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 ≥ $.

Answer 1

Ans). From the question it is given that the price function is VC=3Q³

Where Q is the output per week.

a. The total cost of the firm is given as

TC = VC + FC

TC = 750 + 3Q³

MC = 9Q2²

equilibrium each firm chooses a quantity Such that P = MC,

Then supply of firm at each price follows

P = 9Q²

Q²=P/9

Q^s=(P/9)^0.5

For P>= (minAC)

Now minimum AC with sunk cost is AC=MC

Also 750/Q+3Q²=9Q²

750/Q=6Q²

Q=5

Now MC=ACmin= 225

Now short run supply function is given as

Q^s=(P/9)^0.5   for P>=225

Part B)

when all cost are avoidable

Q^s=(P/9)^0.5 for P>= $