BUSINESS ECONOMICS

Coursework Assignment 2

Coursework Assignment 2

Question 1

In the Cournot model, firms compete in their outputs, firms simultaneously choose how much to produce, and then the market price determined by the inverse market demand function. With or without product differentiation, this Cournot model can be considered a standard game in strategic form, in which firms are players, their attainable output levels are the sets of strategies, and the firms' objectives are to maximize profits.

As in a generic strategic form game, in order to identify possible equilibrium outcomes, we must figure out each firm's best response in this Cournot model. When an oligopolistic firm decides how much to produce, it needs to have an expectation of how much the other firms will produce. Given this belief or expectation, the problem faced by an individual firm becomes a relatively easy decision problem. There is a unique correspondence between the market price and the output of the firm under consideration. The more the firm produces, the lower the market price for its product. Each oligopolistic firm faces a dilemma similar to that of a monopolist, and in choosing how much to produce, it must balance the costs and benefits. When solving this firm's profit maximization problem, we treat the outputs of the other firms as a given. Then, the optimal output level of the oligopolist necessarily depends on how much the others produce. The relation between the optimal output of a firm and the output levels of the other firms provides us with the best response of this firm under consideration. Repeating the same process for every firm, we can identify the oligopolist's best response to the outputs of the other firms. An outcome that satisfies all the best responses of all firms is a Nash equilibrium outcome in the Cournot model, which is also commonly known as Cournot equilibrium.

We characterize Cournot equilibrium by taking account of strategic interaction among the firms, because every firm's strategy in the equilibrium is a best response to the other firms' strategies in the profile, every firm's strategy in Cournot equilibrium is rationalizable. A strategy is rationalizable if it is a best response to the other strategies that are also rationalizable, and are the best responses of some other rationalizable strategies. Rationalizable strategies include all equilibrium strategies.

Another idea to highlight the strategic interaction among the firms is the dynamic adjustment process to reach equilibrium. For any strategy profile, if it is not equilibrium, some firms may want to revise their strategies in the profile. After this revision of strategy, some other firms may want to revise their strategies, or some of firms that revised their strategies may want to revise again. This adjustment process may or may not converge. When it does, this progress will converge into a stable equilibrium. In a non-stable equilibrium, if one firm produces a slightly different amount of output than the one given in the strategy profile, this adjustment process may diverge or converge into a different strategy ...