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 in the short run, if we want to produce 60 units of output, we need __________ units of labor.

Answer 1

In the short run, a firm's production function with fixed capital shows that the quantity of output depends only on the amount of labor employed. To produce 60 units of output, we need 36 units of labor.

Step-by-step explanation:

In the short run, when the firm's capital is fixed at 25, the production function becomes Q = f(L), which means the quantity of output depends only on the amount of labor employed. The production function, q(L,K) = 2L0.5K0.5, indicates that the output is a function of both labor (L) and capital (K).

To produce 60 units of output, we need to find the value of L when Q = 60. Substituting the values into the production function:

60 = 2L0.5(25)0.5

Simplifying the equation:

60 = 2L0.5(5)

L0.5 = 6

L = 36

Therefore, we need 36 units of labor to produce 60 units of output.