1. The “graying of America” is named after a situation where there will be a sub

Question

1.The “graying of America” is named after a situation where there will be a substantial increase in the fraction of the U.S. population that is retired in the decades to come. To illustrate the implications of this on U.S. living standards, suppose that over the 49 years following 2009 (2009 to 2058), the share of the population that is working returns to its 1960 level, while average labor productivity increases by as much as it did during between 1960 and 2009). Specifically, the following data is estimated:

Year

Average Labor Productivity

(in real US$)

Share of the Population Employed

2009

$99,763

46.0%

2058

$219,080

37.8%

Under this scenario, what would be the change (not percentage change) in real GDP per person between 2009 and 2058?

Year

Average Labor Productivity

(in real US$)

Share of the Population Employed

2009

$99,763

46.0%

2058

$219,080

37.8%

Explanation / Answer

Use the following formula

    Real GDP per capita in year t = Real GDP in year t ÷ Population in year t                        … (1)

Since

    Labor productivity in year t (in real dollars)

            = Real GDP in year t / number of people employed in year t,

Equation (1) becomes

   Real GDP per capita in year t

            = [Labor productivity in year t (in real dollars) × number of people employed in year t]

                        ÷ Population in year t

Let population in year 2009 is a.

Real GDP per capita in year 2009

            = [Labor productivity in 2009 (in real dollars) × number of people employed in 2009]

                        ÷ Population in 2009

            = [$99,763 × 0.46a] ÷ a

            = $45,890.98

Let population in year 2058 is b.

Real GDP per capita in year 2058

            = [Labor productivity in 2058 (in real dollars) × number of people employed in 2058]

                        ÷ Population in 2058

            = [$219,080 × 0.378b] ÷ b

            = $82,812.24

Change in Real GDP per capita from year 2009 to 2058

            = Real GDP per capita in year 2058 Real GDP per capita in year 2009

            = 82,812.24 $45,890.98

            = $36,921.26

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