Suppose that there are only two firms (Firm A and Firm B) in the market for decorative lampshades. Let the inverse demand function and the total cost function be given by: P = 50 –Q and TC = 2Q
Assume that Firm A and Firm B sell identical lampshades. The firms compete with each other bychoosing the quantity of lampshades the wish to produce. Firms set their quantities simultaneously.
(a) Derive the reaction function for Firm A.
(b) Derive the reaction function for firm B.
(c) Sketch the reaction functions on a graph. Put the quantity produced by Firm A on the x-axis and thequantity produced by Firm B on the y-axis.
(d) Solve for the equilibrium quantity produced by Firm A. Solve for the equilibrium quantity producedby Firm B.
(e) Solve for the market price for the lampshades.
(f) Solve for the profit earned by each firm. What’s the industry profit?