Problem 1
Suppose that we have two firms that face a linear demand curve \(p(Y)=\) \(a-b Y\) and have constant marginal costs, \(c,\) for each firm. Solve for the Cournot equilibrium output.
Problem 2
Consider a cartel in which each firm has identical and constant marginal costs. If the cartel maximizes total industry profits, what does this imply about the division of output between the firms?
Problem 4
Suppose there are \(n\) identical firms in a Cournot equilibrium. Show that the absolute value of the elasticity of the market demand curve must be greater than \(1 / n\). (Hint: in the case of a monopolist, \(n=1\), and this simply says that a monopolist operates at an elastic part of the demand curve. Apply the logic that we used to establish that fact to this problem.)
