1. The sugar industry is a duopoly. The two firms, Sweet and Sour, compete through Cournot quantity-setting competition. The inverse market demand is given by P = 400 – 2Q, where Q is the total quantity produced by Sweet and Sour. Each firm has a marginal cost of £40 and no fixed cost.
a. Derive Sweet’s best response function and illustrate it on a graph.
b. Derive Sour’s best response function and illustrate it on the graph which you drew in part (a).
c. Derive the Cournot-Nash equilibrium to this game and illustrate the equilibrium on the graph which you drew in part (b). What are the profits for each firm in the equilibrium?
d. Derive the monopoly output, i.e., the one that maximizes total industry profit?
e. Why isn’t producing one half the monopoly output a Nash equilibrium outcome (the solution to part (b))?
f. Now assume that the marginal cost for each firm increases to £60. Draw the best response functions for both firms. How does your answer differ from part (c)?
