Question

A price-taking firm's variable cost function is

        VC=3Q³,

where Q is its output per week. It has a sunk fixed cost of $750 per week. Its marginal cost is

         MC=9Q².

a. What is the firm’s supply function when the $750 fixed cost is sunk?

    Instructions: Enter your answer as a whole number.

     Q = (P/9)^0.5 for P ≥ $.

b. What is the firm’s supply function when the fixed cost is avoidable?

     Instructions: Enter your answer as a whole number.

     Q = (P/9)^0.5 for P ≥ $.

please make sure each answer is clear/boxed

Answer 1

VC=3Q³,
MC=9Q²

a.

Price taking firm sets quantity where:

MC=P

9Q²= P

Q²= P/9

Raise power 0.5 on both sides:

Q= (P/9)^0.5

Q= P^0.5 /3 For P greater than equals to $0 Firm's supply curve

b.

In case of price taking firm, the fixed cost does not play an important role in determining supply function because supply depends on the marginal cost and price only. So:

Price taking firm sets quantity where:

MC=P

9Q²= P

Q²= P/9

Raise power 0.5 on both sides:

Q= (P/9)^0.5

Q= P^0.5 /3 For P greater than equals to $0 Firm's supply curve