Malthusian regime: The Dynamical System 6

Over time, the slow growth in population that takes place in the Malthusian regime will raise the rate of technological progress and shift the p(et+i) locus in Figure 4a upward so that it has the configuration shown in Panel B. At this point, the dynamical system of education and technology will be characterized by multiple, history-dependent steady states. One of these steady states will be Malthusian, characterized by constant resources per capita, slow technological progress, and no education

The other will be characterized by a high level of education, rapid technological progress, growing income per capita, and moderate population growth. For the story that we want to tell in this paper, however, the existence of multiple steady states turns out not to be relevant. Since the economy starts out in the Malthusian steady state, it will remain there. If we were to allow for stochastic shocks to education or technological progress, it would be possible for an economy in the Malthusian steady state of panel В to jump to the Modern Growth steady state, but we do not pursue this possibility.

Panel С of figure 4 shows that the increasing size of the population continues to raise the rate of technological progress, reflected in a further upward shift of the g(et) function. At a certain level of population, the steady state vanishes, and the economy transitions out of the Malthusian regime. Increases in the rate of technological progress and the level of education feed back on other until the economy converges to the single, stable steady state shown in the figure.

While the evolution of education and technological progress traced in panel С of Figure 4 are monotonic once the Malthusian steady state has been left behind, the evolution of population growth and the standard of living, which can be seen in Panel С of figure 5, are more complicated. The reason for this complication is that technological progress has two effects on the evolution of population, as shown in proposition one. First, by inducing parents to give their children more education, technological progress will ceteris paribus lower the rate of population growth. But, second, by raising potential income, technological progress will increase the fraction of their time that parents can afford to devote to raising children. Initially, while the economy is in the Malthusian region of Figure 5, the effect of technology on the parent’s budget constraint will dominate, and so the growth rate of the population will increase. This is the Post-Malthusian regime.

The positive income effect of technological progress on fertility only functions in the Malthusian region of Figure 5, however. As the figure shows the economy eventually crosses the Malthusian frontier. Once this has happened, further improvements in technology no longer have the effect of changing the amount of time devoted to child-rearing, while faster technological change will continue to raise the quantity of education that parents give each child. Thus once the economy has crossed the Malthusian frontier, population growth will fall as education and technological progress rise.

In the modern growth regime, resources per capita will rise, as technological progress outstrips population growth. Figure 4C shows that the levels of education and technological progress will be constant in the steady state, provided that population size is constant (i.e., population growth is zero). This implies that the growth rate of resources per capita, and thus the growth rate of output per capita, will also be constant.