Question

Suppose a perfectly competitive​ firm's total cost of production​ (TC) is:

T(C)= q^3 -4 q^2 +60q +15

and the firm's marginal cost of production (MC) is
MC(q)= 3q^2- 8q +60.

The firm's short-run supply curve is given by :________

Answer 1

The firm's short-run supply curve is P = 3q^2- 8q + 60 for prices above $56

Step-by-step explanation:

Given Data;

TC(q) = q^3 - 4q^2 + 60q + 15

MC = 3q^2 - 8q + 60

But,

Fixed Cost, FC = TC(0) = 15

Therefore, the variable cost becomes

VC(q) = TC(q) - FC

= q^3 - 4q^2 + 60q

Since average variable cost = VC(q) /q, the equation becomes;

AVC(q) = VC(q)/q

= (q^3 - 4q^2 + 60q)/q

= q^2 - 4q + 60

When the curve is at a minimum point, AVC'(q) = 0

Therefore,

q2 - 4q + 60 = 0

2q - 4 + 0 = 0

2q = 4

q = 4/2

q = 2

Since q = 2,

AVC(2) = 22 - 4*2 + 60 = 4 - 8 + 60 = $56

Therefore, the short-run supply curve of the firm is P = 3q2- 8q + 60 for prices above $56

Answer 2

P = 3q^2 - 8q + 60 for prices above $56

Step-by-step explanation:

The firm's short run supply curve is the portion of its marginal cost curve. The firm's marginal cost of production is the change in its total cost of production from producing one additional unit. The firm's short run supply curve lies above its average variable cost curve. If the price in market rises the firm will sell more products. The short run supply curve is upward sloping because quantity supplied increases when the prices are increased.