Economics 101
Homework 3
Chapters 7 & 8
1) Consider an economy with no population growth or technological change with the following production function: Y = F(K,L) = K1/2L1/2.
a) What is the per worker production function Y/L = f(Y/L)?
b) Assume that K = 40,000 and L = 10,000. What is Y? What is labor productivity computed from the per-worker production function? Is this value the same as labor productivity computed from the original production function?
c) Assume that 10 percent of capital depreciates each year. What gross saving rate is necessary to make the given capital-labor ratio the steady state capital-labor ratio?
d) If the saving rate equals the steady-state level, what is the consumption per worker?
2) Suppose that two countries are exactly alike in every respect except that the citizens of country A have a higher saving rate then the citizens of country B.
a) Which country will have the higher level of output per worker in the steady state? Illustrate graphically.
b) Which country will have the faster rate of growth of output per worker in the steady state?
3) China’s real per-person GDP growth rate (percent change in output) has been much greater than that in the U.S. in the last decade. For example, China grew about 8% last year, compared to about 5% for the U.S.
a) Using the Solow growth model, is there reason to believe this disparity in growth rates will disappear in time? What about the disparity in income levels per capita?
b) How is your conclusion affected if you were told that China has a higher saving rate than the U.S.?
c) What if the saving rates are the same, but China has a higher population growth rate?
d) How would your conclusion in (a) change if you considered labor-augmenting technological progress in the Solow model, where the rate of technological progress was the same in both countries?
e) How would your conclusion in (a) change if you considered an “endogenous growth” model, using the production function Y = AK?
4) According to the Solow model, how would each of the following affect the level of output per worker in the long run (that is, in the steady state)? Explain.
a. The destruction of a portion of the nation’s capital stock in a war.
b. A permanent increase in the rate of immigration (which raises the overall population growth rate).
c. A rise in energy prices.
d. A temporary increase in the saving rate.
e. A permanent increase in the fraction of the population in the labor force (the population growth rate is unchanged).
5) An economy is in a steady sate with no productivity change. Because of an increase in acid rain, the rate of capital depreciation rises permanently.
a. According to the Solow model, what are the effects on steady-state capital per worker, output per worker, consumption per worker, and the long-run growth rate of the total capital stock?
b. In an endogenous growth model, what are the effects on the growth rates of output, capital, and consumption of an increase in the depreciation rate of capital?
6) True-False:
Say if the following statements are True or False. If they are false write the correct statement
a) The standard of living in a country improves if and only if its total income Y grows at a positive rate.
b) Since the 1950 all poor countries in the world have experienced a “convergence” of their GDP per capita to the level of GDP per capita of rich countries.
c) In an economy with no technological progress and no population growth, income per capita remains constant when the saving rate increases.
d) Saving rate has no effect of the transitory (before reaching steady-state) growth rate of output per worker.
e) In a Solow growth model with no technological change, the long run growth rate of output per worker is zero because of the law of diminishing marginal productivity of capital.
f) Convergence hypothesis states that poor countries will eventually catch up with rich countries in output per capita.
g) The evidence support convergence on all countries.
h) Convergence is the result of capital accumulation.
7) Do poor countries generally grow more or less rapidly than affluent ones? Do small countries generally grow more or less rapidly than large ones? Does economic growth theory suggest answers to these questions? What is the empirical evidence?
8) The prime minister asks you to draw up a list of policy measures designed to stimulate economic growth. Does it matter much whether the country in question is Jamaica, Japan, or Jordan? If so, how? What information about the country in question do you request before you offer your advice?
9) Suppose the government decides to lower taxes. What other information do you need in order to be able to determine whether the tax cut is likely to stimulate economic growth or not?
10) How does increased depreciation of capital resulting from low-quality investment in the past reduce economic growth? How is that different from a increased physical depreciation due?
Handout #1
This is useful for answering some of the questions in HW3
1- A Broader Look Across Time and Space
Looking across two millennia
• From the end of the Roman Empire to 1500,
no output per capita growth in Europe
• 1500-1700 -- Small growth in output per capita
(0.1%/year and 0.2%/year 1700 to 1820)
• 1820-1950 -- Modest growth (U.S. = 1.5%)
• The high-growth of the 1950s and 1960s is unusual
• 1st Millennium to the 15th century, China had the highest output/capita
• Leaders in output/capita change frequently: Italy, Netherlands, U.K., U.S.
2- Some empirical Observations
• Strong growth 1950-1998
• Growth rates among OECD countries have decreased since the mid 1970s
1950-1978 4.4% (GDP/capita doubles every 16 years)
1973-1998 1.9% (GDP/capita doubles every 37 years)
3- Are output/capita across countries converging?
Looking Across Some Countries
Convergence of Output/Capita in some countries
Looking Across Countries- Convergence Not the Rule
Three Conclusions:
• OECD countries are converging
• Asian countries are converging
• African countries are not converging
4- Capital Accumulation vs. Technological Progress
The Findings
• 1950-1973 high growth of output per capita due
to technological progress
• Since 1973 slowdown in growth of output per
capita due to a decrease in the rate of technological progress
• Convergence is the result of technological progress
There was a worldwide slowdown in economic growth during 1972-1995. Why?
Most developed economies grow at the same rate that the “technological frontier” grows.
Convergence – countries inside of the technological frontier move towards the technological frontier.
Divergence – countries inside of the technological frontier grow at a rate less than the technological frontier.
Some Data: Distribution of World GDP in 2000
From Barro, 2003 – includes 147 countries. Horizontal axis is a log scale.
All data are in 1995 U.S. dollars.
Growth Rate of GDP Per Capita: 1960 - 2000
From Barro, 2003 – includes 111 countries.
Convergence of Income Across U.S. States: 1940 - 1980
Convergence of Income Across U.S. States: 1980 - 2000