Suppose that a firm faces a demand curve for its product of $P = 10 - Q ^ { d }$ . The corresponding marginal revenue curve is $M R = 10 - 2 Q$ . The firm has a constant marginal cost of $4 per unit. If the firm engages in first-degree price discrimination, how much producer surplus will it capture?
A) $21.
B) $18.
C) $9.
D) $4.50

Question

Quizplus · Accepted Answer

In first-degree price discrimination, the firm charges each consumer their maximum willingness to pay. Since there is no consumer surplus in this scenario, all the surplus goes to the producer.

To find the profit-maximizing output, set marginal revenue equal to marginal cost and solve for Q:

$10 - 2Q = $4
Q = 3

Therefore, the firm will produce and sell 3 units of the product.

To find the price the firm will charge, plug Q = 3 into the demand equation:

P = $10 - 3 = $7

The total revenue the firm will earn is:

TR = P × Q = $7 × 3 = $21

Since the constant marginal cost is $4 per unit, the total cost to produce and sell 3 units is:

TC = $4 × 3 = $12

Therefore, the producer surplus for the firm is:

PS = TR - TC = $21 - $12 = $9

So the answer is B.

Suppose That a Firm Faces a Demand Curve for Its P=10−QdP = 10 - Q ^ { d }P=10−Qd

Suppose That a Firm Faces a Demand Curve for Its $P = 10 - Q ^ { d }$