Malthusian regime: The Dynamical System 4

Hence, the XX Locus, as depicted in Figure 5 in the space (et) xt), is a vertical line above the Conditional Malthusian Frontier at a level e.

Lemma 3 holds as long as consumption is above subsistence. Click Here In the case where the subsistence constraint is binding, the evolution of xti as determined by equation (26), is based upon the rate of technological change, gu the effective resources per-worker, xt as well as the quality of the labor force, et.

Hence, the Conditional Malthusian Frontier, the XX Locus, and the XX\gt Locus, as depicted in Figure 5 in the (et,xt) space, coincide at (e,x).

The EE Locus

Let EE be the locus of all triplets {euguxt) such that the quality of labor, e*, is in a steady-state. That is,
As follows from the analysis in section 3.1, the steady-state values of et are independent of the values of xt and gt. The locus EE evolves through three phases in the process of development, corresponding to the three phases that describe the evolution of education and technology depicted in Figures 4(a), 4(b), and 4(c).

Panel a. In early stages of development, when population size is sufficiently small, the joint evolution of education and technology is characterized by a globally stable temporary steady-state equilibrium, (e:g) — (0,(/), as depicted in Figure 4a. The corresponding EE Locus, depicted in the space (etlxt) in Figure 5a, is vertical at the level e = 0, for a range of small population sizes. Furthermore, for this range, the global dynamics of et in this configuration are given by: