A monopolist faces inverse demand $P = 400 - 4 Q ^ { d }$ and has constant marginal cost $M C = 80$ . If this monopolist engages in first-degree price discrimination, total output will equal:
A)20 units
B)40 units
C)60 units
D)80 units

Question

Quizplus · Accepted Answer

Under first-degree price discrimination, the monopolist charges each consumer their reservation price and captures the entire consumer surplus. Thus, the monopolist will sell where marginal cost equals the reservation price of the 80th unit, which can be found by setting the inverse demand equation equal to MC:
$$400 - 4Q = 80$$
$$Q = 80$$
So the monopolist will produce and sell 80 units. With first-degree price discrimination, the firm charges each customer a price equal to their willingness to pay. This means the monopolist's total revenue will be equal to the sum of each individual customer's willingness to pay. The monopolist will produce at the point where marginal cost equals the sum of each customer's marginal willingness to pay.

To find the total output, we need to first determine the monopolist's marginal revenue.

$TR = PQ = (400-4Q_d)Q_d = 400Q_d - 4Q_d^2$

$MR = \frac{dTR}{dQ_d} = 400 - 8Q_d$

Setting $MR = MC$, we get:

$400 - 8Q_d = 80$

$Q_d = 40$

Therefore, the monopolist will produce 40 units when they engage in first-degree price discrimination.

A Monopolist Faces Inverse Demand P=400−4QdP = 400 - 4 Q ^ { d }P=400−4Qd

A Monopolist Faces Inverse Demand $P = 400 - 4 Q ^ { d }$