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EC441 – In the long run, output per person

Question
EC441: Problem Set 5
Multiple-choice questions
The next four questions concern the Malthusian model. Suppose that the productivity of land
increases so for a given level of labor, output increases. Answer the following questions about the
effect on the economy relative to the initial (pre-change) steady state:

1. In the long run, output per person will be
A) Greater
B) Lower
C) No change
D) Ambiguous

2. In the long run, population will be
A) Greater
B) Lower
C) No change
D) Ambiguous

3. In the long run, total (aggregate) output will be
A) Greater
B) Lower
C) No change
D) Ambiguous

4. In the long run, the death rate (at the new steady state) will be
A) Greater
B) Lower
C) No change
D) Ambiguous
5. Suppose that in the Solow model the long run capital per capita is 5. Suppose that the current
capital per capita is 2. Then current savings
A) Equals depreciation plus population growth
B) Is greater than depreciation plus population growth
C) Is greater than depreciation plus population growth
1 D) Cannot say with numbers provided

6. Suppose that the world is a collection of countries each following the Solow model with the
same fundamentals (production function, population growth, depreciation), but different levels
of capital per worker. Which of the following should happen:
A) The poor countries should grow faster than the rich
B) The rich countries should grow faster than the poor
C) All countries grow at the same rate
D) There is no growth in any country

The next four questions concern the Solow model. Suppose the government discourages savings
by taxing capital and using the money to subsidize consumption. Think of this as a decline in
the savings rate. Answer the following questions about the effect on the economy relative to the
initial (pre-change) steady state:

7. In the long run, output per person will be
A) Greater
B) Lower
C) No change
D) Ambiguous (cannot sign the change for certain)

8. Compared to the original steady state, consumption per person in the new long-run steady state
will be
A) Greater
B) Lower
C) No change
D) Ambiguous (cannot sign the change for certain)

9. Along the transition to the new steady state, output per person will be:
A) Increasing
B) Decreasing
C) Constant
D) Ambiguous (cannot sign the change for certain)

10. In the new long-run steady state, the growth rate of output per capita compared to the original
steady state will be:
A) Greater
B) Lower
C) No change
D) Ambiguous (cannot sign the change for certain) 2 Short-answer questions

1. Consider the effect of giving aid to a developing economy. Let a be the amount of aid per person
given each year. “Total income available” for a country in per capita terms is then y + a, where y
is the amount of domestic output per capita. Start each economy from a steady state.
(a) Describe what happens in a Malthusian economy. In particular, assume that what determines
mortality and fertility is total income available. Describe what happens in the new steady
state to (a) per capita output produced, (b) per capita consumption (which is equal to per
capita total income available, as there is no saving in this model), and (c) population.

(b) Describe what happens in a Solow economy. In particular, assume that savings is an s
fraction of total income available (s is the saving rate). Describe what happens in the new
steady state to (a) per capita output produced, (b) per capita consumption, and (c) capital
per capita.

(c) Drawing on your answers from above, do you think that aid will help the poorest countries grow faster? Give some intuition of why growth may have different effects given the
underlying nature of the economy. 3

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