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?

Rating

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。