This Malthusian model has the property that any improvement in the technology for producing goods
leads to increased population growth, so that in the long run there is no improvement in the standard of
living. The population is sufficiently high that there is no increase in per capita consumption and per
capita output. Consistent with the conclusions of Malthus, the model predicts that the only means for
improving the standard of living is population control.
Next, we study the Solow growth model, which is the most widely used model of economic growth,
developed by Robert Solow in the 1950s.4 The Solow growth model makes important predictions
concerning the effects of savings rates, population growth, and changes in total factor productivity on a
nation’s standard of living and growth rate of GDP. We show that these predictions match economic data
quite well. A key implication of the Solow growth model is that a country’s standard of living cannot
continue to improve in the long run in the absence of continuing increases in total factor productivity.
economic growth facts
1. Before the Industrial Revolution in about 1800, standards of living differed little over time and
across countries.
2. Since the Industrial Revolution, per capita income growth has been sustained in the richest
3.
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countries. In the United States, average annual growth in per capita income has been about 2%
since 1900.
There is a positive correlation between the rate of investment and output per worker across
countries.
There is a negative correlation between the population growth rate and output per worker
across countries.
. Differences in per capita incomes increased dramatically among countries of the world
between 1800 and 1950, with the gap widening between the countries of Western Europe, the
United States, Canada, Australia, and New Zealand, as a group, and the rest of the world.
There is essentially no correlation across countries between the level of output per capita in
1960 and the average rate of growth in output per capita for the years 1960–2007
Richer countries are much more alike in terms of rates of growth of real per capita income than
are poor countries.
The malthus theory
Malthus argued that any advances in the technology for producing food would inevitably lead to further
population growth, with the higher population ultimately reducing the average person to the subsistence
level of consumption they had before the advance in technology. The population and level of aggregate
consumption could grow over time, but in the long run there would be no increase in the standard of
living unless there were some limits on population growth. Malthusian theory is, therefore, very
pessimistic about the prospects for increases in the standard of living, with collective intervention in the
form of forced family planning required to bring about gains in per capita income.
The following model formalizes Malthusian theory.
We start with an aggregate production function that specifies how current aggregate output, Y, is
produced using current inputs of land, L, and current labor, N; that is, Y = zF(L, N), let y be the food If we
let N′ denote the population next period, then N′ = N + Births - Deaths, or N′ = N + N(birth rate - death
rate),
Now, particularly before the Industrial Revolution, it is natural that the birth rate would be an increasing
function of consumption per capita, C N , which is a measure of nutrition, with C denoting aggregate
consumption. As consumption per person rises, and nutrition improves, people will have more children
by choice, as they are then better able to provide for them, and better nutrition also increases fertility.
Similarly, the death rate is a decreasing function of C N , because better nutrition decreases infant
mortality, and generally makes the population more healthy, thus increasing the average life span. This
implies that we can write Equation (7-2) (after dividing both sides by N) as N′ N = g a C N b,