Question

consider a firm operating a perfectly competitive industry and suppose that this firm's total cost function is: TC=10+2q+5q^2. if p=12, which of the following statements is correct:

a) The firm is making profits

b) total revenue of this firm is 2

c) total cost of this firm is 17

d) none of the other answers

Answer 1

The total cost function is as follows -

TC = 10 + 2q + 5q²

Derive the marginal cost function -

MC = dTC/dq

MC = d(10 + 2q + 5q²)/dq

MC = 2 + 10q

The price, p, is 12.

A perfectly competitive firm maximizes profit when it produce that level of output corresponding to which price equals marginal cost.

p = MC

12 = 2 + 10q

10q = 10

q = 1

The profit maximizing quantity is 1 units.

Calculate total revenue -

Total revenue = Price * profit-maximizing quantity = 12 * 1 = 12

The total revenue is 12.

Calculate total cost -

Total cost = 10 + 2q + 5q² = 10 + (2 * 1) + 5(1)² = 10 + 2 + 5 = 17

The total cost is 17.

Calculate profit -

Profit = Total revenue - Total cost

Profit = 12 - 17 = -5

The profit is -5.

The negative profit implies loss.

So, the firm is making loss.

Hence, the correct answer is the option (c).