Question

Suppose the candy manufacturing market is a competitive market with the equilibrium price of $1. A typical candy manufacturing firm in the market has a cost function of:
C = 4q³– 2q² + q + 80.
All fixed costs are unavoidable.
a. Find MC and AVC functions of a typical firm.
b. Should a typical firm operate in the market? Determine the profit/loss level of a typical firm.Explain your answers.

Answer 1

(a)

MC = dC/dq = 12q² - 4q + 1

TVC = 4q³ – 2q² + q, therefore

AVC = TVC/q = 4q² - 2q + 1

(b)

Individual firms equate Price with MC, so

12q² - 4q + 1 = 1

12q² - 4q = 0

3q - 1 = 0 (Dividing by 4q)

3q = 1

q = 1/3 = 0.33

When q = 0.33,

AVC = (4 x 0.33 x 0.33) - (2 x 0.33) + 1 = 0.5356 - 0.66 + 1 = 0.7756

Since Price > AVC, a typical firm will operate in market.

Total revenue (R) = P x q = 1 x 0.33 = 0.33

C = 4q³ – 2q² + q + 80 = (4 x 0.33 x 0.33 x 0.33) - (2 x 0.33 x 0.33) + 0.33 + 80 = 0.14 - 0.22 + 0.33 + 80 = 80.25

Profit = R - C = 0.33 - 80.25 = - 79.92 (A loss of 79.92)