Question

Consider a firm providing repairing services. Suppose that the total cost of repairing s cars is given by

c(s) = 2s²+ 100

where s is the number of repair services he provides.

(a) Find the marginal cost.

(b) In the short-run, if the price of repair services is $20, then how many services will be provided?

(c) If the price stays at $20, and the fixed cost of $100 also stays in the long-run (due to the fee for the permit, for example), then what would the firm do? Explain your answer.

Answer 1

a.

Given,

C = 2S^2 + 100

Marginal cost (MC) = derivative of C with respect to S

                                    = (2 × 2)S^(2 – 1) + 0

                                    = 4S (Answer)

b.

Given,

Price (P) = 20

The firm should stay at a level where (P = MC)

P = MC

20 = 4S

S = 20/4 = 5

Answer: there would be 5 services in the short-run.

c.

Generally, all the factors of production are variable in the long-run; therefore, there would be no fixed cost. But it is different here. Profit in the long-run should be calculated first.

Profit = TR – TC

            = ($20 × 5) – {(2 × 5^2) + 100}

            = 100 – (50 + 100)

            = 100 – 150

            = - 50

There is no profit but the loss of 50. It happens because of non-recovering of fixed cost; this situation could be afforded in the short-run but not in the long-run. In order to stay in the long-run a firm must recover all expenses. Since this is not happening, the firm should stop the business in the long-run.