Question

Suppose a firm has the following total cost function: TC = 100 + 4q2.

a. What is the minimum price necessary for the firm to earn profit? You must explain your reasoning and process as to how your found the price you found.

b. Below what price will the firm shut down in the short run?

Answer 1

ANswer
a)
the minimum price necessary for the firm to earn the profit is the price equal to the minimum average total cost
the minimum average total cost is found by equating first order condition of ATC=0
ATC=TC/q=100/q+4q
dATC/dq=4-(100/q^2)=0
100/q^2=4
4q^2=100
q^2=25
taking the root of both sides
q=5
min(ATC)=P=100/5+4*5=20+20=$40
the price is $40
--------------
b)
the firm shut down if the price is below minimum average variable cost to minimize losses
that is found by the FOC of AVC=0
VC=4q^2 ...........the total cost function without constant term
AVC=VC/q=4q
dAVC/dq=4
so the AVC is minimum at 0 units of output and the AVC is also zero
so the firm shut down if the price is below zero.

?