# stackelberg price leadership example

Therefore, Fig. Similarly, we would obtain that if qB is OC” and OC'”, then qA would be, C”F” and c'”F'” respectively, and so on. On the basis of assumptions, we shall obtain the iso-profit curves of each duopolist. This line, shows what would be B’s output at each given level of A’s output. In the next statge, firm B knows the QA and then decides the quantity it wants to produce in respoonse to QA. Price leadership is common in oligopolies, such as the airline industry, whereby a price leader sets the price and all the other competitors feel compelled to lower their prices to match. Essay, 5 pages. (ii) The larger the fixed quantity of qB the smaller would be the profit-maximising quantity of qA. The number of ﬁrms storing and the aggregate That is why, at any output of the two firms taken together, i.e., at any q = qA + qB, we would have MC = 0. 4.9 14.6, this reaction function of A has been obtained to be the line RS. His reaction function (RF) gives us that at qB = 0, qA = OS (or Oa0)—this is the monopoly solution. An oligopoly is a market structure characterized by significant interdependence. 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. We shall continue to make assumptions (i) to (ix) of the Cournot model. 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. Let us denote this combination by E (qA, qB) in Fig. The equilibrium solution can be obtained if we solve the FOCs (14.28) for qA and qB, provided the SOCs (14.29) are satisfied. However, the model helps us to understand what might follow from the given assumptions, and the assumptions, especially assumption (x), is not unrealistic. In period 2, therefore, A has proved correct and B has proved wrong. Stackelberg equilibrium is attained if and only if firm 1 desires to be a leader and firm 2 a follower. There are a number of oligopolistic organizations in the market, but one of them is dominant organization, which is called price leader. If the industry structure includes firms of roughly similar size where no firm can enjoy leadership position, Cournot model is more suitable. Example. Essay, 9 pages. In this paper, I first show that under the standard assumptions of the Stackelberg model, … Stackelberg’s models – “Price leadership” 1. But before doing this, let us note the following. In spite of this assumption proving wrong repeatedly in reality, if the duopolists cling to this assumption, then eventually in some period, their assumption would prove correct, and both of them would reach the equilibrium point. These limitations and weaknesses are rectified by many alternative approached to the model through combining Stackelberg with other models explaining oligopolistic behavior of the firms. An oligopoly is an intermediate market structure between the extremes of perfect competition and monopoly. Example. If we join these points by a line, we would obtain the reaction function of B, which would give B’s output as a function of that of A. B’s reaction function like that of A’s would also be a negatively sloped straight line if the market demand curve for the product is linear. This curve would give us the equilibrium output of B at any given output of 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. The leader chooses the output level due to its capacity of being the first mover. 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. 14.14. At other times, different firms will act as leaders from time to time. ѰB (qA)]                               (14.61), A’s profit now is a function of qA alone, and can be maximised w.r.t. Recent work on this model has contrasted the social cost of Nash equilibria with the best possible social cost. Therefore, at different values of qA, we would obtain the corresponding values of qB that would make the profit of firm B the maximum. 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. 14.11, the outputs of A and B (qA and qB) are measured, respectively, along the horizontal and the vertical axis. Outline the nature of uncertainness in an oligopoly market in which houses set end product degrees. 14.11. Leadership models of oligopoly are of two types — price leadership model and quantity leadership model. 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). This is because we have assumed here that the market demand curve for the product is a (negatively sloped) straight line. We, therefore, obtain here qA as a function of qB. Price is below the minimum of average variable cost. Quantity Leadership: there is a leader and a follower that set their quantities in sequential order. Price Leadership under Oligopoly: Types, Price-Output Determination and Feedback! The leader (F1): larger, more dominant firm in the market, sets its quantity first ( … Therefore, while determining his optimal output, he would recognise the influence that he would exert on the follower. So the market now becomes duopolistic. That is why OR would be equal to ON in Fig. In Fig. Again, since the combination E lies on the reaction function of duopolist B, B sells q*B, given qA =q*A, and maximises his profit (πB). 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. Rival firms then use […] In the Stackelberg model, the leader decides how much output to produce with other firms basing their decision on what the leader chooses. Here, there is no explicit collusion. The equilibrium price is determined by inverse market demand, and since both firms seek to maximize their profits, they end up determining a quantity where their margninal costs equal the marginal revenue (MC=MR) The Stackelberg model follows stages where in the first stage, firm A takes the action of setting the quanity, while firm B does nothing. In this period, we would have A’s output = Oq1 and B’s output = qtq2. 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. Essay, 22 pages. 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. In this figure, at qA = OD = constant, the profit maximising output of B (qB) would be obtained at the point of tangency, G, between the vertical straight line Dy and one of B’s iso-profit curves, viz., If . 14.13. 4.3 Predictions based on LS ratios In Fig. Privacy Policy3. These two functions may be written as. Similarly, if the duopolist B wants to play the role of a leader, his profit function would be, πB = hB [qB, ѰA (qB)]                                (14.62). 14.8. The point of intersection is also known as firm A’s bliss point as it maximizes the marginal utility for firm A. We may obtain the reaction function of duopolist B also following the same procedure. Essay, 15 pages. b. Then the total output in Cournot equilibrium under oligopoly would be nqc/n +1. The model has been increasingly used in many industries across the world to explain the behavior of the firms in oligopoly. For example, for OC’ > OC, we have obtained C’F’ < CF. 14.7. Therefore, if we put qB = 0 in A’s reaction function, we obtain the monopoly solution (qm) of the Cournot model as, Let us now solve the Cournot reaction equations (14.14) and (14.17) for the equilibrium values of qA and qB. 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. identical price rises and falls to be leadership-relevant price changes, i.e. 14.9, the market demand curve is DD1 and the competitive output is Oqc, as they were in Fig. 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. (2016, Oct 24). Essay, 12 pages. Cournot competition is an economic model in which competing firms choose a quantity to produce independently and simultaneously, named after … We have already obtained the reaction functions of the two sellers to be. Today, newyorkcityvoices.org would like to introduce to you Oligopoly Overview: Cournot, Bertrand, Stackelberg Oligopoly, Price Leadership. Together, the duopolists would produce 2/3 of the competitive output (Oqc). 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. Since total output has increased, price would fall from Op1 to Op2. 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. Stackelberg Model of Duopoly Stackelberg’s Model of Duopoly also has to do with companies trying to decide how much of a homogeneous good to produce. In this paper, I first show that under the standard assumptions of the Stackelberg model, … In other words, the points in the output space of Fig. Microeconomics, Product Markets, Pricing, Models, Cournot Model and Stackelberg Model. As there is now B in the market, A has reduced his output from Oq1 to Oq3. Our mission is to provide an online platform to help students to discuss anything and everything about Economics. 4.3 Stackelberg Competition Dynamic version of the cournot model Two rms, F = f1;2g At t = 1 rm 1 (leader) chooses q1 At t = 2 rm 2 (follower) knows q1 and chooses q2 As before, p = a bQ = a b(q1 +q2) c(qf) = cqf f 2 f1;2g The model is solved by\backwards induction"(Sub-game Perfect Equilibrium) { Solve rms 2’s decision at t = 2 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. Let us suppose that initially A has been a monopolist and B suddenly joins the industry to compete with him. This enables the firms to expand their capacities and technology to become the first mover. In the Cournot model, however, there is no scope for price competition since here the duopolists are price-takers. 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. Duopolist A’s reaction function gives the value of qA for any specified value of qB, which maximises πA. 14.14. We may also note that if the duopolists are not satisfied with the present position, then each of them may seek to alter it to his advantage. For instance, Yu, Huanf and Liang (2009) have adopted this model to understand the supply chain of vendor managed invetory production. The Stackelberg model follows stages where in the first stage, firm A takes the action of setting the quanity, while firm B does nothing. 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. Sherali (1984) tried to consider the situation of multiple leader oligopolies with the assumption that each leader firm assumes that its actions do not precipitate responses from other leader firms. Some of the iso-profit curves of duopolists A and B that assume the above features, have been shown in Fig. Given the assumptions (i) to (ix), the profit-indifference curves of the duopolists would be like those of the Cournot model. 14.5. The logic of the follower’s strategy of keeping its level of ouput low is that in that situation, only one firm can possibly act as a market leader. Therefore, now he would produce the output q3q4, which would be determined at the MR = MC (= 0) point. Case (ii) would also result in a determinate equilibrium, since this case is the same as (i) with the two duopolists reversing their roles. 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. Similarly, the straight line MN is the reaction curve of duopolist B. This curve would be concave to the horizontal axis and the highest point of the curve would be F. It is obvious from the construction of the iso-profit curve T1F T2 that the horizontal line Cx touches this curve at the point F. Also, F is the maximum (highest) point of the iso-profit curve T1FT2, since a horizontal straight line (Cx) may touch a concave downward curve (like T1FT2) only at the latter’s maximum point. • The price of selfish Stackelberg Leadership in a two-parallel-links network is 1.169 when one of the cost function is f^4 and the other link cost function is fixed at 5.67. 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 For example, at a price of Op’, B can expect to sell q1q’. 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. However, there are constraints in the simple Stackelberg Model. Since he would produce and sell at the MR = MC (= 0) point, his output would be q1. 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