Economics Assignment-Intermediate Macroeconomic Theory

Economics Assignment-Intermediate Macroeconomic Theory

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1. Suppose you have a production function of the form � = ��%�'.
a. Suppose a = 0.25 and b = 0.5. Demonstrate whether the function is a constant returns to scale
production function. If not, what type is it? Demonstrate or explain.
b. Suppose a = 0.75 and b = 0.5. Demonstrate whether the function is a constant returns to scale
production function. If not, what type is it? Demonstrate or explain.
2. Suppose you have two economies. In each, A = 1, k = 1, d = 0.05, and s = 0.1. In the first, a = 0.25 while in the
second a = 0.5. Show the growth outcomes for each of the next 3 periods. What is the steady state level of
output for each?
3. Suppose you have a production function of the form � = ��%�'.
a. Suppose a = 0.25 and b = 0.75. If A = 1, what is the per capita production function? Derive.
b. Suppose a = 0.5 and b = 0.5. If A = 10, what is the per capital production function? Derive.
4. Suppose disaster hit an economy such that its capital stock per worker fell by 10%. What is the implication of
this negative shock for the short-run growth of the economy? What is the implication of this negative shock for
the steady state level of output for the economy?
5. In 1979, China began the implementation of the one-child policy. Using the Solow model, explain the logic of
slowing population growth as a tool to increase the rate of growth. What is likely missing from this conclusion?
Explain.
6. Sometimes politicians suggest tax reductions on savings as a method for increasing the rate of growth. Using
the logic of the Solow model, explain how such a tax system change could encourage growth.
7. Suppose you have an economy characterized by y = 3k
0.5, s = 30%, d = 10%, and n = 5%.
a. What is the steady state level of consumption?
b. How would consumption change at the steady state if the savings rate increased from 30% to 40%?
c. Using the initial values (s = 30%), what is the steady state level of consumption if population growth
increases to 8%?
8. Using data, explore the idea of “convergence” using the United States, Japan, and China as representative
countries. How robust does the idea appear to be? Data on GDP and growth for these countries may be found
at http://databank.worldbank.org/data/home.aspx.