Question

Q1.

Consider a Cournot oligopoly in which the market demand curve is Q = 60 - P. There are two firms in this market, so Q = q₁ + q₂. The firms in this market are not identical: Firm 1 faces cost function c₁(q₁) = 2q₁², while firm 2's cost function is c₂(q₂) = 28q₂.

In the space below, write down a function for Firm 1's profit, in terms of q₁ and q₂.

Q2.

Refer back to the Cournot oligopoly from Question 1.

In the space below, write down a function for Firm 2's profit, in terms of q₁ and q₂.

Q3.

Refer back to the Cournot oligopoly from Question 1.

In the space below, write down Firm 1's best-response function. (This should be a function of q₂.)

Q4.

Refer back to the Cournot oligopoly from Question 1.

In the space below, write down Firm 2's best-response function. (This should be a function of q₁.)

Q5.

Using your answers to questions 3 and 4, find the Nash equilibrium in this Cournot oligopoly. What quantity will each firm produce?

Your answers should both be whole numbers.

q₁ =

q₂ =

Answer 1