Question

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)?

Answer 1

TC = 250 + q + 0.004 q^2, p = 8 - 0.001 Q MC = d TC/dQ = d/dq (250 + q + 0.004 q^2) MC = 1 + 0.008 q For the competitive (per fact) condision P = MR = MC Therefore P = MC Rightarrow 8 - 0.011 q = 1 + 0.0008 q Rightarrow 7 = 0.009 q Rightarrow q = 777.777 so, the Quantity be q = 777.77 price be p = 8 - 0.0001 Q Rightarrow p = 8 - 0.001 times 77.77 Rightarrow p = 7.222 \r\n E = Equilibrium Quantity C S = consumer surplus P S = produces surface (b) consumer surface = Area of triangle EBC = 1/2 times BE times BC = 1/2 times 777.77 times (8 - 7.22) CS = 303.33 (c) profit = Total Revenue - Total cost \r\n = P times Q - 250 - q - 0.004 q^2 = 7.22 times 777.77 - 250 - 777.77 - 0.004 times (777.77)^2 = 5015.49 - 1027.77 - 3419.70 = 2168.02 so, the profit be 2168.02