Question

Suppose a firm uses labor and capital for its production, the production function is: Q(L,K)=L¹/³K²/³ Labor wage w=2, capital rental rate r=2∗w; the long run cost function is: c(q)=α+βqʸ What is the value of y ?

Answer 1

The value of y in the long run cost function is 1/3.

Step-by-step explanation:

The value of y can be determined by analyzing the long run cost function. In the long run, all factors of production are variable, including labor and capital. The long run cost function is represented as c(q) = α + βq^y, where q is the quantity. Since the production function is Q(L,K) = L^(1/3) K^(2/3), we can substitute this into the cost function to get c(L,K) = α + β(L^(1/3) K^(2/3))^y.

By comparing the exponents on L and K in the cost function with the exponents on L and K in the production function, we can determine that y is equal to 1/3. Therefore, the value of y is 1/3.