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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
Historical Trends in Convergence
Unadjusted 1940-1960
1
MS
.8
ARAL
ND
SD
OK
KY
NC
GA NM
TN
LA
SC
KS
NE
TX
.6
WV
UT MOCO
MNWI
ID
AZ
VA IA
IN
WY
FL
NHOR
VT MT
ME
WA
OH
PA MI
IL
.4
MD
CA
NV
MA NJ NY
CT
RI
.2
DE
2000
4000
6000
8000
Per Capita Income 1940
Fitted values
10000
gr_ipc_40_60
12000
Convergence of Income Across U.S. States: 1980 - 2000
Recent Trends in Convergence
Unadjusted 1980-2000
.5
MA
NH
CT
NC GA
NJ
.4
VT
SCNDSD TN
ME
AL
KY
MS
MO
IN
.3
AR
UTID
WV
.2
RI
NE
NM
IA
AZ
MN
VA
PA
FL
TX
MI
WI
OH
KS
OR
NY
CO
WAIL
DE
CA
LA
MT
MD
NV
OK
.1
WY
15000
20000
Per Capita Income 1980
Fitted values
gr_ipc_80_00
25000