y51108 asked in 教育與參考考試 · 1 decade ago

個體經濟學計算題

the engineer department of consolidated chemicals has developed the

following total cost function for a proposed new plant to produce fertilizer

TC=1016-3.36Q+0.021Q^2

(1)Determine the output rate that will minimize average cost and the

per-unit cost at the rate of output

(2) If the current market price of this fertilizer is $5.5 per unit, and is

expected to remain at that level for the future, should the plant be

built? why?

1 Answer

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  • 1 decade ago
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    The engineer department of consolidated chemicals has developed the

    following total cost function for a proposed new plant to produce fertilizer: TC = 1016 - 3.36Q + 0.021Q2

    (1)Determine the output rate that will minimize average cost and the

    per-unit cost at the rate of output?

    肥料生產的平均成本(AC),即總成本(TC)除以產量(Q):

    AC = 1016/Q - 3.36 + 0.021Q.

    極小化平均成本的產量會令一階導數為零:

    d(AC)/dQ = -1016 / Q2 + 0.021 = 0, ==> Q2 = 1016 / 0.021 = 48381.

    解得Q = 220.

    在該產量水準下,每單位的成本(即平均成本)為:

    AC = 1016/220 -3.36 + 0.021*220 = 5.88.

    (2) If the current market price of this fertilizer is $5.5 per unit, and is

    expected to remain at that level for the future, should the plant be

    built? why?

    由於肥料價為$5.5,換言之,在平均成本最低時的每單位成本要$5.88,生產成本高於肥料所能賣出的價格,建廠後所產生的利潤為負。因此,建議該公司取消建廠的計畫。

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