Question

A competitive firm faces a market price of $15. The firm has a total cost function equal to TC(q) = 30 + 5q + q2 . What quantity does the firm produce? What are its profits? Will the firm shut down in the short run? Explain.

Answer 1

Answer:

Part 1:

the quantity firm produce is 5 unit

Explanation:

Market price (P) = $15

Total revenue (TR) = price ($15) * quantity(q)

TR = $15 * q

TR = 15q

MR is 1st order derivative of TR so;

MR = 15

TC = 30 + 5q + q^2

MC is 1st order derivative of TC so,

MC = 5+ 2q

Equilibrium condition is MC = MR

5 + 2q = 15

q = 15 – 5 / 2

q = 5

the quantity firm produce is 5 unit

part 2:

profit = TR – TC

TR = price * quantity

TR = 15 * 5

TR = $75

TC = 30 + 5q + q^2

TC = 30 + 5*5 + 5^2

TC = 80

Profit = 75 – 80 = - 5

The firm is earning the loss of – 5

PART 3:

Yes the firm will shut down in the short run because the firm is operating below its break even point

Break even point where the price of commodity is equal to its average cost. If firm operating below it that means firm is earning losses so it will leave the market

AC = TC / q

AC = 80 / 5 = $16

Average cost is $15 while the price is $15. The price is less than the average cost so the firm will shut down in the short run