Suppose there are two firms in a market who each choose a quantity of output to produce. Firm 1's quantity is q1, and firm 2's quantity is q2. Firm 1 chooses their quantity, q1, first. Firm 2 observes q1, and then chooses their quantity, q2. The market quantity is Q = q1 + q2. The market demand curve is given by P = 1000 - 5Q. Also, each firm has constant marginal cost equal to 100. There are no fixed costs.
The marginal revenue of the two firms are given by:
MR1 = 1000 - 10q1 - 5 q2
MR2 = 1000 - 5q1 - 10q2.
a) How much output does each firm choose in the Nash equilibrium?
b) What is the market price?
c) How much profit does each firm make?