Question

4) (9 points) 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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