Question

Consider the following production function: y=L

1/2
K
1/2
−1, suppose the prices of Labor and Capital are w and r respectively. What are the firm's conditional input demand functions (amount of K and L as a function of w,r,y that minimizes the costs given the output)?

Answer 1

To find the conditional input demands of Labor and Capital, one must apply cost minimization to the production function (y = L^(1/2)K^(1/2) - 1), considering the prices of labor (w) and capital (r).

Step-by-step explanation:

The student's question revolves around finding the conditional input demand functions for Labor (L) and Capital (K) given a production function: y = L1/2 K1/2 − 1, where the prices of Labor and Capital are w and r respectively. The aim is to minimize costs for a given level of output y. To determine the conditional input demand functions, one would use cost minimization techniques in conjunction with the production function, considering the prices of labor (w) and capital (r).

For example, the production function can be manipulated to find out how many workers (L) and units of capital (K) are needed to produce varying quantities of output (Q). Changes in the input costs, such as an increase in w (the cost of labor) or r (the cost of capital), could shift the demand for labor and capital as the firm adjusts its inputs to produce at a minimum cost.