Question 4 (continuous game) (10 points)
Consider two identical firms, 1 and 2, who compete in Cournot fashion. That is, they
simultaneously choose quantity. Each firm has a constant variable cost of 2. The inverse
demand function is given by the following:
P = 50 - q1 - q2
(Hint: this is a symmetric game, for (a)~(c) and (e), you can do the derivation for one firm
and replace it for the other one.)
a) What is the profit/payoff functions for each firm? (2 points)
b) Find the best response functions for each firm. (3 points)
c) Verify that the profit/payoff functions for either firm is strictly concave i.e. hilled shape.
(2 points)
d) Solve for the Nash Equilibrium of the game. What is it? (2 points)
e) What is the price? And what are the profit for each firm? (1 point)