In: Economics
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.
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