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to such a change.7. a. If workers are free to move between sectors, then the wage in each sector will be equal. If the wages were not equal then workers would have an incentive to move to the sector with the higher wage and this would cause the higher wage to fall, and the lower wage to rise until they were equal. b. Since there are 100 workers in total, LS = 100 – LM. We can substitute this expression into the labor demand for services equation, and call the wage w since it is the same in both sectors: LS = 100 – LM = 100 – 4w LM = 4w. Now set this equal to the labor demand for manufacturing equation and solve for w: 4w = 200 – 6w w = $20. Substitute the wage into the two labor demand equations to find LM is 80 and LS is 20. c. If the wage in manufacturing is equal to $25 then LM is equal to 50. d. There are now 50 workers employed in the service sector and the wage wS is equal to $. e. The wage in manufacturing will remain at $25 and employment will remain at 50. If the reservation wage for the service sector is $15 then employment in the service sector will be 40. Therefore, 10 people are unemployed and the unemployment rate is 10 percent.8. Real wages have risen over time in both the United States and Europe, increasing the reward for working (the substitution effect) but also making people richer, so they want to “buy” more leisure (the ine effect). If the ine effect dominates, then people want to work less as real wages go up. This could explain the European experience, in which hours worked per employed person have fallen over time. If the ine and substitution effects approximately cancel, then this could explain the . experience, in which hours worked per person have stayed about constant. Economists do not have good theories for why tastes might differ, so they disagree on whether it is reasonable to think that Europeans have a larger ine effect than do Americans.9. The vacant office space problem is similar to the unemployment problem。 we can apply the same concepts we used in analyzing unemployed labor to analyze why vacant office space exists. There is a rate of office separation: firms that occupy offices leave, either to move to different offices or because they go out of business. There is a rate of office finding: firms that need office space (either to start up or expand) find empty offices. It takes time to match firms with available space. Different types of firms require spaces with different attributes depending on what their specific needs are. Also, because demand for different goods fluctuates, there are “sectoral shifts”—changes in the position of demand among industries and regions that affect the profitability and office needs of different firms.Chapter 7—Unemployment and the Labor Market 59