Review Questions
1.  What explains the longrun growth
of aggregate GDP?

Growth of labor, capital, and
technology.


2.  Is it possible for an economy to
continue growing forever solely by accumulating more capital?

No.  
3.  How does an increase in the saving
rate affect economic growth?

A higher saving rate does not
permanently affect the growth rate in the Solow model. A higher saving rate does
result in a higher steadystate capital stock and a higher level of output.
The shift from a lower to a higher steadystate level of output causes a temporary
increase in the growth rate. In some newer theories of growth, a higher saving rate
may permanently raise the rate of economic growth. These newer theories have not
been subjected to rigorous empirical testing, however.


4.  How does an increase in the
population growth rate affect economic growth?

In the Solow model, an increase in
the population growth rate raises the growth rate of aggregate output but has no permanent
effect on the growth rate of per capita output. An increase in the population growth
rate lowers the steadystate level of per capita output.


5.  What explains the longrun growth of per capita GDP?  Technical progress, which in turn
stimulates growth of the capital stock.


6.  Why do countries like the United
States, Germany, and Japan all seem to be converging to the same level of per capita GDP?

They have similar technologies and are converging to similar percapita stocks of capital.  
7.  Why don’t all countries converge to the same level of per capita GDP as the United States, Germany, and Japan?  Some countries seem to have
different levels of technology (interpreted broadly to include factors like political
stability, the legal system, the security of property rights, the ability to enforce
contracts, etc.).


8.  How does an increase in the tax rate on income from capital affect economic growth?  In the Solow model, the capital income tax rate has no permanent effect on the growth rate of output. An increase in the capital income tax rate lowers the saving rate, however. The effects of a change in the saving rate are discussed in question 3 above. 
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Answers to Selected Textbook Problems
Mankiw, Macroeconomics, fourth edition, chapter 4, problems and applications
6.  The longrun effect will be a lower growth rate of aggregate output, a higher level of per capita output, and no change in the growth rate of per capita output. 
Mankiw, Macroeconomics, fourth edition, chapter 5, problems and
applications
4.  a.  The two countries have the same growth rate of aggregate output (which is determined by the population growth rate and the rate of technological progress). 
b. 
The country with the higher education level has higher income per worker, because each worker embodies more effective labor units.  
c. 
The two countries have the same technology, saving rate, and population growth rate, so they will converge to the same ratio of capital per effective unit of labor, implying that the have the same rental rate of capital.  
d. 
By the reasoning in part (c), the two countries will have the same wage rate per effective labor unit. The country with the higher education will have a higher wage rate per worker because each worker embodies more effective labor units. 
Mankiw, Macroeconomics, fourth edition, chapter 5,
appendix, more problems and applications
1. 
a. 
In the initial year after men start working, output goes up by 1/3 of 5 percent, or 1.67 percent. The percentage change in output per worker is the percentage change in output (1.67) minus the percentage change in workers (5), so output drops by 3.33 percent. Total factor productivity is unchanged. 
b.  Total factor productivity falls from 2.52 to 2.41.  
3.

Remember that the text interprets the rate of technical progress to mean the growth rate of output per worker, not the growth rate of total factor productivity. Using the notation Dln to denote the growth rate, the growth accounting equation is 

DlnY = DlnA + 0.3DlnK + 0.7DlnL.  
Substituting the numbers given in the problem gives  
0.03 = DlnA + 0.3*0.03 + 0.7*0.01 = DlnA + 0.009 + 0.007,  
implying that the growth rate of TFP is 0.014. 