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The production manager at Nike estimates that the total annual cost of producing tennis shoes is...

The production manager at Nike estimates that the total annual cost of producing tennis shoes is given by C = 5000 +4100Q – 8Q2 + 0.004Q3. Assume the market price of shoes is constant. What is the shutdown price in the short run?

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Answer #1

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

FC=5000

VC=TC-FC

VC= 5000 +4100Q – 8Q^2 + 0.004Q^3 -5000

VC=4100Q – 8Q^2 + 0.004Q^3

AVC=VC/Q

AVC=(4100Q – 8Q^2 + 0.004Q^3)/Q

AVC=4100 – 8Q+ 0.004Q^2

the shutdown price is the price below the minimum average variable cost

min(AVC) is found by differentiation the funtion and equating to zero

dAVC/dQ=-8+0.008Q=0

Q=8/0.008

Q=1000

minAVC)=4100-8*1000+0.004*(1000^2)

=$100

the shutdown price is $100 or any price below $100.

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