Answer to Question #252616 in Microeconomics for DAXW

Question

XYZ Co. operates in a competitive market. Its marginal product of labor is 1/L, and it takes the
wage and price as given. Derive the firm's short-run demand for labor as a function of w and p.
How much labor will the firm hire if W=à ƒ ƒ ¢ ‚ µ20 and P=à ƒ ƒ ¢ ‚ µ100?

Answer 1

A perfectly competitive firm demands labor at the following point in the short run.

MPL = W/P

Where

MPL is the marginal product of labor.

W is the nominal wage rate.

P is the price of output.

So, to derive the short-run demand for labor set MPL = W/P

=> MPL = W/P

=> (1 / L) = (W/P)

=> L = (P / W)

Therefore, the short-run labor demand function is L = (P / W).

L = (P / W)

Set P = 100 and W=20

=> L = (100 / 20)

=> L = 5

The firm will hire 5 labors when the P=100 and W=20