Question

What is the formula for the wage elasticity of labor supply?

Short answer

The formula for the wage elasticity of labor supply is: E_w = \(\frac{\text{d}L}{\text{d}W} * \frac{W}{L}\) Where E_w is the wage elasticity of labor supply, L is the quantity of labor, and W is the wage rate. This formula measures the responsiveness of the quantity of labor supplied to changes in the wage rate.

Step-by-step solution

Define Wage Elasticity of Labor Supply

Wage elasticity of labor supply measures the responsiveness of the quantity of labor supplied to a change in wages. It is an important concept in labor economics that helps in understanding how sensitive workers are to changes in their wages. The elasticity can be positive (i.e., as wages increase, workers will supply more labor) or negative (i.e., as wages increase, workers will supply less labor due to income effect).

Define Labor Supply Curve

The labor supply curve represents the relationship between the wage rate and the quantity of labor supplied by workers. In general, the curve is upward-sloping, indicating that as wages increase, workers are willing to supply more labor, all else being equal. However, in some cases, the curve may bend backward at higher wage levels due to income effects (i.e., workers might choose to work fewer hours as they earn more).

Derive the Elasticity Formula

Wage elasticity of labor supply is calculated as the percentage change in the quantity of labor supplied divided by the percentage change in the wage rate. Using calculus, this can be expressed as: E_w = \(\frac{\text{d}L/L}{\text{d}W/W}\) Where: E_w = Wage elasticity of labor supply L = Quantity of labor W = Wage rate Using the chain rule of calculus, we can rewrite this formula as: E_w = \(\frac{\text{d}L}{\text{d}W} * \frac{W}{L}\) The term \(\frac{\text{d}L}{\text{d}W}\) represents the slope of the labor supply curve, which reflects the change in the quantity of labor supplied as the wage changes.

Formula for Wage Elasticity of Labor Supply

The formula for the wage elasticity of labor supply is: E_w = \(\frac{\text{d}L}{\text{d}W} * \frac{W}{L}\) This formula shows the responsiveness of the quantity of labor supplied to changes in the wage rate. A higher value for E_w indicates a greater responsiveness of workers to changes in their wages.