries simultaneously. The profit-maximizing duopolists set the prices for their products in each of the two markets which are segmented on the demand side. We then study the qualitative effect of an exogenous exchange-rate change on the Bertrand-Nash equilibrium. Under the strong assumption of linear demand and cost functions we have normal exchange-rate pass-through. However, allowing for more general cost structures in this simple static model enables us to show that the import prices in both countries might move in counterintuitive directions.     

Unionized oligopoly and vertical integration

Labor market structures may have important effects on imperfectly competitive rivalries between firms. This paper examines the consequences of unionization for the rivalry between duopoly firms in two types of contracts: vertical integration and vertical separation. If a franchise fee is used to extract the retailer’s profit, then it is in the individual interest of each manufacturer to choose vertical separation and charge his retailer a wholesale price in excess of the unit production cost, depending on the specific time structures. These arguments could make integration preferable for the manufacturer if the wage bargaining power of the union is relatively powerful.     

Stability and instability in oligopoly

For regular oligopolies (both homogeneous and heterogeneous) the (local) Cournot-Nash equilibria are the (non-degenerate) critical points of a Morse-Smale vector field, defined on the feasible region of non-negative prices and outputs. When at the boundary of this feasible region this vector field points inwards, it follows from the Morse inequalities that there is at least one stable equilibrium. When there is a unique, non-stable, interior equilibrium, necessarily the vector field points outwards somewhere along the boundary of the feasible region. This raises to a stable boundary equilibrium.     

Bilateral oligopoly and quantity competition

Bilateral oligopoly is a market game with two commodities, allowing strategic behavior on both sides of the market. When the number of buyers is large, bilateral oligopoly approximates a game of quantity competition played by sellers. We present examples which show that this is not typically a Cournot game. Rather, we introduce an alternative game of quantity competition (the market share game) and, appealing to results in the literature on contests, show that this yields the same equilibria as the many-buyer limit of bilateral oligopoly, under standard assumptions on costs and preferences. We also show that the market share and Cournot games have the same equilibria if and only if the price elasticity of the latter is one and investigate the differences in equilibria otherwise. These results lead to necessary and sufficient conditions for the Cournot game to be a good approximation to bilateral oligopoly with many buyers and to an ordering of total output when they are not satisfied.     

Labor-managed Cournot oligopoly and industry output

It is known that in imperfectly competitive situations a labor-managed firm produces less output than an equivalent entrepreneurially controlled firm. However, it has also been suggested that there would be more labor-managed firms than entrepreneurial firms, ceteris paribus. Analysis shows that, in the context of a Cournot model of oligopoly with free entry, the latter contention is false, so the labor-managed industry would not be “more competitive.” Some extensions and comments on this result are also offered.     

Behavioural heterogeneity and Cournot oligopoly equilibrium

It is not uncommon to see studies of imperfect competition or of industrial organization rest upon questionable foundations such as the hypothesis that inverse market demand is, whenever it is positive, concave or even linear. Assumptions of this sort are not robust (i.e. “additive”) in the sense that they are not usually preserved through aggregation of different sectors that would satisfy them individually. The present paper investigates an alternative specification that is based upon the plausible existence of significant heterogeneities among demanders. It is demonstrated that specific forms of demand heterogeneity tend to stabilize market expenditures. In a partial equilibrium context, sufficient demand heterogeneity is shown to imply existence and unicity of a Cournot oligopoly equilibrium.     

Price dispersion in oligopoly

In the world of perfect markets consumers are assumed to respond instantly to every small price change. However, in the real world it is not clear that any small price change will have a great impact on consumers' decisions and that, regardless of their habit, they will shift from one brand to the other. The purpose of this paper is to examine oligopolistic price competition under the assumption that consumers are non-responsive to small price differences. The paper proves the existence of equilibrium in which firms do not necessarily charge the same price; however some of the firms charge their monopolistic price and others charge prices close to that price.     

Taxation within Cournot oligopoly

When the production of output causes pollution, we often consider taxation as a means to reduce it. This paper examines various forms of taxation to control pollution within Cournot oligopoly. It shows that two commonly used forms can actually increase pollution. In contrast, both of these forms unambiguously reduce pollution within the competitive model. The paper provides conditions, in terms of demand and technology, that make taxation effective in the Cournot oligopoly case. Another implication of the analysis is that, outside the price-taking framework, asymmetry of cost functions is particularly important and deserves careful attention when we examine the effect of taxation.     

Forward trading and collusion in oligopoly

We consider an infinitely repeated oligopoly in which at each period firms not only serve the spot market by either competing in prices or quantities but also have the opportunity to trade forward contracts. Contrary to the pro-competitive results of finite-horizon models, we find that the possibility of forward trading allows firms to sustain collusive profits that otherwise would not be possible to achieve. The result holds both for price and quantity competition and follows because (collusive) contracting of future sales is more effective in deterring deviations from the collusive plan than inducing the previously identified pro-competitive effects.     

Forward trading in exhaustible-resource oligopoly

We analyze oligopolistic exhaustible-resource depletion when firms can trade forward contracts on deliveries – a market structure relevant for some resource markets (e.g., storable pollution permits, hydro-based power pools) – and find that trading forwards can have substantial implications for resource depletion. We show that when firms’ initial resource-stocks are the same, the subgame-perfect equilibrium path approaches the perfectly competitive path as firms trade forwards frequently. But when the initial stocks differ, firms can credibly escape part of the competitive pressure of forward contracting. It is a unique feature of the resource model that equilibrium contracting and the degree of competition depends on resource endowments.     

The quadratic oil extraction oligopoly

Each extractor has a distinct initial endowment of oil and a distinct quadratic extraction cost and faces a linear industry demand schedule. We observe in a discrete-time model with a finite number of periods that the open loop and closed loop solutions are the same if initial stocks are such that each competitor is extracting in every period in which her competitors are extracting.     

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.