Question

All firms in a competitive industry have the following long-run total cost curve: where q is the output of the firm. a. Compute the long run equilibrium price and explain how you obtain the result [20 marks] b. Suppose the market demand is given byp 10- Q. Determine the long-run equilibrium number of firms in the industry c. Suppose that the same market is instead served by a monopolist who shares the same technology described by the long-run total cost curve above. Find the price and quantity offered by the monopolist. [10 marks] 120 marks]

Answer 1

a) C = q^3 - 2 q^2 + 4q AC = q^3 - 2 q^2 + 4 AC is minimised when partial differential AC/partial differential q = 0 partial differential AC/partial differential q = 2q-2 = 0 q = 1 AC = 1-2 + 4 = 3 Thus Price = 3 & q = 1 b) Q = 10 - P = 7 No. of firms = 7 c) If monopoly Then P = 10-Q M^2 = 10-2 Q M C = partial differential T C/partial differential Q = 3 q^2 - 4 q + 4 10 - 2q = 3 q^2 - 4 q + 4 3 q^2 - 2 q - 6 = 0 q = 2 plusminus squareroot 4 + 72/6 = 2 plusminus squareroot 76/6 = 1.7862 & P = 8.213