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.

Answer 1

Profit = TR - TL = 7.3 times 700 - (250 + 700 + 0.004 (700)^2) = 5110 - 2910 = 2,200 c) when q = 0 MC = 1 and MR = 8 when MR = MC, q = 700 when q = 700 = > MC = 1 + 0.008q = 1 + 0.008 (700) = 6.6 Producer surplus = 1/2 times 700 = (6.6 - 1) = 1960 d) consumer surplus = 1/2 times 700 times (8 - 7.3) = 245 \r\n a) In monopoly, profit maximization is at MR = MC TC = 250 + q + 0.004 q^2 MC = Partialdifferential TC/Partialdifferential q = 1 + 0.008q TR = p times q = 8q - 0.001 q^2 MR = Partialdifferential TR/Partialdifferential q = 8 - 0.002q so, MR = MC 8 - 0.002 q = 1 + 0.008 q 7 = 0.01 q output rightarrow q = 700