Malthusian regime: The Dynamical System

Hence, the rate of technological progress between time t and t 4- 1 is a positive, increasing, strictly concave function of the size and level of education of the working generation at time t. Furthermore, the rate of technological progress is positive even if labor quality is zero read more.

As will become apparent, the dynamical system of the described economy is rather complex. Population size does not play a qualitative role in the evolution of the economy, except for its significant role in the takeoff from the Malthusian Regime. Hence, in order to simplify the exposition without affecting the qualitative results, the dynamical system is analyzed initially under the assumption that population size has no effect 011 technological progress. In particular, let

The Dynamical System

The development of the economy is characterized by the evolution of output per worker, population, technological level, education per worker, human capital per worker, and effective resources per worker. The evolution of the economy, given (A4) is fully determined by a sequence {e*, that satisfies (21), (26), and Lemma 1 in every period t.

The dynamical system is characterized by two regimes. In the first regime the subsistence consumption constraint is binding and the evolution of the economy is governed by a three dimensional non-linear first-order autonomous system:
where the initial conditions eo, go>Xo are historically given.