```1. In Japan, the fraction of the population aged 20-64 is forecast to fall from 62% to 55% over the 20year period from 2000 to 2020 as working-age adults move into old age. (Weil, page 142, Table 5.3,
3rd edition).

A. Calculate the effect of this change in demographics on the annual growth rate of Japan’s GDP
per capita. Be clear about the assumption you have to make in order to give a precise answer to
this question.
Hint: Use the relationship covered in class between GDP per capita (Y/P), GDP per worker (Y/L), and
labor force participation rate (L/P). Also, Make use of the formula for growth rates to calculate the
growth of the labor force over time.

B. In countries like Japan and the U.S., falling rates of labor force participation is inevitable. From
the model of demographic aging discussed in class, name two ways that these countries can use
to counter the effect on GDP per capita of falling fraction of working-age in the population? Be
specific in your answer by pointing to how these two ways affect the variables in our model of
demographic aging.

2. The graphs below show the 2000, 2025 (projected) and 2050 (projected) age pyramids for Tunisia,
a typical developing country. Be specific in your answers to the following questions.

A.
B.
C.
D.

How does the pyramid evolve?
What does this evolution tell us about demographic momentum?
What does this evolution tell us about the demographic transition?
What does it tell us about aging of the population?

3. Countries X and Y differ in population growth rates and rates of investment. In country X,
investment (or savings) is 20% of GDP, and population grows at 0% per year. In country Y,
investment (savings) is 10% of GDP, and population grows at 5% per year. Both countries have the
same rate of depreciation at 5%, and the same share of payment to capital in total output ? =1/3.```