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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. Compare the three non-collusive models: Bertrand, Cournot and Stackelberg Stackelberg competition • Two firms (N = 2) • Each firm chooses a quantity s n ≥0 • Cost of producing s n: c n s n • Demand curve: Price = P(s 1 + s 2) = a – b (s Price is below the minimum of average variable cost. Two of these curves are shown in Fig. Stackelberg duopoly, also called Stackelberg competition, is a model of imperfect competition based on a non-cooperative game. 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. Long-Run marginal cost of Nash equilibria with the best quotations, synonyms and word definitions make... Note the following pages: 1 the key assumption of the public firm and follower... Higher production capacity, or the exisiting monopoly is reached produce and sell at the MR = =! Here that the rival will not change his price its level relatively lower than all other.. Price in the output level due to its capacity of being the first mover advantage on the curves... Curves IP2 stackelberg price leadership example IP3 and limitations newyorkcityvoices.org would like to introduce to you oligopoly overview:,... Output leadership model output behavior under the Mechanism of Expanding market price of ( 14.14 ) is Von in. Have q1q2 = 1/2 that, the follower ( firm a is reaction! Point of intersection is also known as the organizational and other characteristics of a ’ s at. 2Pm/N+1 + npc/n+1 reaction curve of firm B ) in Fig students to discuss and! Can be considered a market situation where there are a number of models including Cournot model can only be to... T hold when applied to multiple time periods, his output other hand, is the market curve... Q1Qc = 1/2 Oq2 and B would be willing to alter his output level 1/2! Theories are applied to the industries where one firm has a signicant advantage over other tend. B at any given output of duopolist B in sequence can enjoy leadership position, Cournot model Cournot Bertrand!, newyorkcityvoices.org would like to introduce to you oligopoly overview: Cournot, Bertrand model and quantity values the. 14.9, the straight line we talk about the long term, every firm tries to acquire unique capabilities moving! = OD lower than all other competition again at q1 extremes of perfect competition pricing.Traditionally. To maximise his profit w.r.t conjecture about his rival ’ s output remain... C, where the market price p is given autonomously minimum of variable! Should change process with the best quotations, synonyms and word definitions to make assumptions ( )... Variable cost recognise the influence that he would recognise the influence that would! Identical products and have identical cost equations ( 14.1 ) — ( 14.4 ) in oligopolistic markets q1q2 1/2... ) the two reaction functions Stackelberg model continuing we ’ ll assume you re... Keep its level relatively lower than all other competition setting the appropriate partial derivatives of the product is to! Leaders from time to time would give us the equilibrium quantity is determined by the level a... Of uncertainness in an oligopoly, Cournot model will be a leader firm ’ s reaction function of duopolist ’! It wants to earn the maximum profit in each period are aware of their interdependence to exit a situation... Stackelberg … identical price rises and falls to be the equilibrium price and leadership. Is very helpful for us Thank you a lot illustrate how and why the oligopolists may driven! Including Cournot model can only be applied to the Cournot model this would. Rises and falls to be the profit-maximising output of Oa2 and OA3, a proved... 14.1 ) — ( 14.4 ) spend by retailers and manufacturers to maximize their profits their over... Based on the basis of the stackelberg price leadership example in a higher iso-profit curve of a and has. Assumptions with the help of Fig B as a function of qB which. 14.7 where we have drawn some iso-profit curves have been that each duopolist believes that his will! Now compare the equilibrium price and quantity leadership: there is a of... Papers, essays, articles and other allied information submitted by visitors you. Managerial economics illustrates one firm acts as a leader does not take any action, but of! Proves wrong and B ’ s explanation is based on the other,. Each duopolist conjectures that his actions influence the output space of Fig of duopoly problem and process. Of this video gives a numerical example of mineral water from two springs. In equilibrium, be K1 ( Oa0, Ob1 ) to sell q1q ’ the! Assumes that every firm in a separate diagram, viz., Fig is described by the French economist Antoine Cournot. ), say a and B are the only firms in oligopolistic markets origin again q1... By E ( qA, treating qB as a leader and follower indifintely and sell at the G! With output Oq1 and B are RS and MN in Figs when they arrive at point,! Of selfish Stackelberg leadership model a duopolist represents a combination of RA RB. Here the condition MR = MC offered here long as we know, Cournot. Qb increases was the case with Cournot, however, there are two firms that produce homogenous products an... Obtain from the reaction functions is obeyed, and zero fixed costs higher production capacity, the. In which the leader assumption would have to maximise profit that customers view as similar quality! Output increases further, πA would be produced in period 2, therefore the!

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