Question

Problem 1. Tanner owns a car dealership and sells used cars. Tanner buys a used car at price $p and has no other costs.

(a) What is Tanner’s total cost if he sells 10 cars?
(b) What is Tanner’s total cost if he sells 20 cars?
(c) What is Tanner’s total cost if he sells y cars, TC(y)?
(d) What is Tanner’s average cost function, AC(y)?
(e) For every additional car Tanner sells, by how much do his costs increase? (f) What is Tanner’s marginal cost function, MC(y)?
(g) Draw Tanner’s average and marginal costs curves if p20.

Answer 1

a. In order to sell cars, Tanner has to buy cars first at the price $P. Thus, when he sells 10 cars, his total cost was number of cars multiplied by their buying amount,i.e., 10P.

b. Similar logic applies here as in the previous question. Thus, the total cost becomes 20P.

c. If Tanner sells y cars, he has to buy y number of cars. Thus, TC (y) = P.y

d. Tanner's average cost function is given by dividing the total cost function by the number of cars sold.

Or, AC (y) = TC ( y)÷ y = P.y ÷ y = P

e. Tanner'e marginal cost can be calculated by finding out the change in total revenue due to change in quantity.

This can also be found by taking the first order derivative of the total cost function.

It also comes out to be P.

Hence, marginal cost is P.

f. When P = 20, MC and PC both will be equal to 20.

Thus, the shapes of the cost curves will be horizontal straight lines at price level of $20 on y axis.