Question

Consider a firm that produces output that sells in the product market for a price P = 1. The firm uses the production technology Y = F(L) = 10 ∗ ln(L), where L is the number of laborers hired in production. The firm takes the hourly wage W as given. Capital is not used in production.

1.1 Suppose the wage rises from W = 1 to W = 2. What is the firm’s elasticity of demand over this range?

1.2 Suppose that this firm is called “Firm A.” Another firm (“Firm B”) has an elasticity of demand equal to 1 (in absolute value) when the wage rises from W = 1 to W = 2. Based on this information, which firm’s workers would a union be more successful at convincing to let it negotiate with management for a $1 increase in wages (from W = 1 to W = 2)? Explain.

Answer 1

Solution:

Given

price P = 1.

Y = F(L) = 10 ∗ ln(L)

1.1 Suppose the wage rises from W = 1 to W = 2 , the firm’s elasticity of demand over this range is:

The elasticity will be calculated as below:

= -0.5

Therefore when the wage changes from 1 to 2,

the change in the demand for labor is reduced by 0.5 times.

1.2 Firm B has an elasticity of demand equal to 1 when the wage rises from W = 1 to W = 2.

firm’s workers would a union be more successful at convincing to let it negotiate with management for a $1 increase in wages (from W = 1 to W = 2) is:

MAX =  π = PF(L) - WL

π = (1)10 ∗ ln(L) - WL

dπ/dx = 10/L - W = 0

10 / W = L *

MPL = dF(L) /dL = 10 / L

L* = 10 / W

For W = 1,

L* = 10 / 1 = 10

For W = 2,

L* =10 / 2 = 5

L* = 10 / W

dL / dW * W / L = -10 / W2 * W / 10/W

= -1

so elasticity is -1 for all W values