Question

Suppose in short run, a firm's capital is fixed at 25 , i.e. K=25. This firm has a production function: q(L,K)=2L⁰.⁵K⁰.⁵ If w=5,r=4, the short run cost function is: c(q)=α+βqʸ What is the value of α ?

Answer 1

The value of α in the short run cost function, which represents the fixed cost of capital, is calculated as α = K × r. In this case, with K = 25 and r = 4, the value of α is 100.

Step-by-step explanation:

The question asks for the value of α in the short run cost function c(q) for a firm where capital K is fixed at 25 and the production function is q(L,K) = 2L0.5K0.5. Given the wage rate w is 5 and the rental rate of capital r is 4, we can find α, which represents the fixed costs in the short run, primarily the cost of capital since K is fixed.

α is calculated by multiplying the fixed amount of capital K by the rental rate r: α = K × r. With K = 25 and r = 4, we have α = 25 × 4 = 100. Therefore, regardless of the quantity produced q, the firm will always incur a fixed cost (α) of 100 in the short run due to the cost of utilizing the fixed capital.