Suppose that the inverse demand for bean sprouts is given by P(Y) = 370 - 4Y and the total cost of producing Y units for any firm is TC(Y) = 10Y. If the industry consists of two Cournot duopolists, then in equilibrium each firm's production is

Question

Quizplus · Accepted Answer

To find the Cournot equilibrium, we need to calculate each firm's reaction function. Firm 1's reaction function is given by:

Q1 = (1/2)*(370 - 4Q2 - 10)

where Q2 is the quantity produced by the other firm. Similarly, Firm 2's reaction function is:

Q2 = (1/2)*(370 - 4Q1 - 10)

To find the equilibrium, we need to solve for Q1 and Q2 such that they are simultaneously satisfied. Substituting Firm 1's reaction function into Firm 2's gives:

Q2 = (1/2)*(370 - 4*((1/2)*(370 - 4Q2 - 10)) - 10)

Simplifying this expression gives:

Q2 = 23.125

Substituting this value of Q2 into Firm 1's reaction function gives:

Q1 = (1/2)*(370 - 4(23.125) - 10) = 30

Therefore, each firm's production in equilibrium is 30 units.

Suppose That the Inverse Demand for Bean Sprouts Is Given