Question

2. A monopolist has a cost function given by TC 250+q+.004q2. The inverse market demand for boxes is given by p 8-.0010. The monopolist is currently able to exclude rivals from the market because of a special governmental zoning rule. (a) What is its output and what price does it charge for boxes? (b) Calculate the firm's profit at this output level. (c) Calculate the firm's producer's surplus at this output level. (d) Calculate the consumer's surplus in this situation. 3. The zoning rule is revoked, and the monopolist in problem 2 can no longer exclude others from using the same technology and producing boxes, so the market structure changes from monopoly to perfect competition. (That is, assume that all firms are price-takers and that they produce at minimum average cost in equilibrium.) (a) What will the market price and quantity be? (b) Calculate consumer's surplus under this market structure. (c) Calculate aggregate producer profits and producer's surplus. (d) Comparing the two market structures for this industry, which has a larger social surplus (sum of producer's and consumer's surplus)?

If you can answer both the questions that would be greatly appreciated. Thank you.

Answer 1

TC = 250 + q + 0.004q^2 MC = d TC/dq = d(250 + q + 0.004q^2)/dq MC = 1 + 0.008q P = 8 - 0.001Q Total Revenue = Price times Quantity = (8 - 0.001Q)Q TR = 8Q - 0.001Q^2 Marginal Revenue = d TR/dQ doublerightarrow MR = d(8Q - 0.001Q^2) doublerightarrow MR = 8 - 0.002Q doublerightarrow MR = 8 - 0.002q Monopoly Condition be P > MR = MC So, MR = MC doublerightarrow 8 - 0.002q = 1 + 0.008q doublerightarrow 7 = 0.010q doublerightarrow q = 7/0.010 doublerightarrow 700 1 q = 700 \r\n So, the price be P = 8 - 0.001Q doublerightarrow P = 8 - 0.001 times 700 doublerightarrow P = 7.3 Profit = Total Revenue - Total cost = p times Q - 250 - q - 0.004q^2 = 7.3 times 700 - 250 - 700 - 0.004 times (700)^2 = 5110 - 950 - 1960 pi = 2200 Consumer Surplus = Area of a triangle AE delta = 1/2 times Base times height = 1/2 AD times ED = 1/2 times 700 times (8 - 7.3) C. S = 1/2 times 700 times .7 C.S = 245