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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?

User JerryN
by
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1 Answer

4 votes

Answer:

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.

User Reza GH
by
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