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Anonymous
Anonymous asked in Social ScienceEconomics · 1 decade ago

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

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    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→∞

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