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Unformatted text preview: Answers for chapters 9-12 Please do not distribute CHAPTER 9 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 L S = 10 w , 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 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? In a free-market equilibrium, L S = L D . Solving yields w = $4 and L S = L D = 40. If the minimum wage is $5, then L S = 50 and L D = 30. The number of people employed will be given by the labor demand, so employers will hire only 30 million workers. L S L D 30 40 50 8 5 4 80 L w 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 w s denote the wage received by the sellers (i.e., the employees), and w b 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 L D ( w b ) = L S ( w s ), and w s w b = 1. Write the second equation as w b = w s 1. This reflects the fact that firms pay $1 less than the wage received by workers because of the subsidy. Substitute for w b in the demand equation: L D ( w b ) = 80 10( w s 1), so L D ( w b ) = 90 10 w s . Note that this is equivalent to an upward shift in demand by the amount of the $1 subsidy. Now set the new demand equal to supply: 90 10 w s = 10 w s . Therefore, w s = $4.50, and L D = 90 10(4.50) = 45. Employment increases to 45 (compared to 30 with the minimum wage), but wage drops to $4.50 (compared to $5.00 with the minimum wage). The net wage the firm pays falls to $3.50 due to the subsidy....
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- Spring '11