Monopoly, Duopoly and Collusion

The market for gingerbread is described by the market demand function X(p) = 1500 p. Firm A produces y units of gingerbread at a cost c₁(y) = y^₂ .

(a) Suppose no other firm produces gingerbread such that firm 1 has monopoly power. Write down firm 1's profit maximisation problem and derive the monopoly price, quantity and profits.

(b) Now suppose firm 2 enters the market also producing y units of gingerbread at cost c₂(y) = y² . Derive the Cournot equilibrium quantities, and determine total supply, price and firms' profits in equilibrium.

(c) If firms 1 and 2 collude what will be the quantities, price and profits of both firms in this cartel?

(d) Compare prices and quantities in all three scenarios and explain the relation.