The graying of America will substantially increase the fraction of the population thats is retired in the decades to come. Suppose over the 48 years following 2008 the share of the population that is working returns to 1960 levels. While average labor productivity increases at the same rate as it did during the 1960-2008. Under this scenario what would be the net change in real GDP per person between 2008 and 2056?
Aver labor Production | Population employed
1960 $42,909 | 0.378%
2008 $89,626 | 0.483%
Net change in GDP $______ Round to nearest dollar amount.
Change in average labor productivity between 1960 and 2008 is given as:
change = (89,626 - 42,909) / (42,909) = 1.089
i.e. the average labor productivity increased by a factor of 1.089 between 1960 and 2008. Since the assumption is given that the same change in labor productivity is expected between 2008 and 2056, the average labor productivity in 2056 is given as:
Avg labor productivity (year 2056) = 2.089 x 89,626 = $ 187,229 (to the nearest dollar).
The real GDP per capita = average labor productivity x fraction of population employed.
Thus, real GDP per capita in 2008 = 89,626 x 0.483/100 = $ 433 (rounded to nearest dollar)
and real GDP per capita in 2056 = 187,229 x 0.378/100 = $ 708 (rounded to nearest dollar)
Therefore, net change in real GDP per capita = $ 708- $ 433 = $ 275.
Looking at the question, it appears that there is some error with the % of population employed. Only 0.483% population employed doesn't seem right. It's probably 48.3% (or 0.483 as a fraction). If we use the corrected % population employed (as 37.8% and 48.3%), the net change in real GDP will be $ 27,484.
Hope this helps.