In the price leadership model, only the dominant firm has monopoly power — only the dominant firm can set price. For the proposed model, we conduct a static analysis and discuss the existence, uniqueness, and computation of an equilibrium solution, as well as study certain issues regarding the relative profits of leader and follower-firms. We have already obtained the reaction functions of the two sellers to be Here, as compared with the quasi-competitive solution, the Stackelberg duopolists produce a smaller output 120 5 ; and the profits of both the sellers are higher 3. The iso-profit curves of A would look like those given in Fig. How much is Grinch's output equilibrium? 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.
Does anyone have a reference or an explanation? Suppose that the industry has two firms, a Stackleberg leader, and a follower. If the follower chose a much larger quantity than its best response, the market price would lower and the leader's profits would be stung, perhaps below Cournot level profits. We will continue to use the case where the firms are identical to allow us to compare this more easily with the Cournot example, so both firm A and firm B have marginal costs of 150. The marginal cost of an extra spectator is zero for both teams. Therefore, while determining his optimal output, he would recognise the influence that he would exert on the follower. Suppose marginal costs were equal for the firms so the leader has no market advantage other than first move and in particular.
The leader-leader model will require both firms to start with incorrect assumptions about each other, and it will lead to non-optimal output in the market. With imperfect information, the threats described above can be credible. 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. As we have seen, case i results in a determinate equilibrium. In the Cournot model, firm A simply notes that the market demand is satisfied by the output produced by it and firm B. It shows clearly that naive behaviour does not pay. In aggregate, the following firms produce q f of output.
Thus, the dominant firm sets the price at P d. The two firms form a cartel and arrange to split total industry profits equally. Now the best response function of the leader is considered. The dominant firm determines price by going from the quantity q d up to its demand curve, d d. Feeding this into the follower's best response function yields. However, it must be that there is imperfect information and the follower is unable to observe the leader's move because it is irrational for the follower not to observe if it can once the leader has moved.
If we join these q A, q B combinations by a curve, we would obtain the required reaction curve of firm B. Another common form of leadership is for the leading firm to set price. 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 Oq 1. There are some variations of this game, if both players are followers then you have a Cournot game. The sophisticated oligopolist becomes in effect the leader, while the naive rival who acts on the Cournot assumption becomes the follower. So with A producing 175 and B producing 87.
Firm A sets it output first, and then firm B reacts to that output. How much is Grinch's output in equilibrium? In equilibrium, total output by the two firms will be There are two firms in the blastopheme industry. Applications The Stackelberg concept has been extended to dynamic Stackelberg games. The profit of firm 1 the leader is , where is the follower's quantity as a function of the leader's quantity, namely the function calculated above. Because firm A, the Stackelberg leader, chooses its output first, then firm B has to respond by choosing its output based on the decision of A.
Each team believes the other's price is independent of its own choice of price and each team sets its own price so as to maximize its revenue. In summary, if only one firm is sophisticated, it will emerge as the leader, and a stable equilibrium will emerge, since the naive firm will act as a follower. 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. If each ignores the other, a price war will be inevitable, as a result of which both will be worse off. The follower wants to choose to maximise its payoff. Differentiating this we get so when. North Bend currently has one McDonald's fast food franchise.
To do this we find a profit function for firm A the leader firm in terms of the quantity it produces and the quantity firm B produces, and we optimise it. To identify all equilibria—exhibiting the leader's own-cost-vs. This we can prove very simply in the following way. Hence, the maximum of with respect to is to be found. The industry consists of just the two Cournot duopolists, Grinch and Grubb. Because, he may then move on to a still lower iso-profit curve giving him a higher level of profit.