Question

5. (5 pts.) A firm has the following short run total cost function: STC = 900 + 500 -2.7Q2 + 0.045Q a. Write equations for AFC, AVC, and MC. b. What level of output minimizes AVC (find Q)? c. What do you expect to be different about cost function in the long run? (2 pts.)

Answer 1

Answer

(a)

Given
STC=900+50Q-2.7Q^2+0.045Q^3

FC=900
AFC=FC/Q
AFC=900/Q

VC=50Q-2.7Q^2+0.045Q^3
AVC=VC/Q
AVC=(50Q-2.7Q^2+0.045Q^3)/Q
AVC=50-2.7Q+0.045Q^2

MC=first derivative of the cost function
MC=d(50Q-2.7Q^2+0.045Q^3)/dQ
MC=50- 5.4Q+0.135Q^2

(b)
AVC=50-2.7Q+0.045Q^2
To find where AVC is minimized we find the first derivative of the AVC
d(AVC)/dQ=-2.7+0.90Q
Let d(AVC)/dQ=0
0.90Q-2.7=0
0.90Q=2.7
Q=2.7/0.90
Q=3
AVC is minimized when Q=3

(c)
The long-run is a period in which there are no fixed costs all costs are variables. In the long run, there will be no fixed costs. The cost function will only consist of variable costs and no fixed costs.