## Malthusian regime: The Dynamical System 5

Panel b. In later stages of development as population size increases sufficiently, the joint evolution of education and technology is characterized by multiple locally stable temporary steady-state equilibria, as depicted in Figure 4b. The corresponding EE Locus, depicted in the space (et, xt) in Figure 5b, consists of 3 vertical lines corresponding the three steady-state equilibria for the value of et. That is, e = 0, e = eu, and e = eh. The vertical lines e = and e = eh shift rightward as population size increases. Furthermore, the global dynamics of et in this configuration are given by:

Panel с. In mature stages of development when population size is sufficiently large, the joint evolution of education and technology is characterized by globally stable steady-state equilibrium at the point (e,

Conditional Steady-State Equilibria

In early stages of development, when population size is sufficiently small, the dynamical system, as depicted in Figure 5a in the space (et, xt)> is characterized by a unique and globally stable conditional steady-state equilibrium.32 It is given by a point of intersection between the EE Locus and the XX Locus. That is, conditional on a given technological level, gt) the Malthusian steady-state (0,x(pt)) is globally stable.33

In later stages of development as population size increases sufficiently, the dynamical system as depicted in Figure 5b is characterized by two conditional steady-state equilibria. The Malthusian conditional steady-state equilibrium is locally stable, whereas the steady-state equilibrium (en, xn) is a saddle point.34 In addition for education levels above eu the system converges to a stationary level of education eh and possibly to a steady-state growth rate of xt.

In mature stages of development when population size is sufficiently large, There system convergence globally to an educational level eh and possibly to a steady-state growth rate of xt.

Analysis

The transition from the Malthusian Regime through the Post-Malthusian regime to the demographic transition and a Modern Growth regime emerges from Proposition 1, Corollary 1, and Figures 2-5. Consider an economy in early stages of development. Population is low enough that the implied rate of technological change is very small, and parents have no incentive to provide education to their children. As depicted in Figure 4a in the space (et}0£), the economy is characterized by a single temporary steady-state equilibrium in which technological progress is very slow and children’s level of education is zero.

This temporary steady-state equilibrium corresponds to a globally stable conditional Malthusian steady-state equilibrium, drawn in Figure 5a in the space (et,xt). For a given rate of technological progress, effective resources per capita, as well as the level of education are constant, and hence as follows from (3) and (10) output per-capita is constant as well. Moreover, shocks to population or resources will be undone in a classic Malthusian fashion. payday loans without a bank account

Population will be growing slowly, in parallel with technology. As long as the size of the population is sufficiently small, no qualitative changes occurs in the dynamical system described in Figures 4a, and 5a. The temporary steady-state equilibrium depicted in Figure 4a gradually shifts vertically upward reflecting small increments in the rate of technological progress, while the level of education remains constant at zero. Similarly, the conditional Malthusian steady-state equilibrium drawn in Figure 5a for a constant rate of technological progress, shifts upward vertically. However, output per-capita remains constant at the subsistence level.