# Explain Cournot, Bertrand and Stackelberg models of oligopoly assuming that the firms have identical costs. Describe circumstances where each model is appropriate.

Explain Cournot, Bertrand and Stackelberg models of oligopoly assuming that the firms have identical costs.  Describe circumstances where each model is appropriate.

The theory of the firm is a set of economic theories that describe the nature, existence and behaviour of a firm and its relationship with the market.  Some of the questions it aims to answer are why firms enter or exit the market, why there are boundaries between the firm and the market, and why firms are structured in a specific way.  An oligopoly is a common market form in which a market or industry is dominated by a small number of sellers.  There are several different ways for firms to behave in an oligopolistic environment, and whereas the Stackelberg and Cournot models compete on quantity produced, the Bertrand model is based on price competition between firms.

Stackelberg

The Stackelberg model is a leadership game in which the leading firm makes the first move and the follower firms adjust their own product decisions accordingly.  The total industry output is based on the output of the leader, y1 and that of the follower, y2.  The profit maximising output of the leader depends on how the follower will react and assuming that the follower will also want to profit maximise, his problem will be: .  Even though the follower’s profit depends on the output of the leader, from his point of view, the output is predetermined and therefore can be seen as a constant.  The follower would want to produce at the level of output where marginal cost equals marginal revenue: .  A reaction function describes how the follower will react to the leader’s choice of output and can be written as: .  Firm two’s profit function: for the inverse demand function that takes the form and therefore the marginal revenue would be equal to .  Assuming that costs are zero, firm two’s reaction function takes the form: .  The profit maximisation problem for the leader is such that .  As we have assumed that costs are zero, the leader’s profits can be written as:
.  Marginal revenue for the first firm is therefore:  and setting marginal costs to zero,  and , thus total industry output is .

The Stackelberg equilibrium is when the leader, firm one, chooses a point on firm two’s reaction curve that touches the firm one’s lowest possible isoprofit line, thus yielding the highest possible profits for firm one.

Cournot

A problem that arises with the Stackelberg model is that it assumes that one firm is able to make its decision before the other firm.  The Cournot model is a static one and is used when two firms are simultaneously trying to decide what quantity to produce.  In this scenario, firms forecast the other firm’s output in order to make a sensible output forecast ...