Question

From time to time, Congress has raised the minimum wage. Some people suggested that a government subsidy could help employers finance the higher wage. This exercise examines the economics of minimum wage and wage subsidies. Suppose the supply of low-skilled labor is given by

L^S= 10w

where, L^S is the quantity of low-skilled labor (in millions of persons employed each year), and w is the wage rate(in dollars per hour). The demand for labor is given by

L^D= 80 - 10w

a. What will be the free-market wage rate and employment level? Suppose the government sets a minimum wage of \(5 per hour. How many people would then be employed?

b. Suppose that instead of a minimum wage, the government pays a subsidy of \)1 per hour for each employee. What will the total level of employment be now? What will the equilibrium wage rate be?

Short answer

1. The free market wage rate would be $4 per hour and employment level 40 million. At a minimum wage rate of $5, the number of people employed would be 30 million.

2. The total employment after the subsidy would be 45 million. The new wage rate would be $4.5 per hour.

Step-by-step solution

Step 1. Determining the free market wage rate and employment level and employment level after minimum wage.

• Free market employment level.

The wage rate and employment level at which the quantity of demanded labor is equal to the quantity of supplied labor is the free market wage rate and employment level. The free market wage rate is calculated below:

L^s= L^D

10w = 80-10w

20w=80

w=4

The free market wage rate is $4 per hour.

The free market employment level is calculated by putting the value of ‘w’ in the L^S equation.

$$\begin{gathered} L^S=10w \\ =10\times 4 \\ =40 \end{gathered}$$

The free market employment level is 40 million.

• Employment level after the government sets a minimum wage rate of $5 per hour.

After implementing the minimum wage rate, the new employment level is calculated by determining the demanded quantity of laborers at this wage rate.

$$\begin{gathered} L^D=80-10\left(5\right) \\ =80-50 \\ =30 \end{gathered}$$

The new employment level after the implementation of the wage rate is 30 million.

Step 2. Calculation of change in employment level and wage rate after the government subsidy

The subsidy of $1 by the government on wage rates will shift the demand curve for labor to its right. Thus, the demand for labor would increase, which will create a new equation for labor demand in the market. The new equation for labor demand (L^D’) is:

$$\begin{gathered} L^D=80-10\left(w+1\right) \\ =80-10w+10 \\ =90-10w \end{gathered}$$

The shift in labor demand will create a new equilibrium position in the market where the demanded quantity of labor would equal the supplied quantity of labor.

$$\begin{gathered} L^S=L^D \\ 10w=90-10w \\ 20w=90 \\ w=4.5 \end{gathered}$$

The new wage rate after the government subsidy is $4.5 per hour.

By putting the value of wage rate in the labor supply equation, the new employment level is calculated below:

$$\begin{gathered} L^S=10w \\ =10\times 4.5 \\ =45 \end{gathered}$$

The new employment level after the implementation of government subsidy on wage rate is 45 million.