Roach Motors has a monopoly on used cars in Enigma, Ohio.By installing secret microphones in the showroom, the friendly salespersons at Roach are able to learn each customer's willingness to pay and can therefore practice first-degree price discrimination, extracting from each customer his entire consumer's surplus.The inverse demand function for cars in Enigma is P = 2,000 - 10Q.Roach Motors purchases its stock of used cars at an auction in Cleveland for $600 each.Roach motors will
A)sell 140 cars at a price of $300 a car.
B)sell 70 cars for a total profit of $49,000.
C)sell 140 cars for a total profit of $98,000.
D)sell 168 cars and make a total profit of $156,800.
E)shut down since revenue will not cover variable costs.

Question

Quizplus · Accepted Answer

Roach Motors will sell cars where marginal cost equals marginal revenue. The marginal cost is $600. Setting the inverse demand function equal to $600 gives 2,000 - 10Q = 600, solving for Q gives Q = 140. The total profit is (Price - Cost) * Quantity = (2,000 - 10*140 - 600) * 140 = $98,000.

Roach Motors Has a Monopoly on Used Cars in Enigma