Question #49403

Consider a monopolist whose total cost function is TC = 40 + 4Q + Q2 and whose marginal cost function is MC = 4 + 2Q. The demand function for the firms good is P = 160 - 0.5Q. 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 52 units of output, charge a price of $134, and earn a profit of $4016
produce 52 units of output, charge a price of $134, and earn a profit of $6968
produce 84 units of output, charge a price of $118, and earn a profit of $7824
produce 84 units of output, charge a price of $118, and earn a profit of $9912

Expert's answer

TC = 40 + 4Q + Q2, MC = 4 + 2Q, P = 160 - 0.5Q.

If the firm uses a uniform pricing strategy, then the firm will produce the output, for which MR = MC at the price from the demand curve:

MR = TR' = (P*Q)' = 160 - Q

4 + 2Q = 160 - Q

Q = 52

P = 160 - 0.5*52 = $134

ATC = TC/Q = 40/Q + 4 + Q = 40/52 + 4 + 52 = 56.77

Total profit TP = (P - ATC)*Q = (134 - 56.77)*52 = $4016

If the firm uses a uniform pricing strategy, then the firm will produce the output, for which MR = MC at the price from the demand curve:

MR = TR' = (P*Q)' = 160 - Q

4 + 2Q = 160 - Q

Q = 52

P = 160 - 0.5*52 = $134

ATC = TC/Q = 40/Q + 4 + Q = 40/52 + 4 + 52 = 56.77

Total profit TP = (P - ATC)*Q = (134 - 56.77)*52 = $4016

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