Countries X and Y differ in population growth rates and rates of investment.

Country X: investment is 10% of GDP, population grows at 1% per year

Country Y: investment is 25% of GDP, population grows at 3% per year.

Both countries have the same rate of depreciation (5%). Use the Solow model to calculate the ratio oftheir steady state levels of income per capita, assuming α =1/2. Interpret your answer.

2. In Country 1 the rate of investment is 2%, and in Country 2 it is 12%. The two countries have thesame rate of depreciation, and there is no growth in its labor force. Assuming that the value of is 1/3,what is the ratio of steady-state output per worker in Country 1 to steady-state output per worker inCountry 2? What would the ratio be if the value of were 2/3? Explain the change in your answer. 3.

Average Annual Growth Rates of Population by Country Group

1950-2000 2000-2050

More Developed 0.8%

0.0%

Less Developed 2.1%

0.8%

Least Developed 2.4%

2.1%

Using the data from the above table (Weil, 3rd edition, Table 5.2, page 136) where the only change is in

the growth rate of population between the two time periods. Assume that rate of depreciation =5% and α

=1/2. Use the Solow model to calculate how much the change in population growth between the period1950-2000 and 2000-2050 would affect the steady state level of output per worker fora) the most developed countries compared to the least developed countries. Verbally, interpret your

answers.b) Suppose that in the least developed group of countries, between the two above time periods, thesavings rate increases from 1% to 2% how would your answer for the least developed countrieschange. Graphically illustrate your answer being careful to label your graph.

4. Consider the Solow model with population growth, as presented in class and in the Weil text. Thereare two countries 1 and 2 are the same in every respect except that population grows at n1 in country 1and n2 in country 2 and n1 > n2. Assume that the population growth rate depends on the level ofoutput per capita (and therefore the level of capital per capita) and is given by

ℎ = {

1, < ∗2, ≥ ∗

(k* represents some hypothetical level of capital per worker and not the steady state).Draw a diagram for this model. Assume that at (n1 + δ)k*> sy and that (n2 + δ)k*< sy. Explain what thediagram says about the steady states of the model.

[HINT: the phenomenon described in this question is similar to the situation of what happens to the steadystate when we assume that savings rate depends on income – endogenous savings rate on page 71-74 andFigure 3.9 in Weil. In this question, instead of savings, population growth depends on income andtherefore capital per worker.]

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