Suppose that each firm in a perfectly competitive market has

Suppose that each firm in a perfectly competitive market has a cost of TC = 75 + 500Q – 5Q2 + 0.5Q3

a) Determine if this is a short-run or long-run cost function (motivate):

b) Calculate the output that minimizes the firm\'s AVC. ??

c) What is the firm\'s shutdown price?

Answer a)

IF Cost function has fixed part that is the part which is independant of Q then that function is called as Short run Cost function

Hence above cost function has 75 as fixed part therefore given function is short run cost function

ANs b)

VC=500Q-5Q^2+0.5Q^3

AVC=500-5Q+0.5Q^2

Finding FOC we get

-5+Q=0

Q=5 hence output of Q=5 minimizes AVC because double differentiation of AVC function would yield value >0

Ans C

For Perfectly competitive firm Price can be calculated as

P=MC
P=500-10Q+1.5Q^2

For SHut Down Price

Revenue<Cost

P*Q<75+500Q-5Q^2+0.5Q^3

Price<AC