Question

The inverse demand function for computers is P = 60 − Q, where Q is the total quantity of computers. There are two computer manufacturers, Apple and IBM, and they operate as Cournot duopolists. Apple has a M C of 10 and IBM has a M C of 20. How many computers would Apple produce in equilibrium?

Answer 1

In a Cournot duopoly, each firm determines its level of output independently to maximize its profits. To find the equilibrium quantity of computers that Apple would produce, we need to find the point where its marginal cost (MC) is equal to the marginal revenue (MR) it receives from selling the computers.

Step-by-step explanation:

In a Cournot duopoly, each firm determines its level of output independently to maximize its profits. To find the equilibrium quantity of computers that Apple would produce, we need to find the point where its marginal cost (MC) is equal to the marginal revenue (MR) it receives from selling the computers.

Given that Apple's MC is 10 and the inverse demand function for computers is P = 60 - Q, we can find MR as the derivative of the demand function with respect to Q.

So, P = 60 - Q, MR = dP/dQ = -1.

Now we can set MR equal to MC and solve for the equilibrium quantity:

-1 = 10 => Q = 11.

Therefore, in equilibrium, Apple would produce 11 computers.