In Fig. In this paper, I first show that under the standard assumptions of the Stackelberg model, … Firm 1 is the leader and firm 2 is the follower. Through analysis and careful investigation of the Stackelberg Model of Oligopoly, the following conclusions have been derived: The significance and relevance of the model depends on the market situation and the characteristics of the oligopoly. His analysis is illustrated by means of Fig. Under the circumstances, equilibrium in the Cournot model can occur only at the point of intersection of the two reaction functions. QA represents the quantity decided and produced by firm 1 and QB the quantity the follower firm B will produce in sequence. 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). b. In many cases, the lowest price attracts significant revenue. Help. This can be seen in the industries that are dominated by fewer huge firms that take lead in the introduction of a new idea or product concept. Example 3. A, therefore, cuts his output level to 1/2 Oq1 leaving B to produce 1/2 Oq1 = q1q2. Since each duopolist assumes the output of his rival to remain constant at where it is, the relation between A’s output (qA) and the price of the product (p) would be given now by the segment dD1 of the market demand curve DD1. However the remaining two models have made contributions towards overcoming the limitations of the Cournot Model. For example, A may try to convince B, by threat or rumour, to accept a reaction curve that lies below the present one, viz., MN. Present Stackelberg’s equilibrium + graph 4. For, at the point F, the firm is on the lowest possible iso-profit curve, i.e., on the highest possible level of profit subject to B’s output = OC = constant. 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). Competition, Innovation, and Antitrust-Federico Etro 2007-09-05 This book reviews recent progress in the theory of oligopoly and market leadership and provides new results on the theory of Stackelberg competition and Nash competition with strategic investment under endogenous entry. Now if the duopolist A produces the output Oq1 = 1/3 Oqc, then the duopolist B’s demand curve would be the segment AD1 of the market demand curve DD1 and his MR curve would be MR2, both with origin at q1. 4.9 Each firm incurs a marginal cost of $ 10 per unit of output, and zero fixed costs. 24.5 we also show Cournot equilibrium point c, where the two reaction curves meet. At other times, different firms will act as leaders from time to time. We may now easily verify that if each duopolist produces an output of 1/3 Oqc, then the Cournot model will be in equilibrium. The TR function of firm A is. It is easily seen in Fig. This video shows you how to solve for the equilibrium price and quantity for both firms in a price leadership duopoly. In Fig. On the other hand, if B suspects that A knows about his autonomous behaviour, he would try to convince A that he will react along a curve that lies above MN. Putting these values in (14.36) we obtain the Cournot reaction functions to be. There are a number of oligopolistic organizations in the market, but one of them is dominant organization, which is called price leader. 7. 14.7. Boosta Ltd - 10 Kyriakou Matsi, Liliana building, office 203, 1082, Nicosia, Cyprus. This function would give us the profit-maximising output of B as a function of A’s output. Stackelberg model has been extended and modified to adjust a number of real market scenarios. This process would go on in the Cournot model, A’s output decreasing and B’s output increasing until both A and B produce the same output of 1/3 qc. output, and he would react along his reaction function MN, and B also thinks that A would behave autonomously, and he (A) would react along his reaction function RS. 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’. In simple words, let us assume a market with three players – A, B, and C. Recent work on this model has contrasted the social cost of Nash equilibria with the best possible social cost. The equilibrium solution can be obtained if we solve the FOCs (14.28) for qA and qB, provided the SOCs (14.29) are satisfied. Abstract. It follows from the properties of iso-profit curves that the profit of firm B will increase as it moves to the iso-profit curves further to the left (i.e., nearer the qB-axis). In order to do that, we have to understand the relation between the outputs and profits of the duopolists, A and B, subject to the assumptions given above. We obtain from the reaction function RS that, as qB rises to OR, qA reduces to zero. For example, Apple can be considered a market leader due to its ability to come up with new technology before anyone else does. An interesting example of conjectural variation is contained in Stackelberg’s analysis of leadership and followership. In this paper, I first show that under the standard assumptions of the Stackelberg model, … The illustration below shows price leadership. The example gives us: a= 100, b = 0.5, d = 5, e = 0, g = 0and h = 0.5. In this period, we would have A’s output = Oq1 and B’s output = qtq2. Stackelberg’s model: Leader’s demand curve; 2. Oligopoly firms might compete (noncooperative oligopoly) or cooperate (cooperative oligopoly) in the marketplace. Lastly, we should note that although the duopolists in the Cournot model are able to maximise their individual profits subject to the given assumptions, their joint profit and, therefore, their individual profits (obtained after the joint profit is appropriately distributed), might have been larger if they acted collusively and formed a multi-plant monopoly. At other times, different firms will act as leaders from time to time. As is evident from the form of equation (14.14), the reaction function of A has been obtained as a (negatively sloped) straight line (like RS in Fig. The retailers on the other hand are treated as followers. Along this demand curve, as qA increases (and p diminishes) over the range C’F’, RA, and also πA, increases, since over the segment d’E’ of his present demand curve, d’D1, he has eA > 1. The model ignores the fact that with time, each and every firm tries to acquire unique capabilities by moving up the learning curve. 14.2 and now represented in Fig. Price is below the minimum of average variable cost. The output combination in period 2, therefore, would be K2(Oa2, Ob1). In Fig. 14.11, the outputs of A and B (qA and qB) are measured, respectively, along the horizontal and the vertical axis. Let us denote this combination by E (qA, qB) in Fig. Type: 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. Since MC = 0, the competitive output here is the q at which p = MC = 0. (478). one for Bertrand, one for Stackelberg … In many cases, the lowest price attracts significant revenue. Furthermore, it will be discussed that how realistic the model is in today’s world though economic diagrams and relevant theories. The effect will be a decrease in profits for both firms. It is named after the German economist Heinrich Freiherr von Stackelberg who published Market Structure and Equilibrium (Marktform und Gleichgewicht) in 1934 which described the model. It is given by equation (14.17). As we have already obtained 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. This website includes study notes, research papers, essays, articles and other allied information submitted by visitors like YOU. 14.9. But let us first explain the shape of the iso-profit curves that are given in Fig. 14.10. For example, if A produces and sells CF quantity of output, then the total quantity of output sold would be OF, and we can know from the demand curve, DD1, that the price of the product at this quantity would be EF. If we put qA = 0 in the reaction function of (14.14) of A, we obtain. it will help you have an overview and solid multi-faceted knowledge . Abstract-Cognitive wireless is a new engineering for bettering frequence spectrum use in radio webs. Since the demand curve for the product has been assumed to be linear, this reaction curve also would be linear like the line MN in Fig. Abstract. This enables the firms to expand their capacities and technology to become the first mover. 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. The Sum of QA and QB will result in the market demand. Cournot competition is an economic model in which competing firms choose a quantity to produce independently and simultaneously, named after … Stackelberg model is a leadership model that allows the firm dominant in the market to set its price first and subsequently, the follower firms optimize their production and price. But we have q1q2 = 1/2 q1qc = 1/2 . identical price rises and falls to be leadership-relevant price changes, i.e. As such, the reaction function of duopolist A would be obtained if we solve the first equation of (14.28) for qA in terms of qB and the reaction function of duopolist B would be obtained if we solve the second equation of (14.28) for qB in terms of qA. The Stackelberg leadership model is a strategic game in economics in which the leader firm moves first and then the follower firms move sequentially. This function is called the (Cournot) reaction function of duopolist A. That is, as qB rises to OR = a/b, qA falls to zero. Quantity Leadership - Stackelberg. From this curve, we can know what would be the equilibrium output of A at any given output of B. 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. For, at the point G, B is on the lowest possible iso-profit curve subject to qA = OD. Economists and researchers use it to understand and evaluate their behavior in an oligopoly. (14.20)]. 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. The points of intersection (and tangency) between this line and A’s profit indifference curves, viz., the points like L1, I, and L2, give us the alternative levels of profit that the duopolist A may earn at different levels of his output in combination with B’s output. There are a number of oligopolistic organizations in the market, but one of them is dominant organization, which is called price leader. While the Cournot model is one of simultaneous quantity setting, the Stackelberg model a quantity leadership model. Not only this, but also A would have to accept B’s present pattern of reaction as given by his reaction function MN, and B must remain ignorant of the fact that A knows his reaction function. and he would have to maximise his profit w.r.t. Bertrand Stackelberg Cartels Midterm 2 Bring pencil/pen, bluebook, pink scantron 8 MC questions, like last time Important skills: Find monopoly p;q Analyze e ects of policy (e.g. In period 3, B would produce ob3, assuming that A would produce his previous period’s output, Oa2, and A would actually produce this output (Oa2), assuming (wrongly) that B would produce his period 2 output, viz., Ob1, The output combination in period 3, therefore, would be K3(Oa2, Ob3). The Stackelberg leadership model results in a higher market quantity and lower price for the good as compared to the Cournot model. Let us assume there are two firms that produce identical products and have identical cost. That is, in this model, A is the output-leader and B the output-follower. As per our assumption (x), A thinks that B would behave autonomously w.r.t. To explain how it works, lets consider two firms, A and B that produce homogenous products in an oligopoly. The leader chooses the output level due to its capacity of being the first mover. Essay, 12 pages. In period 1, therefore, A proves wrong and B correct. A natural model to study such markets is the Stackelberg quantity leadership model, where firms choose their quantities (capacities) while observing the moves of earlier entrants. By continuing we’ll assume you’re on board with our cookie policy. 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