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# For A Duopoly Involving Homogeneous Products, Explain And Contrast A Cournot, Stackelberg And Bertrand Equilibrium.

2199 words - 9 pages

The critical problem faced by a firm in an oligopoly is that its decisions affect the prices and quantities of its rivals. The oligopoly problem arises because, where there are only a few suppliers to the market; the demand for the product of one firm depends significantly on the price and output. A non-cooperative duopoly is an industry consisting of two firms in which firms take their decisions independently and can be classified according to whether firms treat quantity or price as the key strategic variable. When it comes to quantity setting there are two major models put forward. The first, developed by Cournot in 1838 is based on firms setting quantities simultaneously where each firm is setting the output that maximises its profit given the output of its rival. In 1934 Stackelberg argued that one firm takes the role of 'leader' with the other firm acting as a 'follower' emphasising the quantity leadership view. Here the leader anticipates the response of the follower and uses this to its own advantage.Bertrand in 1883 argued that price, not output, should be the firms decision variable where rivalry between the duopolists would result in both setting a zero price. Each of the models provides a different equilibrium output and welfare levelWe assume a linear market demand curve, P(Q) which is given by a - Q where a is a positive parameter. Further we assume that all firms would incur the same constant per unit production cost, c, where c < a and for simplicity we follow Cournot in supposing that there are no costs of production (c = 0).The Cournot model puts forward a case for simultaneous quantity setting where at the beginning of each period the firms take their decision independently and simultaneously. Here the profits of firm f (same as TR) will depend on both outputs which is given by ∏1 = q1(a - q1 - q2). The interdependence between the 2 firms results in the profit-maximising output for firm 1 depending on the output of firm 2 and vice versa which is modelled using reaction function/curves. Firms 1's reaction curve q1 = R1(q2) shows that the profit maximising output of firm 1 is a function of the output of firm 2. As production costs are zero and the assumed market demand, the specific form of the reaction function is linear over the relevant range R1(q2) = (a-q2)/2. To confirm 1's optimal response to q2 we partially differentiate ∏1 (q1,q2) with respect to q1 to obtain the first order condition:Further reaction curves can be derived using iso-profit curves which show the output combinations that yield firm 1 the same profit. The can be used to show firms 1's optimal response to q2. Where the slope of the iso-profit curves are zero we get a line going through to indicate the firms reaction curve. Asthe model involves symmetry between the firms, the reaction curve for firm 2 over the relevant range is given by q2 = r2(q1) = (a - q1)/2In a Cournot equilibrium firms choose their outputs simultaneously so a firm chooses it...

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