# suppose a firm hs the following TC function: STC= 300 + 40Q - 8Q^2 + (2/3)Q^3?

A. what are the equations for the average fixed cost, average variable cost, and average total cost?

B. what will be the vaule of shortrun average cost when Q=60?

C. write the marginal cost equation for this firm.

D. what will MC be when Q= 20?

E. for this firm, what will be the dollar value of AVC at its minimum?

F. what is output level when MC is at its Maximum?

### 1 Answer

- 1 decade agoFavorite Answer
A

AFC=FC/Q = 300/Q

AVC=VC/Q = 40-8Q+2Q²/3

ATC=TC/Q = 300/Q +40-8Q+2Q²/3

B

ATC[60] =300/Q +40-8Q+2Q²/3= 5+40-480+2400=1965

C

MC=∂TC/∂C = 40-16Q+2Q²

D

MC[20] = 40-320+800 = 520

E

AVC→MIN if AVC=MC

40-8Q+2Q²/3 = 40-16Q+2Q²

8Q-4Q²/3 =0

Q(8-4Q/3)=0

Q=0 ; Q=6

Q=6

F

MC→MAX if ∂MC/∂Q=0 [FOC] & ∂²MC/∂Q²<0 [SOC]

∂MC/∂Q = ∂(40-16Q+2Q²)/∂Q = -16+4Q=0 → Q=4

∂²MC/∂Q² = +4 [MC→MIN]

∂²MC/∂Q² > 0 , thus there is no fixed maximum

MC→MAX if Q→∞

- Login to reply the answers