In order to minimize the cost of a particular level of output,a firm should produce where
A)labor input equals capital input
B)the RTS (of L for K) = $\frac { v } { w }$
C)the RTS (of L for K) = $\frac { w } { v }$
D)the MRS = $\frac { v } { w }$

Question

Quizplus · Accepted Answer

The RTS (of L for K) = $\frac { w } { v }$ represents the rate at which a firm can substitute labor for capital while keeping the level of output constant. To minimize costs, the firm should choose a combination of labor and capital such that the RTS equals the ratio of their prices (in this case, the wage rate and the rental rate of capital). This is because if the RTS is higher than the price ratio, it is cheaper to substitute labor for capital, while if the RTS is lower than the price ratio, it is cheaper to substitute capital for labor. Therefore, the firm should produce where the RTS (of L for K) = $\frac { w } { v }$ in order to minimize costs.

In Order to Minimize the Cost of a Particular Level vw\frac { v } { w }wv​

In Order to Minimize the Cost of a Particular Level $\frac { v } { w }$