Question

Problem 5: A firm has total cost function: ?(?) = 50? 2 + 40? + 30 A) What is the total fixed cost? B) What is the average fixed cost? C) What is the total variable cost? D) What is the average variable cost? E) What is the marginal cost? F) What is the average total cost? For parts G) and H), suppose the firm is in a competitive market. G) what is the lowest price at which the firm will supply a positive quantity in long-run equilibrium? H) What price maximizes the firm’s profit? I) How much would the firm supply at the price in part H) J) At what quantity is the firm’s marginal cost equal to its average cost?

Answer 1

?(?) = 50?^2 + 40? + 30

A.

fixed cost is the constant term in the cost function

so FC = 30

B.

Average fixed cost is fixed cost per unit or AFC=FC/y

=30/y

C.

variable cost is the cost function which depends on output level

so VC=50?^2 + 40?

D.

Average variable cost is variable cost per unit or AVC=VC/y

AVC=50?^2/y + 40?/y

AVC=50? + 40

E.

Marginal cost is first order derivative of the cost function

MC=dC/dy = 100y+40

F..

Average total cost = C/y = 50?^2/y + 40?/y + 30/y

= 50? + 40 + 30/y