A representative firm with short-run total cost given by TC = 50 + 2q + 2q² operates in a competitive industry where the short-run market demand and supply curves are given by Q_D = 1,410 - 40P and Q_S = -390 + 20P.Its short-run profit-maximizing level of output is:

Question

Quizplus · Accepted Answer

To find the profit-maximizing level of output, we need to find where marginal revenue (MR) equals marginal cost (MC). The firm's MR is equal to the market price, which is given by the demand curve: P = 35.25 - 0.025Q To find the firm's MC, we take the derivative of its total cost function: MC = 2 + 4q² Setting MR equal to MC and solving for q, we get: 35.25 - 0.025Q = 2 + 4q² 33.25 = 0.025Q + 4q² Substituting the market equilibrium quantity (Q = 60) into the above equation yields: 33.25 = 0.025(60) + 4q² 33.25 = 1.5 + 4q² 31.75 = 4q² q² = 7.9375 Since it is not possible to produce a fraction of a unit, the firm's profit-maximizing level of output is 7 units (rounded up).

A Representative Firm with Short-Run Total Cost Given by TC