cournot equilibrium calculator

(c) The higher iso-profit curve of a duopolist represents a lower profit level. We have obtained, therefore, that if qB is OC then A’s (profit-maximising) output, qA, would be CF and if qB is OC’, then qA would be C’F’. Two of these curves are shown in Fig. EDITED: NPV is the net present value. 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. 14.9, the market demand curve is DD1 and the competitive output is Oqc, as they were in Fig. Before publishing your Articles on this site, please read the following pages: 1. 14.4, at qB = OC’ = constant (OC’> OC), the profit-maximising output of A is C’F’ (C’F’ < CF). Therefore, at the points on the line Cx to the left or right of F, e.g., at points H1 or H2, A’s profit would be less than that at the point F. Now at the point H1, i.e., at the output CH, (CH, < CF), the firm A may obtain the same profit as at F, if B’s output diminishes sufficiently, say, by H1T1, from the level of OC, for, if qB diminishes, the price of the product would increase. We may now easily verify that if each duopolist produces an output of 1/3 Oqc, then the Cournot model will be in equilibrium. Stackelberg equilibrium also results in a lower market price than that observed in Cournot equilibrium. In this model, each duopolist determines his maximum profit level from both leadership and followership and desires to play the role which yields the larger maximum. Since MC = 0, the competitive output here is the q at which p = MC = 0. In order to complete our explanation of the geometry of the iso-profit curves, we have to draw another curve like T1F T2. This relationship is summarised by the reaction function, qB = fB(qA). The model’s other assumptions (from which most of the models discussed hereafter will draw) are: (iii) The product is perishable, i.e., they cannot be stored and must all be sold within the duration of the period. 14.13. If qA increases beyond the quantity CF (and p diminishes), then A’s total revenue (RA) and total profit (nA) would be decreasing, since, over the segment ED] of his demand curve, eA is less than one (eA < 1). As there is now B in the market, A has reduced his output from Oq1 to Oq3. We may now illustrate the equilibrium in the Cournot duopoly market with the help of Fig. Therefore, B would produce an output of qjq2 at the point MR = MC (= 0). It was developed by Antoine A. Cournot in his “Researches Into the Mathematical principles of the Theory of Wealth”, 1838. In Fig. 14.11. 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 website includes study notes, research papers, essays, articles and other allied information submitted by visitors like YOU. 14.1, where the output of A is measured along the horizontal axis and that of B along the vertical axis. Now, the reaction function of duopolist B would be obtained in the same way, and this reaction function would be. In other words, the points in the output space of Fig. 14.5, we have measured output of duopolist A along the horizontal axis. He rather behaves autonomously for he assumes that his rival’s output is given autonomously. This assumption is very naive for it implies that the duopolists do not learn from experience—they stick to the belief that the rival would maintain his output at the level of the previous period although they repeatedly prove wrong. The points on any one of these curves are the combinations (qA, qB) of the per-period outputs of the duopolists that give A the same amount of profit per period. As we see in Fig. In Fig. If we compare now the point I with the point L2, we find that at I, the duopolist A lies on a higher iso-profit curve, i.e., on a lower profit level than at point L2, and B lies on a lower iso-profit curve, i.e., on a higher profit level than at L2. Case (iii) also would have a determinate solution which is nothing but a Cournot solution under Stackelberg assumptions, since, here each seller acts autonomously, knowing that the other will also act autonomously. This function is called the (Cournot) reaction function of duopolist A. For, at the point G, B is on the lowest possible iso-profit curve subject to qA = OD. By definition, the TR (or simply R) function of the duopolist A (i.e., RA) is. Therefore, both of them would intend to remain on their respective reaction functions. Second, in the Cournot model, each duopolist believes that the rival will not change his output. In Fig. Let us now suppose that in period 1, duopolist B enters the market and begins to produce the commodity. This we can prove very simply in the following way. Therefore, the competitive output is obtained to be Oqc in Fig. b) Find the Stackelberg equilibrium under the assumption that Firm 1 moves first. plausible equilibrium" (Friedman, 1983) The french mathematician Augustin Cournot presented the first - and probably still the most widely used - model of noncooperative oligopoly.He assumed that each firm acts independently and attempts to maximize its profits by choosing its output. On the basis of the above points, we shall now be able to arrive at the shape of the iso-profit curves of the duopolist A. Let us now suppose that the market demand function for the product and the cost functions of the duopolists are: We may now compare the Cournot solution (14.37) with the quasi-competitive solution by using the example given in (14.5). First consider first the case of uniform-pricing monopoly, as a benchmark. The equilibrium solution of the Cournot model, as we already know, is obtained at the point of intersection of the two reaction functions. Case (ii) would also result in a determinate equilibrium, since this case is the same as (i) with the two duopolists reversing their roles. Similarly, the straight line MN is the reaction curve of duopolist B. 14.10. Here, as compared with the quasi-competitive solution, the Stackelberg duopolists produce a smaller output (120 < 190); sell it at a higher price (40 > 5); and the profits of both the sellers are higher (3.266.67, 868.28 > 0,12.5), and so their combined profit is also higher, (ii) When B is the leader and A the follower, the Stackelberg solution is. A stable solution is thus obtained, which is the monopoly solution. Let n be the number of oligopolists (n > 2), qc the competitive output, pc the competitive price, and pm the monopoly price. His analysis is illustrated by means of Fig. In period 2, duopolist A would revise his production plan for he proved wrong in period 1. Cournot equilibrium is a vector that satisfies , for all and for all . 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. As we already know, if qB is given to be, say, OC = constant, then the duopolist A’s profit-maximising output would be given by the point of tangency, F, between the horizontal straight line Cx and one of his iso-profit curves, here If. Also, as the number of firm’s (n) tends to infinity and the model tends to become a competitive market model, n/n+1 would tend to 1. 14.7 where we have been given the iso-profit map of duopolist B. 14.10. We may illustrate the process with the help of Fig. The demand curve for duopolist B would be the segment AD1 of the market demand curve DD1 with origin at q1. 14.13. Code to add this calci to your website . In the long run, prices and output are stable; that is, there is no possibility that changes in output or prices will make the firm better off. COURNOT DUOPOLY: an example Let the inverse demand function and the cost function be given by P = 50 − 2Q and C = 10 + 2q respectively, where Q is total industry output and q is the firm’s output. Similarly, the farther an iso-profit curve of B would be from the vertical axis, the nearer its maximum point would be to the horizontal axis. Here, there is no explicit collusion. This equilibrium solution is a (qA, qB) combination. In order to calculate Cournot equilibrium, it helps to first understand Nash equilibrium and how companies should deal with the possibility of collusion. Reaction functions, by definition, express the output of each duopolist as a function of his rival’s output. In this period, A would produce Oa2 assuming that B would produce his period 1 output, i.e., Ob1, and B would actually produce Ob1 (wrongly) assuming that A would produce his period 1 output, i.e., Oa0. Putting these values in (14.36) we obtain the Cournot reaction functions to be. The Bertrand Equilibrium model describes consumer purchasing behavior based on prices of products. So A’s iso-profit curves would be concave to this axis. If the market demand curve for the product is. At the point E’, which is the midpoint of the segment d’D1, eA = 1 and, therefore, RA, and also πA, is maximum. Central to Cournot's model are market demand curves, costs and marginal revenue curves. Similarly, if we measure output of duopolist B along the vertical axis, the iso-profit curves of B would be concave to the vertical axis. Since he would produce and sell at the MR = MC (= 0) point, his output would be q1. Since this combination lies on the reaction function of duopolist A, A sells q*A, given qB = q*B, and maximises his profit (πA). - 404 - A enjoys a significant first-mover advantage. We may obtain the reaction function of duopolist B also following the same procedure. 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. In the duopoly model, we had n = 2 and pc = 0. 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. Our mission is to provide an online platform to help students to discuss anything and everything about Economics. Again, we obtain from A’s reaction function that, as the output of B reduces to zero, and A becomes a monopolist, i.e., as the duopoly becomes a monopoly, output of A rises to OS which is called the monopoly output. As in the previous case, the line C’x’ would touch this curve at the latter’s maximum point, F’. The follower (firm B) in the output leadership model wants to maximise profit. and he would have to maximise his profit w.r.t. Cournot duopoly solution. 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. This figure may also be called the iso-profit map of duopolist A. Third, in the Cournot model, a duopolist is not able to make any guess about the rival’s reactions to a change in his own 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. Therefore, it would not be difficult for each of them to understand that his rival is not behaving as expected, and so, in the subsequent periods, each would seek some more appropriate conjecture about his rival’s reactions. 14.6). Our assumption (x), in this case, would be that each duopolist assumes that his rival would accept his output as given and constant, i.e., the rival would behave autonomously. Use this Nash Equilibrium calculator to get quick and reliable results on game theory. 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. A market spatial structure model is built. qA, would be a straight line, and this straight line MRA function leads to a straight line reaction function (14.14) when we put MRA = MCA = 0. 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. Let us now see, what would be the output of A if B’s output is given to be q1q2 = q2qc = 1/3 Oqc. The two firms are identical and, therefore, it must … As per our assumption (x), A thinks that B would behave autonomously w.r.t. Similarly, if in Fig. In other words, each iso-profit curve of a duopolist represents a particular amount of profit, and we shall see that a lower iso-profit curve of A (i.e., one nearer the horizontal axis) would give him a higher amount of profit. These can be solved for the equilibrium prices as $8.11 indicated. However, a simple observation will simplify the computations. 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. However, the Cournot solution may be better represented and better explained if we proceed through the reaction functions. (viii) Neither of the firms sets a price for its product, and each accepts the price at which the total planned output can be sold. (v) Each duopolist knows the market demand curve for the product. Share Your PPT File, Welfare Effects of Oligopoly | Microeconomics. 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. That is why OR would be equal to ON in Fig. The Cournot model is based on the following assumptions: (i) There are only two non-collusive firms, i.e., there exists the simplest example of oligopoly, viz., duopoly. Bertrand Equilibrium at B $10.44 $12.72. Let us suppose that the total revenue (R) function of the follower is. Here each assumes that he need not obey his reaction function, and rival’s behaviour is governed by his (the rival’s) reaction function. The first is what the best response functions for Cournot model’s look like, and the other is what the collusion function looks like. 14.5. Again, by assumption (x), A would assume that B would continue to produce the output of q1q2 = q2qc, which B would actually do assuming A’s output to be Oq1. 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. His marginal revenue curve would be MR2 with origin again at q1. In this period, A would prove wrong and B would prove correct in their assumptions about each other’s production plan. In period 2, therefore, A has proved correct and B has proved wrong. Cournot equilibrium calculator Cournot equilibrium calculator this single variable (qA). In this paper, a general equilibrium Cournot game is proposed based on an inverse demand function. In the Cournot model, at each value of qA and qB, we have assumed MCA = MCB = 0 [assumption (vi)]. In Fig. However, in the Nash equilibrium, the quantities of production are larger than in the case of cartel agreement (and the price is lower). Here OA = a and OB = a/b. Let us suppose that the market demand curve for the product is, q = quantity of market demand for the product, a = vertical intercept of the market demand curve (14.9) = positive constant, -b = slope of the market demand curve (14.9) = negative constant. In Fig. 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. 14.11, ever since B entered the market, A’s output has decreased in the adjustment process and B’s output has increased, and so, the output combination would alternately move first from B’s RF to the west on A’s RF (as from K1 to K2) and then from A’s RF to the north on B’s RF (as from K2 to K3) and then again to west, and so on, till the output combination becomes E (q *A, q*B) at the point of intersection of the two reaction curves, where the output quantity of each duopolist would be obtained to be q*1 = q*2 = 1/3 a/b [eq. The TR function of firm A is. Therefore, if we put p = 0 in (14.9), we would obtain the competitive solution (output) in the Cournot model: qc = a/b                                            (14.18). As we know, the condition for a competitive equilibrium is p = MC. This function is superimposed on the best response function of firm 1 in the following figure. Similarly, we would obtain that if qB is OC” and OC'”, then qA would be, C”F” and c'”F'” respectively, and so on. Now, if E be the midpoint of segment dD1, then B’s output (qB) remaining the same at OC = constant, if qA increases from zero onwards (and p diminishes), A’s total revenue (RA) and total profit (πA) would also increase till qA becomes equal to CF. 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. Proceeding in the same way as in the previous case, we will find that profit levels at the points T3 and T4 would be the same as that at the point F’. It is named after Antoine Augustin Cournot (1801–1877) who was inspired by observing competition in a spring water duopoly. To find the level of output for each firm that would result in a stationary equilibrium, we solve for the values of Q 1 and equilibrium The NASH equilibrium is stable. Instead, he simply assumes that the duopolists are aware of their interdependence. The point of intersection I of the Cournot reaction functions of the duopolists gives us the equilibrium in the Cournot model. The iso-profit curves of A would look like those given in Fig. The total quantity supplied by all firms then determines the market price. Similarly, duopolist B’s reaction function gives the value of qB for any specified value of qA, which maximises πB. For the sake of simplicity, we have assumed here that the market demand curve (14.9) is a (negatively sloped) straight line. 2/3 Oqc = 1/3 Oqc. Equilibria in Cournot’s and Bertrand’s models generate different economic outcomes: • equilibrium price in Bertrand’s model is c • price associated with an equilibrium of Cournot’s model is 1 3(α+2c), which exceeds c since α > c. Does one model capture firms’ strategic reasoning better than the other? From this curve, we can know what would be the equilibrium output of A at any given output of B. Therefore, in period 2, A would have to relocate his demand curve by horizontally shifting DD1 leftward to D’q2 by the amount q2qc (= q1q2) i.e., he would now re-determine his demand function by subtracting the amount q2qc from each quantity of his original demand. Along with this assumption, Bertrand brings in only one more assumption which states that each duopolist has sufficient capacity to satisfy the entire market.

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