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1. Following the Solow model, how is determined the long-run growth rate of GDP 
per capita? How is determined the long-run growth rate of GDP? (2%)
In the Solow model, the long-run growth rate of GDP per capita is determined by 
the exogenous growth rate of technological progress (or productivity). The 
long-run growth rate of GDP is then determined by the sum of the exogenous growth 
rate of technological progress and the exogenous growth rate of population.

2. Following the Solow model, how is determined the growth rate of GDP per capita 
in the transition? Explain the difference with respect to the first question. (3%)
In the Solow model, the growth rate of GDP per capita in the transition is determined 
by the sum of the exogenous growth rate of technological progress and the 
transitional growth rate of capital per capita. Because of constant returns to 
scale, the transitional growth rate of capital converges to 0 in the long run 
and the exogenous growth rate of technological progress remains the sole support 
of long-run growth.

3. Is there any convergence of growth between some countries over the last 70 
years? If yes, what are these countries? How this could be explained by the Solow model? (3%)
Over the last 70 years, we observe some convergence between OECD countries: 
  they all converge towards the most developed country, the US. In the Solow model, 
  this can be explained by the Absolute Convergence property: the transitional 
  growth rate of GDP per capita is a decreasing function of the initial level 
  of capital. As a result, the poorer the country with respect to the US, 
  the larger its growth rate. This property relies on the fact that OECD 
  countries are all characterized by the same structural parameters.

4. Is there any form of non-convergence between some countries over the 
last 70 years? If yes, what are these countries? How this could be explained 
by the Solow model? (4%)
Over the last 70 years, we do not observe any convergence between poor 
(African, South American) countries and rich (OECD) countries. We may even 
observe some cases of divergence. In the Solow model, this can be explained by 
the Conditional Convergence property: considering that poor countries are not 
characterized by the same structural parameters as rich countries, the two sets 
of countries do not converge towards the same long-run level of development 
and we can find cases where a poor country is characterized by a lower growth 
rate than a rich country.

5. What are the main three critics of the Solow model? (1.5%)
The three critics are the following:

The saving rate is constant.
The population that is considered is only the working population. Kids and 
retired people are not considered.
The growth rate of technological progress, which provides the only explanation 
of long-run growth of GDP per capita, is exogenous.
6. Is the Solow model able to properly evaluate the speed of convergence 
between countries? How could it be modified to be improved? (3%)
Considering empirically relevant values for the structural parameters, 
the Solow model leads to a too large speed of convergence and thus a 
too small half-life of convergence. This is due to the too low value 
of the share of capital income within GDP. The model could be improved 
considering a second type of capital: human capital. In this case, the 
total share of capital income in GDP (both physical and human) is larger 
and the speed of convergence can be decreased.

7. What is the structure of population in the overlapping generations model? (3%)
In the overlapping generations model, we consider that each individual is living 
two periods: a first one where he is young, works, and receives a wage 
to consume and save, and a second one where he is old and consumes on the basis 
of the proceedings of his savings. Then at each period, young and active 
individuals coexist with old and retired individuals.

8. How is savings endogenized in the overlapping generations model? (3%)
In the overlapping generations model, savings is endogenized considering that 
each individual maximizes his utility function over his life cycle subject to 
the budget constraints when young and old. Depending on the evolution of wages,
the splitting between consumption and savings is adjusted every period.

9. What is the Golden Rule? (2%)
The Golden Rule is the level of the stock of capital per capita that maximizes 
the total stationary (long-run) level of consumption (the sum of young and 
old consumption living at the same period).

10. What is the difference between over-accumulation and under-accumulation of 
capital? (3%)
Over-accumulation is the case where the long-run value of the stock of capital 
per capita in the overlapping generations model is larger than the capital stock 
of the Golden Rule. Under-accumulation is the case where the long-run value 
of the stock of capital per capita in the overlapping generations model is lower 
than the capital stock of the Golden Rule.

11. What are the optimality properties of the two cases of over-accumulation 
and under-accumulation of capital? (4%)
The case of under-accumulation is obtained as over 
time generations do not save enough and the accumulation of capital is not 
large enough. The only possibility to be closer to the Golden Rule would be to 
force at least one generation to save more, i.e. to consume less, but this 
would decrease its level of utility (welfare). This case is therefore Pareto 
optimal.

On the contrary, the case of over-accumulation is obtained as over time 
generations save a too large amount and the accumulation of capital is therefore 
too large. The only possibility to be closer to the Golden Rule would be to 
force at least one generation to save less, i.e. to consume more, and this 
implies a larger utility. This case is therefore not Pareto optimal: it is 
possible to improve the welfare of every generation without any negative impact.

12. In the case of non-optimality, what kind of policy could restore optimality? Explain. (3%)
In the case of over-accumulation, a pay-as-you-go pension system could restore 
the optimality as it is possible to define an amount of taxes on each generation 
that generate lower savings and thus a lower accumulation of capital.

13. What is the structure of a pay-as-you-go pension system? (3%)
The pay-as-you-go pension system is based on the fact that at each period young 
and working individuals are taxed on their wage income in order to finance at the 
same period the pensions of old and retired individuals. It then generates a 
transfer between generations.