In 1996 Congress raised the minimum wage from $4

In 1996 Congress raised the minimum wage from $4.25 to $5.15 per hour. 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 IN A MAKE-BELIEVE COUNTRY.

Suppose the supply of low skilled labor is given by LABOR SUPPLY = 10*w millions where w is the wage rate [in dollars per hour]. The demand for labor is given by LABOR DEMAND = 80 - 10*w millions.

a) What will be the free market wage rate and employment level?
Wage rate and employment level for a free market is when SUPPLY = DEMAND. Thus:
10w = 80 - 10w
20w = 80
w = $4 (/hr)
Employment level = 10*4 = 40 (millions)

b) Suppose the government sets a $5.00 per hour minimum wage. What will be the employment level?
When government sets a $5 minimum wage, the supply increases but demand reduces. The employment level is that of the demand, thus
Employment level = 80 - 10*5 = 30 (millions)

c) Suppose the government pays a subsidy of $1 per hour directly to the employee. What will be the market wage and employment level? How much will the government pay per week [suppose every laborer works 40 hours].
When there is a subsidy of $1, the market wage will be $5-$1 = $4 effectively, thus the employment level is 40 (millions).
The government will pay 40M*1*40 = 1.6 (billion/week)