In the section Gains and Adjustment Costs for the United States under NAFTA, we calculated the lost

Question:

In the section "Gains and Adjustment Costs for the United States under NAFTA," we calculated the lost wages of workers displaced due to NAFTA. Prior experience in the manufacturing sector shows that about two-thirds of these workers obtain new jobs within three years. One way to think about that re-employment process is that one-third of workers find jobs in the first year, and another one-third of remaining unemployed workers find a job each subsequent year. Using this approach, in the table that follows, we show that one-third of workers get a job in the first year (column 2), leaving two-thirds of workers unemployed (column 4). In the second year, another (1/3) €¢ (2/3) = 2/9 of workers get a job (column 2), so that 1/3 + 2/9 = 5/9 of the workers are employed (column 3). That leaves 1 - 5/9 = 4/9 of the workers unemployed (column 4) at the end of the second year.

a. Fill in two more rows of the table using the same approach as for the first two rows.
b. Notice that the fraction of workers finding a job each year (column 2) has the formula:
Fraction Finding Job = 1/3 €¢ (2/3)Year€“1
Using this formula, fill in six more values for the fraction of workers finding a job (column 2), up to year 10.
c. To calculate the average spell of unemployment, we take the fraction of workers finding jobs (column 2), multiply it by the years of unemployment (column 1), and add up the result over all the rows. By adding up over 10 rows, calculate what the average spell of unemployment is. What do you expect to get when adding up over 20 rows?
d. Compare your answer to (c) with the average three-year spell of unemployment on page 186. Was that number accurate?