Chap013Solutions

# Chap013Solutions - CHAPTER 13 13-1 Suppose there are 25,000...

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89 CHAPTER 13 13-1. Suppose there are 25,000 unemployed persons in the economy. You are given the following data about the length of unemployment spells: Duration of Spell (in months) Exit Rate 1 0.60 2 0.20 3 0.20 4 0.20 5 0.20 6 1.00 where the exit rate for month t gives the fraction of unemployed persons who have been unemployed t months and who “escape” unemployment at the end of the month. The data can be used in the problem to calculate the number of workers who have 1 month of unemployment, the number who have 2 months of unemployment, and so on, and how many months of unemployment are associated with workers who get a job after a given duration. Duration (Months) Exit Rate # Unemp: Start of Month # of Exiters # of Stayers # Months For Duration 1 0.60 25,000 15,000 10,000 15,000 2 0.20 10,000 2,000 8,000 4,000 3 0.20 8,000 1,600 6,400 4,800 4 0.20 6,400 1,280 5,120 5,120 5 0.20 5,120 1,024 4,096 5,120 6 1.00 4,096 4,096 0 24,576 (a) How many unemployment-months will the 25,000 unemployed workers experience? The 25,000 workers will experience 58,616 months of unemployment, an average of 2.34 months per worker. (b) What fraction of persons who are unemployed are “long-term unemployed” (that is, are in unemployment spells which last 5 or more months)? Only 5,120 of the 25,000 workers (20.5 percent) are in spells lasting 5 or more months. (c) What fraction of unemployment months can be attributed to persons who are long-term unemployed? Although only 20.5 percent of workers are unemployed for 5 or more months, they account for 29,696 of the 58,616 (50.7 percent) of months of unemployment.

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90 (d) What is the nature of the unemployment problem in this example: too many workers losing their jobs or too many long spells? Most spells are short-lived, but workers in long spells account for most of the unemployment observed in this economy. Thus, the main problem is too many long spells. 13-2. Consider Table 599 of the 2002 U.S. Statistical Abstract. (a) How many workers aged 20 or older were unemployed in the United States during 2001? How many of these were unemployed less than 5 weeks, 5 to 14 weeks, 15 to 26 weeks, and 27 or more weeks? In total, 5,554,000 workers aged 20 years or older were unemployed in the U.S. in 2001. Of these, 40 percent, or 2,221,600 workers, were unemployed for less than 5 weeks; 32.2 percent, or 1,788,388 workers, were unemployed between 5 and 14 weeks; 15.5 percent, or 860,870 workers, were unemployed 15 to 26 weeks, and 12.9 percent, or 716,466 workers were unemployed for 27 or more weeks. (b) Assume that the average spell of unemployment is 2.5 weeks for anyone unemployed for less than 5 weeks. Similarly, assume the average spell is 10 weeks, 20 weeks, and 35 weeks for the remaining categories. How many weeks did the average unemployed worker remain unemployed? What percent of total months of unemployment are attributable to the workers that remained
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Chap013Solutions - CHAPTER 13 13-1 Suppose there are 25,000...

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