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 decade agoFavorite Answer
AFC=FC/Q = 300/Q
AVC=VC/Q = 40-8Q+2Q²/3
ATC=TC/Q = 300/Q +40-8Q+2Q²/3
ATC =300/Q +40-8Q+2Q²/3= 5+40-480+2400=1965
MC=∂TC/∂C = 40-16Q+2Q²
MC = 40-320+800 = 520
AVC→MIN if AVC=MC
40-8Q+2Q²/3 = 40-16Q+2Q²
Q=0 ; Q=6
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→∞