1. Suppose a country enacts a tax policy
that discourages investment: suppose the policy reduces the investment rate immediately
and permanently from.png"> bar to.png">’. Assuming
the economy starts in its initial steady state, use the Solow model to explain
what happens to the economy over time and in the long run. Draw a graph showing
how output evolves over time (put.png"> on the vertical axis with a ratio scale, and
time on the horizontal axis), and explain what happens to economic growth over
time.

2. Suppose the level of TFP in an economy
rises permanently from.png"> to.png">.

(a) Assuming the economy starts in its
initial steady state, use the Solow model to explain what happens to the economy
over time and in the long run.

(b) Draw a graph showing how output evolves
over time, and explain what happens to the level and growth rate of per capita
income.

(c) Suppose that.png"> grew at a constant rate, instead of being
constant. Explain in words what you think would happen to GDP over time.

(d) How is the response of the economy to
an increase in TFP different from the economy’s response to an increase in the
investment rate?

3. (a) Use the production function in
equation (.png">) and the
rules for computing growth rates:.png"> to write the growth rate of per capita GDP as
a function of the growth rate of the capital stock. (Hint: Because the labor
force is constant, the growth rates of GDP and per capita GDP are the same.)

(b) Combine this result with the last
equation in.png"> to get a solution for the growth rate of per
capita GDP as a function of the current level of capital.png">. Be sure
to write your answer in terms of.png"> and parameters of the model only.

4. The table below reports per capita GDP
and capital per person in the year 2007 for 10 countries. Your task is to fill
in the missing columns of the table.

(a) Given the values in columns 1 and 2,
fill in columns 3 and 4. That is, compute per capita GDP and capital per person
relative to the U.S. values.

(b) in column 5, use the production model
(with a capital exponent of 1/3) to compute predicted per capita GDP for each
country relative to the United States, assuming there are no TFP differnces.

(c) In column 6, compute the level of TFP
for each country that is needed to match up the model and the data. Comment on
the general results you find.

.png">

5. The Black Death. (Based on Jones,
question 4.3). In the middle of the fourteenth century, an epidemic known as
the Black Death killed about a third of Europe's population. While this was an
enormous tragedy, over the next century wages are estimated to have been higher
than before the Black Death.

(a) Use the production model to explain why
wages might have been higher.

(b) Can you attach a number to your
explanation? In the model, by how much would wages rise if 1/3 of the
population died from disease?