Equilibrium prices in the Bertrand and Cournot oligopolies

The equilibrium prices for the Bertrand and Cournot oligopolies with product differentiation are compared. If all firms have linear demand and cost functions, and if, in addition, the Jacobian matrix of the demand functions has a dominant negative diagonal, the Cournot equilibrium prices are not lower than the Bertrand ones. The general condition for the comparison of the Bertrand and Cournot equilibrium prices can be derived even if the nonlinearity is involved in the cost and/or demand functions.     

Persistent misalignments of the European exchange rates: some evidence from non-linear cointegration

The asymmetric and persistent adjustment of the European real exchange rates is investigated using the framework of non-linear cointegration. The episodes of slow mean-reversion dynamics over the period from 1979 to 1999 are explained. A test of unit root against STAR cointegration is proposed and some complete estimations and stochastic simulations of ESTAR models are presented. The presence of effective non-linear adjustment during the moving of the currencies to their long-run fundamental equilibrium exchange rate value is discussed.     

技术外溢、策略性选址与产业集聚

大型寡头企业的策略性选址对形成地方性产业集聚、带动当地经济发展举足轻重.影响企业选址的因素很多,技术溢出和运输成本是其中的重要因素.文章建立了一个同时考虑技术溢出、运输成本和市场竞争的企业选址与产量竞争模型.研究发现企业集聚是完美纳什均衡,技术溢出是导致企业集聚的重要原因;企业集聚既可能发生在运输成本最低的地区,也可能发生在城市的其他区位,前提是企业在该区位集聚满足"技术溢出效应"大于"运输成本效应";企业在运输成本最低点集聚的均衡产量最大且企业利润最多,而在城市端点集聚的均衡产量最小且企业利润最小.     

A dynamic duopoly model with bounded rationality based on constant conjectural variation

In this paper, we construct dynamic models on the basis of constant conjectural variation. Duopolists with dynamic adjustment behavior of bounded rationality have been considered. Numerical simulation is used to illustrate the complexion of models. The existence of equilibrium points and their stability in this nonlinear system are discussed. We study two special cases of symmetry model and Bertrand model with conjectural variation. When the speed of output adjustment changes, a series of complex phenomena including bifurcation, chaos and strange attractors can be observed in our models. We also analyzed the importance of the initial conditions to the system that a tiny variation of the initial value will cause dramatic fluctuations in output.     

Credit rationing and the adjustment of the loan rate: An empirical investigation

In this paper, models of credit rationing are analyzed using quarterly data on domestic bank loans of four countries. First, models of temporary (dynamic) credit rationing are considered. The price (interest rate) equation proposed by Bowden is estimated assuming equal and unequal adjustment speeds under excess demand and supply conditions. Second, the stability of the interest-rate equation is tested. We motivate this test by the fact that permanent (supply-side equilibrium) credit rationing implies instability of this regression relationship. Statistically significant credit-rationing effects are found for the countries considered, with the exception of the U.S.     

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.     

Optimal debt contracts and product market competition with exit and entry

We show how competition in oligopolies, with the possibility of failure and exit of a levered incumbent, affects the ex-ante design of optimal debt contracts. When a levered firm's profits are unobservable, a debt contract imposes the threat of nonrenewal to induce truthful revelation. Because nonrenewal impacts the future profitability of the surviving competitor, the contract influences the competitor's pricing strategy and the equilibrium profits of both firms. The optimal contract is quite different from a standard debt contract, and induces the competitor to be less aggressive, resulting in higher equilibrium prices and profits, and higher returns for investors.     

An analysis of entry-then-privatization model: welfare and policy implications

This study formulates a new model of mixed oligopolies in free entry markets. A state-owned public enterprise is established before the game, private enterprises enter the market, and then the government chooses the degree of privatization of the public enterprise (termed the entry-then-privatization model herein). We find that under general demand and cost functions, the timing of privatization does not affect consumer surplus or the output of each private firm, while it does affect the equilibrium degree of privatization, number of entering firms, and output of the public firm. The equilibrium degree of privatization is too high (low) for both domestic and world welfare if private firms are domestic (foreign).     

Adjustment of Profits: Evidence from Australian Manufacturing

Studies of industry profitability generally deal with long-run equilibrium models, making no allowance for slow adjustment to equilibrium. In this study, a cross-sectional analysis is carried out against a sample of Australian manufacturing industries at the Australian Standard Industrial Classification (ASIC) four-digit level between 1977–78 and 1984–85. Firstly, a profit model is estimated in equilibrium form as well as allowing for both uniform and variable adjustment rates across industries. The variable adjustment model is superior, with either model implying at least half adjustment to equilibrium within the seven-year sample period. Secondly, results are examined for the impact of firm homogeneity of firms within industries. Homogeneity of firms is found to have substantial impact,increasing both the estimated profits-concentration relationship and the estimated speed of adjustment.     

A new look for Stackelberg-Cournot equilibria in oligopolistic markets

Summary. This note deals with Cournot type oligopolies in which the market clearing price occasionally may be non-unique. A Stackelberg leading producer is present. Given that setting we explore continuity properties of the followers' reaction and provide sufficient conditions for existence of equilibrium. Received: June 20, 2000; revised version: April 24, 2001     

Regulating oligopolistic industries: A generalized incentive scheme

This paper deals with the design of regulatory mechanisms for oligopolistic industries. The proposed incentive scheme consists of two parts: a subsidy depending upon a firm's contribution to an equilibrium price reduction, and a tax equal to the profit of the previous period. This mechanism is as effective in regulating oligopolies as the well-known incremental surplus subsidy scheme in a monopoly framework. The proposed scheme provides appropriate incentives to enforce competitive behavior in a Cournot oligopoly. The scheme is welfare improving even if firms collude.     

Does timing of decisions in a mixed duopoly matter?

We determine the endogenous order of moves in a mixed price-setting duopoly. In contrast to the existing literature on mixed oligopolies we establish the payoff equivalence of the games with an exogenously given order of moves if the most plausible equilibrium is realized in the market. Hence, in this case it does not matter whether one becomes a leader or a follower. We also establish that replacing a private firm by a public firm in the standard Bertrand?CEdgeworth game with capacity constraints increases social welfare and that a pure-strategy equilibrium always exists.     

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.     

Market allocation through search: Equilibrium adjustment and price dispersion

This essay discusses market allocation under uncertainty in a market for a homogeneous good. Market participants contact one another at random times to buy or sell single units of the good. Transactions are carried out at different prices simultaneously. Optimal search rules are employed to describe individuals behavior. Such models provide the framework of a market structure within which equilibrium adjustment processes are analyzed. These decentralized, nontâtonnement processes of price and quantity adjustment are utilized to examine equilibrium. Price dispersion, which characterizes equilibrium, is essentially due to finite lifetimes of market participants.     

Behavioral convergence properties of Cournot and Bertrand markets: An experimental analysis

This paper reports an experiment that examines the relative convergence properties of differentiated-product Cournot and Bertrand oligopolies. Overall, Bertrand markets tend to converge to Nash equilibrium predictions more quickly and more completely than Cournot markets. Further, when products are close substitutes Bertrand markets respond more quickly to an announced nominal shock. As products become weaker substitutes, however, an increased tendency for tacit collusion degrades convergence in Bertrand markets. This effect is particularly pronounced following a nominal shock. Our results suggest that in an oligopoly context variations in decision error costs dominate a ‘Strategic Substitutes Effect’ isolated in previous experimental research.     

Exchange rate dynamics under gradual portfolio adjustment

This paper generalizes the asset market approach to exchange rate determination by introducing gradual adjustment of asset-holder portfolios. The influence of different speeds of portfolio adjustment on exchange rate dynamics is considered. Asset market models characterized by instantaneous portfolio equilibrium appear as a special case. The dynamics of exchange rate adjustment following an open-market operation are shown to be qualitatively similar to those of the orthodox instantaneous portfolio equilibrium models. Thus, gradual portfolio adjustment does not compromise the qualitative results derived with the help of those models. The speed of portfolio adjustment is however shown to influence the degree of exchange rate volatility. In particular, the phenomenon of exchange rate overshooting depends crucially on the speed of portfolio adjustment.     

In Defence of Model-Based Seasonal Adjustment: An Illustration Using Australian Data

It is argued that the X-11 seasonal adjustment procedure suffers from severe drawbacks, and so it should be abandoned in favour of model-based seasonal adjustment. Furthermore, it is argued that Harvey's structural time series model is superior to the conventional seasonal ARIMA models for the purpose of model-based seasonal adjustment. It is shown, with the help of a large number of Australian time series, that the nature of seasonality differs from one series to another, and this is why model selection is crucial for seasonal adjustment. It is further shown that model-based seasonal adjustment could produce results that are significantly different from those obtained by applying the X-11 procedure. Since the X-11 procedure is not based on an explicit model and in view of its other serious drawbacks, it is concluded that the procedure should be abandoned in favour of model-based seasonal adjustment.     

On the stability of the stackelberg oligopoly equilibrium

The stability of the equilibrium in the Stackelberg undifferentiated oligopoly model where each oligopolist strives for leadership is analyzed for general demand and cost functions and for a discrete system with non-instantaneous adjustment.     

The Dynamics of Trustworthiness Among the Few

Conventional stochastic models of evolutionary processes with infinitely many agents are deterministic models in disguise. Only finite population models become truly stochastic. Therefore this paper focuses on an indirect evolutionary model of pair wise interaction in a pool of three (corresponding to analysing oligopolies in terms of duopoly markets). The outcomes of the process over the long haul are characterized by the stationary distribution of the underlying Markov process. Our example indicates that intermediate cases cannot be seen as convex combinations of the two polar non-stochastic cases of two or infinitely many individuals.
JEL Classification Numbers: C72, C73.