Answers for chapters 9-12
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1. In 1996, Congress raised the minimum wage from $4.25 per hour to $5.15 per hour, and then raised it again in 2007. (See Example 1.3 [page 13].) 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 low-skilled labor is given by LS = 10w, where LS 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 LD = 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?
In a free-market equilibrium, LS = LD. Solving yields w = $4 and LS = LD = 40. If the minimum wage is $5, then LS = 50 and LD = 30. The number of people employed will be given by the labor demand, so employers will hire only 30 million workers.
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?
Let ws denote the wage received by the sellers (i.e., the employees), and wb the wage paid by the buyers (the firms). The new equilibrium occurs where the vertical difference between the supply and demand curves is $1 (the amount of the subsidy). This point can be found where
LD(wb) = LS(ws), and
ws – wb = 1.
Write the second equation as wb = ws – 1. This reflects the fact that firms pay $1 less than the wage received by workers because of the subsidy. Substitute for wb in the demand equation: LD(wb) = 80 – 10(ws – 1), so
LD(wb) = 90 – 10ws.
Note that this is equivalent to an upward shift in demand by the amount of the $1 subsidy. Now set...