Endogenous Technological Change, Innovation Diffusion and Transitional Dynamics in a Nonlinear Growth Model*

Spatial perspectives on new theories of economic growth

“…The long-run equilibrium level of the effective capital intensity is given by k à for which k H. Under the specified conditions, such an equilibrium exists and is stable (see Nijkamp and Poot 1993a). The merit of this simple model of endogenous technical change is that, in contrast with the Solow-Swan or Ramsey model, it identifies various sources of differences in growth rates between countries and regions.…”

“…If the diffusion parameter is very large, "overshooting" may take place and the system would then be characterized by saddle-path stability (see Nijkamp and Poot 1993a). Thus, ever increasing growth rates or growth rates reducing to zero are then a possibility.…”

“…An example can be found in Romer (1986), who justifies such a model by the observation that in the very long run (over several centuries) worldwide labour-productivity growth has been accelerating (see also Kremer 1993), although it is equally true that during the last forty years productivity growth exhibited a downward trend among developed countries (Romer, 1989). Nijkamp and Poot (1993b) formulate a model of increasing returns in which such ever-increasing growth is eventually checked by technological, social and economic capacity constraints.…”

“…Moreover, if the productivity growth rate between regions or countries differs, mobile labour may have the same effect as mobile capital which we discussed earlier, namely the final equilibrium may be a corner solution in which all population is concentrated in one region. To avoid such an extreme, it is plausible to introduce some capacity constraint either in terms of technological bottlenecks or congestion of a natural resource (see also Nijkamp and Poot 1993b). Braun (1993) formulates several growth models with endogenous migration.…”

“…This result is obtained by substituting the endogenous rate of technical change (22) into (17) or (21) and by writing down a similar equation for the second country. The equilibrium effective capital intensities k à and k f à can then be found as the steady-state solution to the resulting two simultaneous differential equations (see Nijkamp and Poot 1993a).…”