Question

Consider a firm that has cost function of:

TC = 24 + 10Q + 1.5 Q^2

a) Draw the average cost and marginal cost curves for this firm (label with equation).

b) Draw the supply curve of this firm

c) What are the profits of the firm if the price of output is $44?

Answer 1

Answer

The red line is the MC curve

The blue line is the AC curve

MC=dTC/dQ
MC= d(24 + 10Q + 1.5 Q^2)dQ
MC=10+3Q

AC=TC/Q
AC=(24 + 10Q + 1.5 Q^2)/Q
AC=24/Q+10+1.5Q

10+ 3x AC & MC 24/x + 10 +1 undefined 35.5 25 0 quantity

b)

The rising portion of the MC above the minimum of the AVC is the short-run supply curve of the firm
TC=24 + 10Q + 1.5 Q^2
FC=24
VC=10Q + 1.5 Q^2
AVC=VC/Q
AVC=(10Q + 1.5 Q^2)/Q
AVC=10+1.5Q

The red line is the supply curve of the firm

c)

AVC & MC 10 + 3x 10 + 1.5x 10 11.5 quantity

The firm produces at MC=P
MC=10+3Q
P=44
10+3Q=44
3Q=34
Q=11.33
Profit =TR-TC
TR=P*Q=44*11.33=498.52
TC=24+10*11.33+1.5*(11.33^2)
=329.85335
Profit=498.52-329.85335
=168.66665
=169
the profit is $169