Malthusian regime: The Dynamical System 3

Global Dynamics

This section analyzes the evolution of the economy from the Malthusian Regime, through the Post-Malthusian Regime, to the demographic transition and the Modern Growth regime.

Phase Diagrams

The global analysis is based a sequence of phase diagrams that describes the evolution of the system within each regime and in the transition between the different regimes. The phase diagrams, as depicted in Figure 5, are based on three central elements:

The Malthusian Frontier

As was established in (27) and (28) the economy exits from the subsistence consumption regime when potential income, z^ exceeds the critical level z = c/(l — 7)(l+r). This switch of regime changes qualitatively the nature of the dynamical system from a two to a three dimensional system.

Let The Malthusian Frontier be the set of all triplets of (eu xt: gt) for which individuals income equal z.31 Using the definitions of zt and z, it follows from (10), (15) and (19) that the The Malthusian Frontier, MM, is
Let The Conditional Malthusian Frontier be the set of all pairs (et,xt) for which, conditional on a given technological level gu individuals incomes equal z. Following the definitions of Zt and z, equations (10), (15) and (19) imply that The Conditional
Hence, the Conditional Malthusian Frontier, as depicted in Figure 5, is a strictly convex, downward sloping, curve in the space. Furthermore, it intersects the xt axis and approaches asymptotically the et axis as xt approaches infinity. The frontier shifts upward as gt increases in the transition to a modern growth regime. Electronic Payday Loans Online