Question

关于经济学的问题，求助。谢谢！

suppose Honda's total cost of producing four cars is ＄225000 and its total cost of producing five cars is＄250000. what is the average total cost of producing five cars？ what is the marginal cost of the fifth car？ Draw the marginal cost curve and the average total cost curve for a typical firm and explain why these curves cross where they do？

Answer 1

1.average total cost AC=TC/Q=250000/5=50000

2.MC(Q)=△TC(Q)/△Q，边际成本(Marginal cost)，增加一单位的产量(Output)随即而产生的成本增加量即称为边际成本。

这道题中可以直接用total cost of producing five cars减去total cost of producing four cars计算，所以the marginal cost of the fifth car=250000-225000=25000

3.

边际成本曲线（MC）与平均成本曲线（AC）的最低点相交

证明：在AC的最低点有：dAC/dQ=0； 又：AC=TC/Q，则：
d(AC)/dQ=d(TC/Q)/dQ=（TC*dQ/dQ-Q*dTC/dQ）/Q^2=0
由dTC/dQ=MC,dQ/dQ=1,上式整理为：
TC-MC*Q=0，整理可得：MC=TC/Q=VC/Q=AC
也就是说：对于AC曲线的那点的Q=Q1值，有MC(Q1)=AC(Q1)，即P-Q平面上的这两点[Q1,MC(Q1)],[Q1,AC(Q1)]重合，或者说边际成本曲线（MC）与平均成本曲线（AC）的最低点相交。