Problem Set 1
Dynamic Macroeconomics
Economics Degree
1. Consider two economies where their production functions, the initial efficiency levels (A0), the rate of
technical progress (g) and depreciation rates ()are identical. Additionally, their saving rates (s) and
population growth rates (n) are:
sa=sb; na=nb:
a. Obtain the key accumulation equation of the Solow model.
b. If the two economies are on their balanced growth path, which is the rate of growth of per capita
income in both economies? And the rate of growth of income in efficiency units?
c. Now assume that
sa> sb; na=nb:
Which is the rate of growth of per capita income in both economies? And the rate of growth of
income in efficiency units? Which economy will show a higher per capita income? And a higher level
of income in efficiency levels?
d. Explain how are your answers affected in the case
sa> sb; na> nb:
2. Assume that the long-run performance of Spain and Germany could be explained by the Solow model.
Assume that population growth rates, depreciation rates, exogenous rates of technical progress and
production functions were the same in both countries.
a. Compare analytically and graphically the steady-state level of output in efficiency units in both
countries if sE< sG:
b. Now assume that Germany is on its balanced growth path whereas Spain is below its steady state in
period t. Which are the convergence perspectives of the Spanish economy? What are the differences
between absolute and conditional convergence?
c. Show graphically the time profile of the rate of growth of income in efficiency levels for both
economies from tonwards.
d. Show graphically the time profile of the log of per capita income for both economies from tonwards.
3. Discuss if the following assertion is true or false: in the Solow model the variation of the saving rate
does not affect per capita income because this variable is fully determined by the efficiency level of the
economy.
4. According to Kaldor stylized facts Y=L shows a positive rate of growth over the long run whereas Y=K
has been relatively constant. Which fact can be derived from this evidence? What are the additional facts
needed to conclude that the rate of return of capital has been steady over the long run?
5. The empirical evidence shows that many poor countries had lower rates of growth than advanced
economies, therefore rejecting the convergence implications of the Solow model. Discuss if the preceding
assertion is true or false.
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