Question

Consider a firm with a short run Total Cost (TC) given by TC=200 + 30Q - 5Q^2 + Q^3.
What is the firm’s fixed cost? What is the firm’s marginal cost? What is firm's shut down price?

Answer 1

FC=the cost is same at all level and it is equal to the total cost at Q=0 and FC=$200

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MC is the change in the total cost and a change in function found by differentiation

MC=dTC/dQ=30Q-10Q+3Q^2

MC=30-10Q+3Q^2

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VC=TC-FC

=200-30Q-5Q^2+Q^3-200

=30Q-5Q^2+Q^3

AVC=VC/Q

AVC=(30Q-5Q^2+Q^3)/Q

AVC=30-5Q+Q^2

the AVC is minimum at AVC=MC

30-5Q+Q^2=30-10Q+3Q^2

2Q^2=5Q

2Q=5

Q=2.5

AVC=30-5Q+Q^2=30-5*2.5+2.5^2=23.75

the shutdown price is equal or below $23.75