Consider a monopoly whose total cost function is TC = 20 + 10Q + 0.3Q2 and whose
ID: 1220631 • Letter: C
Question
Consider a monopoly whose total cost function is TC = 20 + 10Q + 0.3Q2 and whose marginal cost function is MC = 10 + 0.6Q. The demand function for the firms good is P = 120 - 0.2Q. The firm optimizes by producing the level of output that maximizes profit or minimizes loss. If the firm uses a uniform pricing strategy, then the firm will:
produce 110 units of output, charge a price of $98, and earn a profit of $6030
Please show the steps!
produce 90 units of output, charge a price of $102, and earn a profit of $9180Explanation / Answer
produce 110 units of output, charge a price of $98, and earn a profit of $6030
MC = 10 + 0.6Q
TR = P*Q = (120 - 0,2Q)*Q
MR = dTR/dQ = 120 - 0.4Q
Monopoly will produce till MR = MC, , so equating, MR =MC
10 + 0.6Q = 120 - 0.4Q
Q = 110
Price or P = 120 - 0.2Q = 120 - 0.2*110 = 120 - 22 = 98
Profit = TR - TC = P*Q - TC
= 98*110 - 20 - 10*110 + 0.3*(110)^2
= 6030
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