University of California Intermediate Quantitative Economics Questions 1. U.S. and Chinese GDP Growth in the Long Run. China is a country with a very high

University of California Intermediate Quantitative Economics Questions 1. U.S. and Chinese GDP Growth in the Long Run. China is a country with a very high savings rate s, about 40%. The U.S. has a much lower savings rate, closer to 15%. (There are many reasons for this difference.) For this question, assume that the population growth rate n, technology growth rate g, depreciation rate δ, and production function f(k) in China are the same as in the U.S.

a) According to the full Solow growth model (with technology growth), what does this higher savings rate imply about the steady state of China’s output per effective worker relative to the U.S.? Draw a diagram to help illustrate your answer.
b) China’s GDP/person has been growing at about 8.2%/year for the past 25 years, while GDP/person in the U.S. has been growing closer to 2%/year. According to the full Solow growth model (with technology growth), how will the growth rate of China’s GDP/person compare to that of the U.S. once these two economies reach their steady states?
c) According to your analysis in part b, can China’s GDP/person continue to grow at its historical average rate of 8.2%/yr. for the indefinite future, while the U.S.’s steady-state growth rate of GDP/person is around 2%/yr.?
Solow Growth Model and Convergence. Mexico and Guatemala are two neighboring countries in North/Central America. Given that they have similar geographic locations and access to the same technologies, let’s assume that their technology growth rate g, depreciation rate δ, and production function f(k) are the same.
a) A major difference between Mexico and Guatemala is that the national savings rates s in the two countries are different: in Mexico, the savings rate is about 22 percent, while in Guatemala it is lower, only about 5 percent. According to the Solow growth model (with technology growth and population growth), which country should have a higher standard of living in the long run, Mexico or Guatemala? (Assume that these savings rates are constant over time and that the population growth rates in the two countries are the same.) Draw a diagram to help illustrate your answer.
b) Contrary to what we assumed in part a, above, the population growth rate in Guatemala is actually higher than in Mexico: about 2.2%/yr in Guatemala vs. 1.6%/yr. in Mexico. Suppose that the savings rates s in the two countries is equal. According to the Solow growth model (with technology growth and population growth), which country should have a higher standard of living in the long run in this case? Draw a diagram to help explain your answer.
c) Suppose that the U.S. has the same savings rate and population growth rate as Mexico in the long run (and also the same g, δ, and f(k)). The standards of living in Mexico and Guatemala are currently lower than in the U.S. Should we expect the standards of living in Mexico and in Guatemala to converge to that of the U.S. in the long run? Briefly explain why or why not.
Production Functions and Convergence. Sweden and Norway are two neighboring countries in Northern Europe with similar savings rates, population growth rates, technology growth rates, and depreciation rates. However, Norway differs from Sweden in that Norway has large

deposits of oil all along its coast, which makes it very easy for Norway to produce large quantities of crude oil every year with relatively little capital and labor.

a) Draw a Solow Growth diagram that compares Sweden and Norway. What is the maindifference between the two countries in the diagram?
b) According to the Solow Growth Model, which country would have a higher standard ofliving in the long run? Which country would have a higher growth rate of its standard ofliving in the long run?
c) Suppose now that, in the long run, oil becomes obsolete and has no value because it isuneconomical relative to renewable energy sources like solar and wind power. What would this do to your Solow Growth diagram in part a? How would the standard of living in Norway and Sweden compare in the long run in that case? Econ 105C: Problem Set 8
due in Gradescope on Tuesday, June 2, 11am (California Time)
1. U.S. and Chinese GDP Growth in the Long Run. China is a country with a very high savings
rate s, about 40%. The U.S. has a much lower savings rate, closer to 15%. (There are many
reasons for this difference.) For this question, assume that the population growth rate n,
technology growth rate g, depreciation rate δ, and production function f(k) in China are the same
as in the U.S.
a) According to the full Solow growth model (with technology growth), what does this higher
savings rate imply about the steady state of China’s output per effective worker relative to
the U.S.? Draw a diagram to help illustrate your answer.
b) China’s GDP/person has been growing at about 8.2%/year for the past 25 years, while
GDP/person in the U.S. has been growing closer to 2%/year. According to the full Solow
growth model (with technology growth), how will the growth rate of China’s GDP/person
compare to that of the U.S. once these two economies reach their steady states?
c) According to your analysis in part b, can China’s GDP/person continue to grow at its
historical average rate of 8.2%/yr. for the indefinite future, while the U.S.’s steady-state
growth rate of GDP/person is around 2%/yr.?
2. Solow Growth Model and Convergence. Mexico and Guatemala are two neighboring
countries in North/Central America. Given that they have similar geographic locations and
access to the same technologies, let’s assume that their technology growth rate g, depreciation
rate δ, and production function f(k) are the same.
a) A major difference between Mexico and Guatemala is that the national savings rates s in
the two countries are different: in Mexico, the savings rate is about 22 percent, while in
Guatemala it is lower, only about 5 percent. According to the Solow growth model (with
technology growth and population growth), which country should have a higher standard of
living in the long run, Mexico or Guatemala? (Assume that these savings rates are constant
over time and that the population growth rates in the two countries are the same.) Draw a
diagram to help illustrate your answer.
b) Contrary to what we assumed in part a, above, the population growth rate in Guatemala is
actually higher than in Mexico: about 2.2%/yr in Guatemala vs. 1.6%/yr. in Mexico.
Suppose that the savings rates s in the two countries is equal. According to the Solow
growth model (with technology growth and population growth), which country should have
a higher standard of living in the long run in this case? Draw a diagram to help explain
your answer.
c) Suppose that the U.S. has the same savings rate and population growth rate as Mexico in
the long run (and also the same g, δ, and f(k)). The standards of living in Mexico and
Guatemala are currently lower than in the U.S. Should we expect the standards of living in
Mexico and in Guatemala to converge to that of the U.S. in the long run? Briefly explain
why or why not.
3. Production Functions and Convergence. Sweden and Norway are two neighboring countries
in Northern Europe with similar savings rates, population growth rates, technology growth
rates, and depreciation rates. However, Norway differs from Sweden in that Norway has large
deposits of oil all along its coast, which makes it very easy for Norway to produce large
quantities of crude oil every year with relatively little capital and labor.
a) Draw a Solow Growth diagram that compares Sweden and Norway. What is the main
difference between the two countries in the diagram?
b) According to the Solow Growth Model, which country would have a higher standard of
living in the long run? Which country would have a higher growth rate of its standard of
living in the long run?
c) Suppose now that, in the long run, oil becomes obsolete and has no value because it is
uneconomical relative to renewable energy sources like solar and wind power. What would
this do to your Solow Growth diagram in part a? How would the standard of living in
Norway and Sweden compare in the long run in that case?

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