A firm with market power faces the demand function q = 1,000 - P. The firm's total cost function is TC(q) = 5q + q² + 500. The output that maximizes total surplus in this market is ____. A) 421.67 B) 354.25 C) 331.67 D) 248.75

Question

Quizplus · Accepted Answer

Total surplus in a market is maximized where marginal cost (MC) equals marginal benefit (MB), which is the demand curve in this case. The demand function given is q = 1,000 - P, which can be rearranged to find the price as a function of quantity, P = 1,000 - q. To find the MC, we differentiate the total cost (TC) function with respect to q, which gives MC = 5 + 2q. Setting MC equal to MB (the inverse demand function, P), we get 5 + 2q = 1,000 - q. Solving for q gives q = 331.67, which is the output level that maximizes total surplus.

A Firm with Market Power Faces the Demand Function Q