Question

g a firm produces according to the production function q=K.8 L.2, where q denotes units of output and k units of capital and L units of labor. The price of capital is $24 per unit, and the price of labor is $12 per unit. What is the optimal capital/labor ratio?

Answer 1

1.25

Step-by-step explanation:

The production function is correctly sated as follows:

`q = K^(0.8)L^(0.2)`

`MP_(K) = 0.8K^(-0.2)L^(0.2)`

`MP_(L) = 0.2K^(0.8)L^(-0.8)`

Where,
`MP_(K)` represents marginal product of capital, and
`MP_(L)` represents marginal product of labor.

At the optimal level, we have:

`(MP_(K))/(MP_(L)) = (P_(K))/(P_(L))`

Where,
`P_(K)` represents price of capital, and
`P_(L)` price of labor.

`(0.8K^(-0.2)L^(0.2))/(0.2K^(0.8)L^(-0.8)) = (24)/(12)`

`0.4(L)/(K) = 2`

`(L)/(K) = 0.8`

`(K)/(L) =(1)/(0.8) = 1.25`

Therefore, the optimal capital/labor ratio is 1.25.