Answer to Question #89059 in Microeconomics for Darren

Question

Consider a Cournot duopoly with the following inverse demand function:p(Q) =a−Q where p is the price of the product and Q is the total amount of goods exchanged in the market. The total costs areC(q1) = 300q1, C(q2) = 300q2 for firm 1 and firm 2, respectively. But the demand is uncertain (i.e., a new product may be introduced soon which will decrease the demand drastically). Firm 1 learns whether demand will be high (a =1800) or small (a=900) before it makes its quantity decision. However, firm 2 knows just the probability of high demand (1/4) and the probability of low demand (3/4). All of this is common knowledge. In particular, firm 2 knows that firm 1 knows the demand for certain. The two firms simultaneously choose quantity. What is the Bayesian equilibrium of the game (price in both states of the world and quantity produced by each firm)?

Answer 1

If we suppose, that the demand for both firms is p = 900 - Q, where Q = q1 + q2, then as the firms have similar cost functions, they will produce the same output, or q1 = q2, and p = 900 - 2q1.

Each firm maximizes profits, when MR = MC, so:

MR = TR' = 900 - 4q1.

MC = C' = 300.

900 - 4q1 = 300,

q1 = q2 = 150.

p = 900 - 2×150 = 600.