Roach Motors is the dominant used-car dealer in a small Midwestern city.After paying $50,000 for overhead, Roach Motors' cost per car is $500.There are 5 other small used-car lots in this town, but since they are not large enough to purchase cars through the same discount sources as Roach, each firm faces the cost function C = 5,000 + 700Q + 5Q².The demand for used cars is Q = 200 - P₁/10.Assuming Roach is aware of its competitors' costs, what price should Roach set for a used car?

A) $708.33
B) $575
C) $616.67
D) $604.17
E) $925

Question

Lahiru Prasanga · Accepted Answer

Final Answer : A, Explanation :  Roach Motors is a dominant used-car dealer, so it is a price setter. It will set a price to maximize its profit, which is equal to total revenue minus total cost. Total revenue is equal to price times quantity, and total cost is equal to fixed cost plus variable cost. Roach Motors' fixed cost is $50,000, and its variable cost is $500 per car. The other five used-car lots have a total variable cost of 5,000 + 700Q + 5Q^2. The demand for used cars is Q = 200 - P1/10.To maximize its profit, Roach Motors will set a price that equates marginal revenue to marginal cost. Marginal revenue is the change in total revenue divided by the change in quantity, and marginal cost is the change in total cost divided by the change in quantity.For Roach Motors, marginal revenue is equal to P1 - 10, and marginal cost is equal to $500. Setting marginal revenue equal to marginal cost, we get:P1 - 10 = $500P1 = $510Therefore, Roach Motors should set a price of $510 for a used car.

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