Question #49416

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 is able to practice first degree (or perfect) price discrimination then it will

A)produce 62.4 units of output and rounded to the nearest dollar it will earn a profit of $3854

B)produce 62.4 units of output and rounded to the nearest dollar it will earn a profit of $4827

C)produce 72.8 units of output and rounded to the nearest dollar it will earn a profit of $3367

D)produce 72.8 units of output and rounded to the nearest dollar it will earn a profit of $8998

A)produce 62.4 units of output and rounded to the nearest dollar it will earn a profit of $3854

B)produce 62.4 units of output and rounded to the nearest dollar it will earn a profit of $4827

C)produce 72.8 units of output and rounded to the nearest dollar it will earn a profit of $3367

D)produce 72.8 units of output and rounded to the nearest dollar it will earn a profit of $8998

Expert's answer

TC = 40 + 4Q + Q2, MC = 4 + 2Q, P = 160 - 0.5Q. If the firm is able to practice first degree (or perfect) price discrimination. So the profit is equal to the sum of consumer surplus and producer surplus. The marginal consumer is the one whose reservation price equals to the marginal cost of the product. The seller produces more of his product than he would to achieve monopoly profits with no price discrimination, which means that there is no deadweight loss.

Then it will produce output at point, where MC = D

4 + 2Q = 160 - 0.5Q

2.5Q = 156

Q = 62.4 units

P = 160 - 0.5*62.4 = 128.8

Total profit = (P - ATC)*Q = (128.8 - 40/62.4 - 4 - 62.4)*62.4 = $3853.76

So, the right answer is A) produce 62.4 units of output and rounded to the nearest dollar it will earn a profit of $3854.

Then it will produce output at point, where MC = D

4 + 2Q = 160 - 0.5Q

2.5Q = 156

Q = 62.4 units

P = 160 - 0.5*62.4 = 128.8

Total profit = (P - ATC)*Q = (128.8 - 40/62.4 - 4 - 62.4)*62.4 = $3853.76

So, the right answer is A) produce 62.4 units of output and rounded to the nearest dollar it will earn a profit of $3854.

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