Question

The nation of Ectenia has 80 competitive apple orchards, which sell apples at the world price of $2 per apple. The following equations describe the production function and the marginal product of labor in each orchard: 3

Q = 80L - L2
MPL = 80 - 2L where Q is the number of apples produced in a day, L is the number of workers, and MPL is the marginal product of labor. What is each orchard's labor demand as a function od the daily wage W?
L= 80 - 2W L= 40 - 0.5W L= 40 - 0.25W L= 3,200 - 20W

Answer 1

To find each orchard's labor demand as a function of the daily wage (W), equate the value of the marginal product (VMP) to the wage rate and rearrange the equation. The resulting labor demand function is L = 40 - 0.25W.

Step-by-step explanation:

The labor demand for an orchard is determined when a firm equates the value of the marginal product (VMP) of labor to the wage rate (W). The value of the marginal product is calculated by multiplying the marginal product of labor (MPL) by the market price of apples ($2 per apple). In the given scenario for Ectenia, we have a price of $2 and the marginal product of labor as MPL = 80 - 2L.

To find the labor demand as a function of the daily wage (W), we set the VMP equal to W.

Calculate the VMP: VMP = MPL x Price = (80 - 2L) x $2.

Set VMP equal to the wage rate: 160 - 4L = W.

Rearrange to find L as a function of W: L = (160 - W) / 4.

Therefore, the labor demand function based on the daily wage (W) is L = 40 - 0.25W.