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.


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.

A. Use the Solow model to calculate the ratio of their steady state levels of income per capita.
Verbally interpret your answer.

Suppose now the savings rate s in X and Y is identical, but the population growth rate becomes
endogenous and depends on the level of output per capita (and therefore the level of capital per
capita). Specifically, in both countries, population grows at the higher rate if , or at a lower rate if .
The cutoff satisfies ( and

B. Draw a diagram for this model. Explain what the diagram says about the steady state of the
model and relate this to the concept of the poverty trap in poor countries.
Hint: Consider the endogenous savings rate example discussed in class (on page 71-74 Weil).

4. The following tables show data on investment rates and output per worker for two pairs of
countries. Assuming that all countries have the same production function, , the same values of s,
and that the value of ? is 1/3.
Pair I: Nigeria and Turkey

Output per Worker in 2009

Average Investment Rate

Pair II: Japan and New Zealand
New Zealand

Output per Worker in 2009
$49, 837

Average Investment Rate

A. For each country pair, calculate the ratio of GDP per worker in steady state that is predicted by
the Solow model.
B. Now calculate the actual ratio of GDP per worker for each pair of countries.
C. For which pairs of countries does the Solow model do a good job of predicting relative income?
For which pairs does the Solow model do a poor job? Briefly explain.

5. Carefully read the article below in the New York Times, answer the following questions:
A. Compare the average total fertility rate in Sub-Sahara Africa to that in Asia and Latin America.
B. High fertility rates in the past means that the population in countries like Nigeria is subject to
the echo effect. From the introductory paragraphs of the article, state two specific factors
preventing Nigeria, unlike countries in Asia and Latin America, from benefiting from this echo
C. In the section under Women Left Behind, name two specific factors that keep family size large
in Nigeria
D. In the section under Cultural Factors, explain the role that rising income and urbanization play
in reducing family size in Nigeria.

April 14, 2012
Nigeria Tested by Rapid Rise in Population, By ELISABETH ROSENTHAL
LAGOS, Nigeria — In a quarter-century, at the rate Nigeria is growing, 300 million people — a
population about as big as that of the present-day United States — will live in a country roughly the size
of Arizona, New Mexico and Nevada. In this commercial hub, where the area’s population has by some
estimates nearly doubled over 15 years to 21 million, living standards for manare falling.
Lifelong residents like Peju Taofika and her three granddaughters inhabit a room in a typical apartment
block known as a “Face Me, Face You” because whole families squeeze into 7-by-11-foot rooms along
a narrow corridor. Up to 50 people share a kitchen, toilet and sink — though the pipes in the
neighborhood often no longer carry water.
At Alapere Primary School, more than 100 students cram into most classrooms, two to a desk.
As graduates pour out of high schools and universities, Nigeria’s unemployment rate is nearly 50
percent for people in urban areas ages 15 to 24 — driving crime and discontent.
The growing upper-middle class also feels the squeeze, as commutes from even nearby suburbs can run
two to three hours.
Last October, the United Nations announced the global population had breached seven billion and
would expand rapidly for decades, taxing natural resources if countries cannot better manage the
Nearly all of the increase is in sub-Saharan Africa, where the population rise far outstrips economic
expansion. Of the roughly 20 countries where women average more than five children, almost all are in
the region.
Elsewhere in the developing world, in Asia and Latin America, fertility rates have fallen sharply in
recent generations and now resemble those in the United States — just above two children per woman.
That transformation was driven in each country by a mix of educational and employment opportunities
for women, access to contraception, urbanization and an evolving middle class. Whether similar forces
will defuse the population bomb in sub-Sarahan Africa is unclear.
“The pace of growth in Africa is unlike anything else ever in history and a critical problem,” said Joel
E. Cohen, a professor of population at Rockefeller University in New York City. “What is effective in
the context of these countries may not be what worked in Latin America orKerala or Bangladesh.”
Across sub-Saharan Africa, alarmed governments have begun to act, often reversing longstanding
policies that encouraged or accepted large families. Nigeria made contraceptives free last year, and
officials are promoting smaller families as a key to economic salvation, holding up the financial gains in
nations like Thailand as inspiration.
Nigeria, already the world’s sixth most populous nation with 167 million people, is a crucial test case,
since its success or failure at bringing down birthrates will have outsize influence on the world’s
population. If this large nation rich with oil cannot control its growth, what hope is there for the many