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 $500 each.Roach motors will
A)sell 75 cars for a total profit of $56,250.
B)sell 150 cars at a price of $300 a car.
C)sell 150 cars for a total profit of $112,500.
D)sell 180 cars and make a total profit of $180,000.
E)shut down since revenue will not cover variable costs.

Question

Quizplus · Accepted Answer

To determine the optimal pricing and quantity, we need to find the profit-maximizing level of output. We can start by finding the marginal revenue, which is the derivative of the inverse demand function:

MR = 2000 - 20Q

To find the profit-maximizing level of output, we need to set marginal cost equal to marginal revenue:

MC = 500 (the cost per car)

2000 - 20Q = 500

Solving for Q, we get Q = 75.

Therefore, Roach Motors will sell 75 cars at a price of P = 2000 - 10Q = $1250.

The total revenue will be:

TR = PQ = 1250 x 75 = $93,750

The total cost will be:

TC = 500 x 75 = $37,500

Therefore, the total profit will be:

Profit = TR - TC = $56,250.

Therefore, the correct answer is C, selling 150 cars for a total profit of $112,500 is not optimal as that will exceed the profit maximizing quantity.

Roach Motors Has a Monopoly on Used Cars in Enigma