Question

Briefly describe the three Oligopoly models

Answer 1

The three oligopoly models are:

(i) Cournot Model, (ii) Bertrand's Model (iii) Stackelberg Model,

(i) Cournot Model - In Cournot Model, we make the following assumptions: (a) There are 2 firms, Firm 1 and Firm 2 selling homogeneous product. (b) The cost function of both the firms are identical, (c) The objective of the firms is to maximise their own profit, (iv) In this model, Conjectural Variation (CV) is zero. This means when a firm changes its own output, it considers that the output of the rival firm remains constant.

Here, Conjectural Variation (CV) is defined as the change in output of the jth firm in response to the change in output of the ith firm as perceived by the jth firm, when quantity is the decision variable. Since the product is homogeneous in nature, so both the firms faces the entire market demand curve. Firm 1 chooses output Q1 to maximise its profit, taking output of the other firm as given, in other words, Conjectural Variation (CV) is zero. Profit- maximisation leads to familiar optimality condition, namely MR1 = MC1. Thus, we get the optimal output level of Firm 1. Now, MR1 depends on Q2, i.e. the output of firm 2, and hence optimal level of output of firm 1 depends on Q2. This dependency is, in turn, is captured by the reaction function or Best Response Function. Reaction function is defined as the optimum response of one firm to a change in the output level of the other firm. Equilibrium point is the point where the 2 reaction functions intersect with each other. In industry, all firms should operate on their respective reaction functions and hence intersection is the only solution. We can interpret the Cournot Equilibrium as the Nash Equilibrium. Nash Equilibrium is a situation in which no firm has any incentive for unilateral defection. Now, if the reaction function of the 1st firm is steeper than the reaction function of the 2nd firm, i.e. if absolute value of the slope of R1 is greater than the absolute value of the slope of R2, then we get that the equilibrium is a stable equilibrium. But if R2 is steeper than R1, we get unstable equilibrium in that case.

(ii) Bertrand's Model - Bertrand's Model is similar to the Cournot Model, except that in the later model, strategic variable is output, whereas in Bertrand's Model, strategic variable is price. In Bertrand's Model, each firm assumes that the other firm keeps its price constant. Each firm faces same market demand and its objective is to maximise its own profit, on the assumption that the price of the rival will remain constant. Like Cournot model, Bertrand's model can also be analysed with the help of the reaction function. Let us consider a duopoly market where the product is of homogeneous nature. Let Q1 and Q2 be the output of firm 1 and firm 2 respectively and the prices of the 2 firms be P1 and P2. Then the demand function can be written as Q1 = F1(P1 , P2) and Q2 = F2(P1 , P2). The 1st firm believes that if it fixes its own price at P1, then the 2nd firm fixes price at P2. Total cost corresponding to any particular level of output are given by the 2 functions C1 = F1(Q1) and C2 = F2(Q2). These 2 functions represent that the cost level will depend on the respective output of each firm, but the output levels are again dependent on prices. Hence cost levels C1 and C2 will depend on prices P1 and P2. Ultimately the profit level of the 2 firms will also depend on prices. The first firm assumes that P2 is constant and selects P1 in such a manner that its profit increases. For one level of P2, we get corresponding value of P1, that maximises profit of firm 1. In this way, we get different combinations of P1 and P2 for which the profit of firm 1 is maximum. The locus of all such combinations of P1 and P2 gives the Price Reaction Curve of the 1st seller. It will be an upward rising curve.

(iii) Stackelberg Model - In the Cournot Model, it was assumed that a change in the output level of one firm will have no effect on the output level of the other. This assumption is clearly unrealistic because firms must learn from past experience. A sophisticated model has been developed by german economist Heinrich Von Stackelberg and it is an extension of the cournot model. Stackelberg has constructed the reaction curve by his isoprofit curve approach. If we assume there are two sellers A and B, then an isoprofit curve for firm A is the locus of points defined by the different levels of output of A and his rival B, which yield to A the same level of profit. Similarly, an isoprofit curve for firm B is the locus of points of different levels of output of the 2 competitors which yield to B the same level of profit. The reaction curve of firm A is the locus of points of the highest profits that firm A can attain, given the level of output of rival B. It is called "Reaction Curve", because it shows how firm A will determine its output as a reaction to B's decision to produce a certain level of output. Similarly, we can get the reaction function of B. Stackelberg model states that one firm is sufficiently sophisticated to recognise that his competitor acts according to Cournot's assumption. The recognition allows the firm to determine the reaction curve if his rival firm and incorporate it in his own profit function, which he then proceeds to maximise like a monopolist. As the leader or sophisticated firm takes into account, the follower's reaction function is the profit maximising conduct, its Conjectural Variation is non-zero. But the follower chooses the output level taking the leaders output as given, i.e. follower's Conjectural Variation is zero. Thus the leader has no reaction function for the leader always selects the point on his follower's reaction function, where the profit is maximum.