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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?

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