Reference no: EM132727189
Exercise - (Cournot duopoly)
Consider the market for a homogeneous product. The inverse demand function is p(Q) = 1000 - Q. The market is served by two firms. i = 1.2. Their total cost function is: Ci(qi)= 100qi,.
(a) Suppose firms are price taker (perfectly competitive market). What would be the equilibrium price, quantity and profits of the firms?
(b) If firm 2 is shut down and firm 1 acts as a monopoly, what are the equilibrium price, quantity and profits?
(c) Suppose that the two firms compete setting quantities simultaneously (i.e., a la Cournot): (i) Find and draw the best response functions of the two firms; (ii) Find the equilibrium quantities, price and profits.
(d) Suppose now the owners of the duopolistic firms appoint a manager. The managers have an objective function that includes both the profits but also the size of the firm, i.e., they maximise Al, = x, + eq„ where 0 represents the importance of the size of the firm with respect to the profits. If 0 = 60, what are the Cournot-Nash equilibrium quantities as firms appoint managers? What are the prices?
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