Practice Problems: Malthus and Solow
Econ 302 - Spring 2015
Questions for Review
1. What is the effect of an increase in total factor productivity on steady state population and consumption
per worker in the Malthusian model?
2. What can increase the standard of living in the Malthusian model?
3. Was Malthus right? Why or why not?
4. In the Solow growth model, what are the steady state effects of an increase in the savings rate, of an
increase in the population growth rate, and of an increase in total factor productivity?
5. In what sense does the Solow growth model give optimistic conclusions about the prospects for improvement in the standard of living, relative to the Malthusian model?
Problem 1
(from Williamson, Chapter 7, Problem 2)
In the Malthusian model, suppose that there is a technological advance that reduces death rates. Using
diagrams, determine the effects of this in the long-run steady state and explain your results.
Problem 2
This problem uses the Solow model to analyze the effects of immigration. Suppose that the economy is
initially in the steady state.
1. Suppose that there is a one-time increase in the labor force from immigration, but n (the population
growth rate) remains constant. Analyze the short-run and long-run effects of this change for the levels
of per-capita output, and the growth rates of output per-capita.
2. Suppose that immigration is a continuing process so that n increases to a higher value ñ > n. Analyze
the short-run and long-run effects of this change for the levels of per-capita output, and the growth
rates of output per-capita.
Problem 3
(from Williamson, Chapter 7, Problem 4)
Suppose that the depreciation rate increases. In the Solow growth model, determine the effects of this on the
quantity of capital per worker and on output per worker in the steady state. Explain the economic intuition
behind your results.
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Problem 4
(from Williamson, Chapter 7, Problem 5)
Suppose that the economy is initially in a steady state and that some of the nation’s capital stock is destroyed
because of a natural disaster or a war.
1. Determine the long-run effects of this on the quantity of capital per worker and on output per worker.
2. In the short run, does aggregate output grow at a rate higher or lower than the growth rate of the
labor force?
3. After World War II, growth in real GDP in Ger- many and Japan was very high. How do your results
in parts 1 and 2 shed light on this historical experience?
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