We may illustrate the process with the help of Fig. Our mission is to provide an online platform to help students to discuss anything and everything about Economics. From this iso-profit map, we would obtain a function that would express A’s output per period (qA) as a function of B’s output (qB). Putting these values in (14.36) we obtain the Cournot reaction functions to be. That is why, at any particular qA (output of firm A), firm B will produce that output (qB) at which the ordinate at qA would become a tangent to an iso-profit curve of B. When there are only two sellers (firms) in the market for a product, we may assume that the profit of each seller is a function of the output levels of both: An interesting example of conjectural variation is contained in Stackelberg’s analysis of leadership and followership. That is, in this model, A is the output-leader and B the output-follower. In other words, the points in the output space of Fig. Therefore, Fig. It was developed by Antoine A. Cournot in his “Researches Into the Mathematical principles of the Theory of Wealth”, 1838. This we can prove very simply in the following way. an oligopoly) in which competing companies simultaneously (and independently) chose a quantity to produce. If B produces q2qc, then, A would horizontally shift the demand curve DD1 leftward by the amount q2qc, and it would become D’q2 for A and the corresponding MR curve would be MR1, both with origin at O. In other words, the vertical intercept OR of A’s reaction function is equal to the competitive output. At the point E’, which is the midpoint of the segment d’D1, eA = 1 and, therefore, RA, and also ÏA, is maximum. From this curve, we can know what would be the equilibrium output of A at any given output of B. The example gives us: a= 100, b = 0.5, d = 5, e = 0, g = 0and h = 0.5. Share Your PPT File, Welfare Effects of Oligopoly | Microeconomics. Therefore, each point in this space implicitly represents a combination of RA and RB and, so, of ÏA and ÏB. Equation (14.14) gives us that the profit-maximising (or equilibrium) output of duopolist A(qA) is a function of the output of duopolist B(q0), i.e., from this function, we are able to know the output of A at any particular quantity of output of B. Since total output has increased, price would fall from Op1 to Op2. In period 1, firm A would produce q1 = OS (or Oa0) as in the previous period, assuming that B’s output, qB, would be zero and B would produce the output, Ob1, assuming that A would produce the previous period’s output, OS. (iii) If qA remains constant at a particular quantity like OV in Fig. Again, both OS and OM represent the monopoly solution of the model [14.2.2(d)], and so here OM would be equal to OS. That is why, at any output of the two firms taken together, i.e., at any q = qA + qB, we would have MC = 0. If he succeeds in doing this, A would move on to a point of tangency on a higher iso-profit curve giving him a lower level of profit, and B would be able to move on to a lower iso-profit curve, giving him a higher level of profit. A, however, then realizes that B will change his behaviour if A changes his output, and that the maximum joint profit occurs at the output level Oq1. I was unable to find a textbook that specifically detailed the Cournot Model’s best response function while including a marginal cost, without going into a calculus derivation so I made my own, the demonstration is shown at the bottom of this post. 14.10. What are the resulting market price and profits of each firm? In this figure, duopolist A’s output per period has been measured along the horizontal axis and B’s output per period has been measured along the vertical axis. On the basis of the assumptions made in the Cournot model, we may now derive mathematically the Cournot reaction functions. Let us now represent what we have obtained in Fig. The output combination that would be produced in period 1, would therefore, be K1 (Oa0, Ob1). The general features of these curves (of any duopolist) may now be systematically listed: (a) The iso-profit curves of a duopolist would be concave to the axis along which his output is measured. 14.12. That is, along the approach road to equilibrium, when one of the duopolists happens to produce 1/3 of the competitive output, then the other firm would also produce the same output, and the Cournot model will be in equilibrium. Cournot duopoly, also called Cournot competition, is a model of imperfect competition in which two firms with identical cost functions compete with homogeneous products in a static setting. Under the circumstances, equilibrium in the Cournot model can occur only at the point of intersection of the two reaction functions. The adjustment process that we have underlined above would go on so long as one of the duopolists would prove wrong although the other one proves correctâthe output combination would move from the point K1 on MN to K2 on RS to K3 on MN, and so on. 14.7. Therefore, now he would produce the output q3q4, which would be determined at the MR = MC (= 0) point. What are the firms' outputs in a Nash equilibrium of Cournot's model? As B has now entered the market, and because of his entry, supply of the product has increased and price fallen, A would revise his production plan in the next period, i.e., in period 2. Let us suppose that initially A has been a monopolist and B suddenly joins the industry to compete with him. Together, the duopolists would produce 2/3 of the competitive output (Oqc). Therefore, in the above discussion, we have obtained: (i) If qB remains unchanged at any particular quantity (e.g., OC in Fig. However, the Cournot solution may be better represented and better explained if we proceed through the reaction functions. 14.13. 14.9. 14.11. Although Cournot’s model was based on some unrealistic assumptions, his method of analysis has been useful for subsequent theoretical development in the areas of duopoly and oligopoly. Therefore, here the condition for competitive equilibrium would be p = MC = 0. 14.14. For the sake of simplicity, we have assumed here that the market demand curve (14.9) is a (negatively sloped) straight line. Therefore, under the circumstances, duopolist A’s demand curve would be dDc and the quantity-axis and the price-axis of this demand curve would be, respectively, CT and Cd. If we put qA = 0 in the reaction function of (14.14) of A, we obtain. The NASH equilibrium is stable. This is because the numerical coefficient of price-elasticity of demand (eA) is greater than one (eA > 1) over the segment dE of A’s demand curve, and the total costs of the duopolists (CA and CB) at each output are zero [assumption (vi)]. The model is also useful as it helps us to understand how and why the oligopolists may be driven to bargaining or collusion. Privacy Policy3. However, a simple observation will simplify the computations. The Bertrand Equilibrium model describes consumer purchasing behavior based on prices of products. Some of these iso-profit curves have been drawn in Fig. Let us suppose now that the reaction functions of A and B are RS and MN in Figs. In the Cournot model, by assumption (x), each duopolist fixes his output in any particular period, by assuming that his rival would keep his output unchanged at the quantity he produced in the previous period. Let us suppose that the total revenue (R) function of the follower is. In period 2, A would prove correct in his assumption about B’s output, but B would prove wrong in his assumption about A’s output. Therefore, E is the equilibrium point of the Cournot model of duopoly, where each duopolist would produce: Let us note that Cournot’s model can be generalized into an oligopoly model with more than two firms. 14.13. In Fig. the variable, qB. The profit-maximisation problem of the leader may be analysed, therefore, in the following way. In this figure, the straight line AB is the market demand curve (14.9) for the product. The monopoly solution would be the solution if the two duopolists colluded and formed a multi-plant monopoly. He, therefore, cannot make any conjecture about his rival’s behaviour, i.e., he does not behave conjecturally. In this model, A will first start with the monopolistic price; B then enters the market, reducing the price somewhat, and captures the whole market. We may obtain the reaction function of duopolist B also following the same procedure. We have seen above that the reaction functions of the duopolists have been derived from the profit-maximising conditions, and by assumption, both the duopolists pursue the profit- maximising goal. 2/3 Oqc = 1/3 Oqc. In period 1, therefore, A proves wrong and B correct. Therefore, the curve T3F’T4 becomes another iso-profit curve of duopolist A. It has the following features: In other words, the output leader A would prefer the leadership equilibrium to Cournot equilibrium, and the output follower B would prefer the Cournot equilibrium to the leadership equilibrium. This equilibrium solution is a (qA, qB) combination. A follower obeys his reaction function given in (14.32) and adjusts his output level to maximise his profit, given the quantity decision of his rival, whom he accepts as a leader. This figure may also be called the iso-profit map of duopolist A. d. Calculate the Cournot equilibrium (i.e., the values of Q 1 and Q 2 for which both firms are doing as well as they can given their competitors’ output). Cournot Model 3 RD1(p,q2)=D(p)-q2. In Fig. 14.6, this reaction function of A has been obtained to be the line RS. Duopolist A’s reaction function gives the value of qA for any specified value of qB, which maximises ÏA. EDITED: NPV is the net present value. A starts with output Oq1 and price Op1 in Fig. Code to add this calci to your website . Total duopoly output now would be Oq2. Chamberlin also changes Cournot’s assumption that each duopolist naively believes that his rival’s output would remain unchanged. Thus, here neither of the reaction functions is obeyed, and we encounter a disequilibrium which is known as the Stackelberg disequilibrium. Assumption (x) implies that A knows B’s Cournot reaction function, for as we shall see, he would have to maximise profit subject to the constraint that he remains on B’s reaction function which is given by the line MN in Fig. In order to compute the pair (Q 1 *, Q 1 *), we need to solve equations 6 and 7. It would be a straight line if, the market demand curve for the product is a straight line, and it would be negatively sloped, because, as B’s output increases, profit-maximising output of A diminishes.
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