Question

. Consider the two-firm game of sequential quantity competition that we studied in class. (See slides 33-38 in the “Homogeneous products oligopoly.”) Suppose firm A gets to make one more move after firm B makes its choice of QA, but before price and profits are determined. That is, the order of events will be:

C(Qi) = 10Qi --> for firms B and A

Demand --> P = 40 – 0.01(QA + QB )

i. Firm A announces QA.

ii. Firm B observes the QA announced in (i) and then chooses QB.

iii. Firm A observes Firm B’s choice of QB and can revise/change QA if it wants to.

iv. Individuals quantities are summed for the market Q, price is determined using the demand curve, firms sell their final values of QA and QB, and they collect profits.

Assume that the demand and cost details are unchanged from the example in the slides.

a. Suppose firm A’s second move (in step iii) comes as a surprise to both firms, in other words both firms believed that the game moves directly from step ii to step iv. What quantities do the firms sell, and how much profit do they collect?

b. Suppose both firms are is fully aware of the new order of moves, they know that firm A moves both first and third. What quantities do the firms choose in each stage of the game? How much profit does each collect?

Answer 1

Competition is limited in oligopoly. The number of firms are also limited here, therefore each firm controls a large share of the market and is in a position to influence the price and output in a significant manner. Each firm takes into account the reactions of another firms to its price and output policies.Actually this leads to a good deal of interdependence of the firms and price stickiness. Firm A desires to enhance its sales through a price cut. But before exicuting this, A takes into consideration the possible reactions of B.If B cuts the price by the same amount price cut of A will not have any effect.If B reducing the price by an amount greater than the reduction by A, it will adversely affect the sales of A.For these reasons, A will not resort to a price cut. The other possibilities to increase the sales are either to change the quality of the product or to spend more on advertisement.Firm A cannot take any independent action regarding price.In turn there is greater dependence among A and B.

They will form a collussion on the basis of undestanding among the firms.Intead of competing, they combine together to fix the prices and output.In each stage of the game,on the basis of the size, the efficiency, the experience, the reputation and goodwill and the ability of the firm to forecast future development one leading firm fixes the price and other firms accept it.The price maker is called the leader.The leader calculates the marginal cost(MC) and marginal revenue(MR) for the other.The total output is allocated between both of them on the basis of their own MC

The share of each of the two firmsA and B, is determined QA and QB.Their total profit can be computed as (price-ac)xfirms output.The profit so computed is maximum for each firm.The result is stability of price and output both firms are not interested to change their price and output.