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 a minimum wage and wage subsidies. Suppose the supply of lowskilled labor is given by \\[ L^{s}=10 w \\] where \(L^{5}\) 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}=80-10 w \\] 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?

Understanding labor supply and demand is essential when examining the effects of changes in minimum wage or the implementation of government subsidies. In essence, the labor supply represents the total number of workers willing to work at a given wage rate, while labor demand represents the number of workers that employers are willing to hire at that wage.

In our exercise, the supply of low-skilled labor is mathematically represented as \( L^{s}=10w \), meaning that as the wage increases, more individuals are willing to work. Conversely, the demand for labor is given by the equation \( L^{D}=80-10w \), indicating that higher wages lead to fewer jobs offered by employers as the cost of labor increases.

This interrelationship of supply and demand determines the equilibrium wage rate and employment levels in a free market, without government interventions such as a minimum wage or subsidies.

The equilibrium wage rate is found where the labor supply equals the labor demand. It represents the wage rate at which the number of workers willing to work is exactly matched by the number of jobs available.

As per the step by step solution, by setting \(10w = 80 - 10w\), we find the equilibrium wage rate for the free market. Solving for \(w\) reveals that at the equilibrium wage rate, there is no surplus of labor (unemployment) and no shortage of labor (unfilled jobs). This is a key concept in microeconomic theory, demonstrating how prices (in this case, wages) adjust to balance supply and demand.

A government subsidy provided to employers for each hour worked by an employee can impact the labor market in various ways. In the exercise, a subsidy of \($1\) per hour would effectively reduce the wage the employer has to pay.

This reduction in labor costs can stimulate demand for workers and potentially increase the overall employment level, as it becomes less expensive for employers to hire. The subsidy acts like a shift in the demand curve, as it raises the wage that workers receive and also increases the quantity of labor demanded without raising the cost to employers.

The employment level in an economy is the number of employed workers at a given time. According to the exercise, when government sets a minimum wage that is above the equilibrium wage rate, it can lead to unemployment because the quantity of labor supplied exceeds the quantity demanded.

On the other hand, if the government provides a subsidy, it can increase the employment level as the gap between what employers pay and what workers receive is bridged by the subsidy. The employment level is a crucial indicator of economic health and is significantly influenced by various factors, including minimum wage policies and government subsidies.

Microeconomic theory delves into the behavior of individuals and firms in making decisions regarding the allocation of scarce resources. It provides frameworks to predict and analyze how prices form in markets and how those prices influence decision-making.

In the context of the minimum wage and government subsidies, microeconomic theory explains how wage rates and employment levels respond to these policies. It helps in understanding that setting a minimum wage above the equilibrium wage rate can lead to excess supply of labor, while subsidies can offset this effect by encouraging higher employment levels without directly affecting the wage rate paid by employers.