These empiral examples reveal the usefulness of Stackelberg model in explaining the behavior of firms. 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. In order to compare the Stackelberg solution with the quasi-competitive solution, let us now go back to the example given by (14.5). Sometimes a large dominant firm will act as a natural leader. 14.13. In this period, A would prove wrong and B would prove correct in their assumptions about each other’s production plan. d. Marginal cost is above average variable cost. 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.. In period 2, duopolist A would revise his production plan for he proved wrong in period 1. For example, at A’s output = OA1, B’s output would be L1A1 and A would be on his iso-profit curve IP1. Of course, this autonomous behaviour takes both of them to the intersection point of their reaction functions where they would be in equilibrium, i.e., ultimately they would prove right, although for wrong reasons. By setting this level, the leader makes a commitment that will be adjusted by the follower, then he will benefit by keeping the level of quantity high for itself. When the conditions for a P‐D SE apply, there is a reasonable a priori basis for choosing a particular price leader from the possible alternatives and, hence, a basis for selecting the Stackelberg price leadership model over Bertrand competition. 2/3 Oqc = 1/3 Oqc. Inventories and Endogenous Stackelberg Leadership in Two-period Cournot Oligopoly ... as for example the U.S. automobile industry, and more broadly to investigate how inventory levels vary with the degree ... while the price-cost margin is strictly lower due to the increase in competition caused by inventories. The Stackelberg model of oligopoly within managerial economics illustrates one firm’s leadership in an oligopoly. That is, if A produces 1/3 Oqc, the profit-maximising output of B would also be 1/3 Oqc. 14.4, we have obtained: C’F’ < CF. 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. (b) The output produced by the two firms is homogeneous. 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). The Stackelberg leadership model is a sequential model, which means that the dominant firm first sets the price, which is then used by the other firms to determine their optimal production. Example 3. Stackelberg equilibrium is attained if and only if firm 1 desires to be a leader and firm 2 a follower. TOS4. (c) The higher iso-profit curve of a duopolist represents a lower profit level. In this case, the model states that both firms decide on their output in sequence (due to the oligopoly). The point of intersection is also known as firm A’s bliss point as it maximizes the marginal utility for firm A. As the name suggests, an iso-profit curve of a duopolist, A, gives us the combinations of outputs of the duopolists A and B, which would yield the same amount of profit for duopolist A. Gal-or argues that in opposite to the belief that first mover advantages result in a two-player Stackelberg model, the model can be extended to include multiple players. By assumption (x), he would expect A to produce and sell his output of the previous period, i.e., Oq1, and A would actually produce Oq1 assuming that there would be no rival as in the previous period. This function would give us the profit-maximising output of B as a function of A’s output. By assumption (x) of the model, the leader is aware that his actions influence the output choice of the follower. 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.. 14.8, and B produces q1q2, as was the case with Cournot. 14.3, then πA would be falling as qB increases. As there is now B in the market, A has reduced his output from Oq1 to Oq3. For instance, Yu, Huanf and Liang (2009) have adopted this model to understand the supply chain of vendor managed invetory production. 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. Economists and researchers use it to understand and evaluate their behavior in an oligopoly. A then lowers the price below B’s level and captures the market, and the process will continue. The TR function of firm A is. Each of them may go on experimenting and observing how his rival’s output plan reacts to changes in his own plan, or, each of them may desperately force his rival to react along some reaction function that suits him. In such a situation, other firms tend to follow the capacity and quantity values of the market leader. Therefore, how we may obtain the output combinations of the duopolists that give A the same profit as at the point F, and we have obtained that the curve T1FT2 is one of the iso-profit curves of duopolist A. 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. This curve would give us the equilibrium output of B at any given output of A. The leader has the first mover advantage on the basis of better technology, higher production capacity, or the exisiting monopoly. 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. The leader knows the action of each retailer, and optimizes the investment on advertisements, cycles of raw materials and the finished products to maximize its profits. We may now compare the equilibrium in this leadership model with that in the Cournot model. 14.1, where the output of A is measured along the horizontal axis and that of B along the vertical axis. I.E. Economics 405/505 Introduction to Game Theory Prof. Rui Zhao 9 Stackelberg Model of Oligopoly 9.1 Example Firm 1 and Firm 2 produce non-negative outputs q 1 and q 2 respectively. (14.17), gives us the profit maximising output, qB, of the follower (firm B) as a function of the given (and optimum) output, qA, of the leader (firm A). In many cases, the lowest price attracts significant revenue. 7. The line that would give us this reaction function of duopolist A would be one that joins the points like F, F’,F”,F”‘, etc. So the market now becomes duopolistic. If A’s output increases further, πA would be falling. b. 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. In Fig. To make it simple, it’s assumed that A and B are the only firms in the oligopoly. 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