Kazuhiro Ohnishi

A Model of a Price-setting Duopoly with a Wage-rise Contract

This paper considers a wage-rise-contract between a firm and its employees as the firms strategy, and suggests a wage-rise-contract policy. The policy is a promise by the firm that it will announce a certain output level and a wage premium rate, and if it actually produces more than the announced output level, then it will pay each employee a wage premium uniformly. First, this paper examines the case in which one of two firms unilaterally offers the wage-rise-contract policy by using a two-stage price-setting duopoly model. It is then shown that there exists an equilibrium which coincides with the Stackelberg solution where the firm adopting the policy is the leader. Next, this paper examines the case in which both firms can offer the wage-rise-contract policy in the model. It is then shown that there exists an equilibrium which is more profitable for both firms than in the unilateral case.

On the Effectiveness of the Lifetime-Employment-Contract Policy

This paper examines a subgame perfect equilibrium when one of two duopolists executes a lifetime-employment-contract policy, which is a strategic commitment that generates kinks in the reaction curve, by using a two-stage quantity-setting model. The purpose of the paper is to show concretely in what kinds of cases the policy is effective. Copyright 2002 by Blackwell Publishers Ltd and The Victoria University of Manchester

A Three-Stage International Mixed Duopoly with a Wage-Rise Contract as a Strategic Commitment

This paper examines international mixed competition, where one domestic social-surplus-maximizing public firm and one foreign profit-maximizing private firm can adopt a wage-rise contract as a strategic commitment. The paper considers the following three stages. In the first stage, the domestic public firm can offer the wage-rise contract. In the second stage, the foreign private firm can offer the wage-rise contract. In the third stage, both firms simultaneously and independently choose and sell their actual outputs. The equilibrium of the international mixed duopoly model is discussed.

Strategic Investment in a New Mixed Market with Labor-Managed and Profit-Maximizing Firms

This paper examines a continuous-time mixed model of the strategic investment decisions of a labor-managed income-per-worker-maximizing firm and a profit-maximizing firm in a new mixed market and constructs a set of perfect equilibria of the continuous-time mixed model. The paper shows that there exists a particular equilibrium in which neither firm invests to its steady-state reaction curve. The paper also finds that the existence of the particular equilibrium depends on each firms being able to respond quickly to its rivals investment and that the particular equilibrium is profitable for each firm.

A UNILATERAL PRICING POLICY AND THE STACKELBERG EQUILIBRIUM

Cooper (1986) examines the equilibrium of the retroactive most-favored-customer pricing policy by using a two-period duopoly model. He shows that the most-favored-customer policy enables both firms to offer higher prices and to enjoy higher profits. Neilson and Winter (1992) show that even if one firm in a price-setting duopoly adopts the most-favored-customer policy, the equilibrium does not coincide with the Stackelberg solution. This paper introduces a pricing policy by using a one-period two-stage model and shows that if one firm in a price-setting duopoly adopts this policy, then the equilibrium coincides with the Stackelberg solution.

Wage-Rise Contract and Cournot Competition with Labor-Managed Firms

The pioneering work on a theoretical model of a labor-managed firm was conducted by Ward (1958). Thereafter, many economists have studied the behaviors of labor-managed firms.1 Laffont and Moreaux (1985) examine the welfare properties of free entry Cournot equilibria in labor-managed economies and show that Cournot equilibria are efficient provided that the market is sufficiently large.2 Zhang (1993) and Haruna (1996) apply a Dixit (1980), Bulow et al. (1985) framework of entry deterrence to a labor-managed industry and show that a labor-managed incumbent firm has a greater incentive to hold excess capacity to deter entry than a corresponding profit-maximizing incumbent firm. Okuguchi (1993) examines two models of duopoly with product differentiation and with only labor-managed firms, in one of which two firms’ strategies are outputs (labor-managed Cournot duopoly) and prices become strategic variables in the other (labor-managed Bertrand duopoly). He shows that reaction functions are upward-sloping under general conditions in both labor-managed Bertrand and Cournot duopolies with product differentiation.3 Lambertini and Rossini (1998) analyze the behavior of labor-managed firms in a two-stage Cournot duopoly model with capital strategic interaction and show that labor-managed firms choose their capital commitments according to the level of interest rate, unlike what usually happens when only profit-maximizing firms operate in the market.

ON THE PAYOFF REPRESENTATIONS OF NORMAL FORM GAMES

The literature on normal form games generally depicts the payoff matrices of two or three players. However, many such games discuss n-players. Therefore, this note studies the payoff representations of n-player normal form games.

BERTRAND GAMES WITH LIFETIME EMPLOYMENT CONTRACTS AS A STRATEGIC COMMITMENT

This paper considers lifetime employment contracts as a strategic commitment and discusses the respective equilibrium outcomes of the two cases of a price-setting game with substitute goods and a price-setting game with complementary goods. As a result, it is shown that in each case, the equilibrium coincides with the Bertrand solution with no lifetime employment.

A Note on the Most-Favoured-Customer Pricing Policy

This paper extends the retroactive most-favoured-customer pricing policy examined by Cooper (1986). He showed that the policy enabled both firms in a duopoly to offer higher prices and to enjoy higher profits. This paper introduces a variable into the most-favoured-customer pricing policy. Then, it shows that there is an equilibrium in which the duopolists can further increase their profits.