Chapter 5: Problem 23

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

Short Answer

Expert verified

The formula for the wage elasticity of labor supply (\(E_L\)) is given by: \[E_L = \frac{\Delta L}{\Delta W} \times \frac{W}{L}\] where \(L\) represents the quantity of labor supplied, \(W\) represents the wage rate, \(\Delta L\) denotes the change in labor supplied, and \(\Delta W\) denotes the change in the wage rate.

Step by step solution

Understanding the Wage Elasticity of Labor Supply

The wage elasticity of labor supply measures the percentage change in the quantity of labor supplied in response to a percentage change in the wage rate. In other words, it tells us how sensitive the labor supply is to changes in wages. If the wage elasticity of labor supply is high, it means that workers will significantly alter their labor supply in response to changes in the wage rate. On the contrary, if the wage elasticity of labor supply is low, it means that workers are less responsive to changes in wages.

Identifying the Variables in the Wage Elasticity of Labor Supply Formula

We will denote the quantity of labor supplied as \(L\) and the wage rate as \(W\). The wage elasticity of labor supply (\(E_L\)) is defined as the ratio of the percentage change in the quantity of labor supplied to the percentage change in the wage rate.

Writing the Formula for the Percentage Changes in Labor Supply and Wage Rate

To calculate the percentage change in the quantity of labor supplied, we will use the following formula: \[\text{Percentage change in }L = \frac{\Delta L}{L}\] Similarly, to calculate the percentage change in the wage rate, we will use the following formula: \[\text{Percentage change in }W = \frac{\Delta W}{W}\]

Defining the Formula for the Wage Elasticity of Labor Supply

Now we can define the formula for the wage elasticity of labor supply as the ratio of the percentage change in the quantity of labor supplied to the percentage change in the wage rate: \[E_L = \frac{\text{Percentage change in }L}{\text{Percentage change in }W}\] Plugging in the formulas for the percentage changes from Step 3, we have: \[E_L = \frac{\frac{\Delta L}{L}}{\frac{\Delta W}{W}}\]

Simplifying the Wage Elasticity of Labor Supply Formula

We can simplify the formula for the wage elasticity of labor supply by multiplying both the numerator and the denominator by \(L\) and \(W\). This gives us: \[E_L = \frac{\Delta L}{\Delta W} \times \frac{W}{L}\] This is the formula for the wage elasticity of labor supply. It demonstrates how the responsiveness of the labor supply to changes in the wage rate can be quantified, with the ratio reflecting the change in labor supplied relative to the change in wages.