Chapter 4: Working With The Solow Growth
Model
Chapter Summary:
Chapter 3 introduced the basic neoclassical model of economic growth
and its major results: growth rates tend to diminish over time as the economy
diagram are shifted to illustrate the effects of changing parameter values on the
steady state level of capital.
The concept of absolute convergence is examined next. Since the rate of
capital accumulation per worker is essentially determined by the current stock of
capital per worker, lesser developed countries are predicted by the model to
grow more quickly than developed countries. However, the capital per worker
Outline:
I. Working With The Solow Model
A. A Change in the Savings Rate
B. A Change in the Technology Level
II. Convergence
A. Absolute Convergence
13
III. Appendix: The Speed of Convergence
Teaching Tips:
1. If the students are familiar by this point with the equation for growth in the
capital stock (equation 3.16) and the diagram which illustrates it, the diagrams
2. In many countries in Europe, birthrates have fallen below the replacement
rate, as seen in the data below. The Solow model suggests that this should
generate increasing productivity and a higher steady state level of income.
However, the low birthrates have instead caused public concern and even
Here are some statistics for European fertility rates (2.1 children per woman is
the replacement rate):
Ireland: 1.99
France: 1.90
3. The section on Malthus (Extending the Model, pg. 79) provides fascinating
reading, but it would be a mistake to understand it as a historical argument long
4. Is it right to consider people just another mouth to feed? The late economist
5. The Solow model presented here is used to conduct positive economic
analysis – this causes that. But there are important public policy issues
another.
Answers to Review Questions (pg. 90):
1: Recall that the saving curve in figure 4.4 depends on the average product of
capital per worker: y/k, and that y depends only on output per worker, not the
absolute level of labor or capital (see equation 3.2 on page 49). Therefore, the
2. An increase in n will increase the rate at which capital per worker is depleted
over time. This is illustrated on the graph by an upward shift in the horizontal
3. Convergence, as used in the theory of economic growth, refers to the tendency
of less developed economies to grow more quickly than more mature economies.
The theory is based on the idea that the growth rate will slow as an economy
4. The Solow model does not predict that all countries must reach the same
steady state. If it did, then the results in figure. 4.9 would be problematic. As it
Answers to Problems for Discussion (pg. 90)
5. a. Yes, the growth rate in capital at any given period will depend on the
savings rate in that period. However, the idea that the economy approaches
a steady state level of per-capita income cannot be assumed.
b. A pattern of rising savings rates would offset to some extent the effects of
diminishing returns and depreciation on capital accumulation. The increase
16
6. a. It is valid for each period, however, the idea that the economy approaches
a steady state level of per-capita income cannot be assumed.
b. A pattern of falling population growth would offset to some extent the
effects of diminishing returns and depreciation on capital accumulation.
The increase in the rate of capital accumulation could cause the growth rate
d. Malthus predicted that population growth rates would increase as a
function of income per worker, because it was excess population in his
model which caused population growth to cease; in his view, it was
mortality rates associated with poverty. That poverty was the result of
diminishing returns to agricultural land, which could not be accumulated