Econ 490 – Midterm (Topics in Economic Growth)

Econ 490 – Topics in Economic Growth
Spring 2014
Practice Questions – MIDTERM I
1) A country is described by the Solow Model, with a production function of y=k 1/2. Suppose that k is equal to 400. The fraction of output invested is 50%. The depreciation rate is 5%. Is the country at its steady-state level of output per worker, above the steady state, or below the steady state? Show how you reached your conclusion.

2) The following tables show data on investment rates and output per worker in for three pairs of countries. For each country pair, calculate the ratio of GDP per worker in steady state that is predicted by the Solow model, assuming that all countries have the same values of A and δ and that the value of α is 1/3. Then calculate the actual ratio of GDP per worker for each pair of countries. For which pairs of countries does the Solow model do a good job of predicting relative income? For which pair does the Solow model do a poor job? Why do you think it’s happening?
a) Country Thailand Bolivia
b) Country Nigeria Turkey
c) Country Japan New Zealand

Investment Rate (Average 1975-2009)
35.2%
12.6%

Output per Worker in 2009

Investment Rate
(Average 1975-2009)
6.4%
16.3%

Output per Worker in 2009

Investment Rate
(Average 1975-2009)
29.9%
19.6%

Output per Worker in 2009

$13,279
$8,202

$6,064
$29,699

$57,929
$49,837

3) Country X and Country Y have the same level of output per worker. They also have the same values for the rate of depreciation, δ, and the measure of productivity, A. In country X output per worker is growing, whereas in Country Y it is falling. What can you say about the two countries’ rates of investment?

4) In a country the production function is y=k 1/2. The fraction of output invested, γ, is 0.25. The depreciation rate, δ, is 0.05. a) What are the steady-state levels of capital per worker, k, and output per worker, y?
b) In year 1, the level of capital per worker is 16. In a table such as the following on, show capital and output change over time (The beginning is filled in as a demonstration).

Continue this table up to year 8.
Year
Capital
Output (y=k1/2) Investment(γy) Depreciation(δk)
Change in
Capital Stock
1
16
4
1
0.8
0.2
2
16.2

c) Calculate the growth rate of output between 1 and 2
d) Calculate the growth rate of output between 7 and 8
e) Comparing your answers from parts c and d, what can you conclude about the speed of output growth as a country approaches its steady state?
5) In a country, output is produced with labor and physical capital. The production function in per-worker terms is y = k1/2. The depreciation rate is 2%. The investment rate (γ) is determined as follows:
γ = 0.20 if y≤ 10
γ = 0.40 if y >10
Draw a diagram showing the steady state(s) of this model. Calculate the values of any steady state levels of k and y. Also, indicate on the diagram and describe briefly in words how the levels of y and k behave outside the steady state. Comment briefly on the stability of the steady state(s)

6) Suppose that there are two countries, X and Y, that differ in both their rates of investment and their population growth rates. In Country X, investment is 20% of GDP and the population grows at 0% per year. In country Y, investment is 5% of GDP, and the population grows at 4% per year. The two countries have the same levels of productivity, A. In both countries, the rate of depreciation, δ, is 5%. Use the Solow model to calculate the ratio of their steady-state
levels of income per capita, assuming that α = 1/3.

7) Consider the Solow model with population growth, as presented in the text. Assume that population can grow at two different rates n1 and n2, where n1 > n2. The population growth rate depends on the level of output per capita (and therefore the level of capital per capita). Specifically, population grows to rate n1 when k< k and slows down to rate n2 when k≥k. Draw a diagram for this model. Assume that (n 1 + δ) k > γf(k) and that (n2 + δ) k < γf(k).
Explain what the diagram says about the steady state of the model.

8) Suppose that two countries, A and B, have the same rates of investment and depreciation, the same levels of productivity, and the same levels of output per worker. They differ, however, in their rates of population growth. The growth rate of population in Country A is greater than in Country B. According to the Solow model, which country should have a higher growth rate of output per worker? Explain your answer.

9) a) Why and how might education have externality effects?
b) In our discussion of education and wages, we assumed that education raises a worker’s wage by increasing the amount of output he or she can produce. Suppose that we instead believe that more-educated workers earn higher wages for reasons that have nothing to do with their productivity. For example, suppose that educated and uneducated workers both produce the same amount of output, but that educated workers earn more because they can steal part of what the uneducated produce. If this were true, how would it affect the analysis of education differences among countries?

10) Countries A and B have the same rates of investment, population growth, and depreciation. They also have the same levels of income per capita. Country A has a higher rate of growth than does Country B. According to the Solow model, which country has higher investment in human capital? Explain your answer.