Question

Consider the following production function:

y=L¹/² K¹/² −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 firm's conditional input demand functions from the given production function y = L^1/2 K^1/2 -1, a cost-minimization problem needs to be set up. The demand functions are determined by minimizing the sum of labor and capital costs, subject to the production function constraint, through solving a Lagrangian equation.

Step-by-step explanation:

The student's question relates to the identification of a firm's conditional input demand functions from a given production function. The provided production function is y = L^1/2 K^1/2 -1, where L represents labor, K represents capital, y is output, w is the price of labor, and r is the price of capital. The conditional input demand functions will show the quantity of labor and capital required to minimize costs for a given output level (y).

To determine the conditional input demand functions, we first need to set up the cost minimization problem. The firm's objective is to minimize the total cost, which is the sum of the cost of labor (wL) and the cost of capital (rK), subject to the production function constraint. This is done by forming a Lagrangian equation and solving for L and K, given w, r, and y.