Balance between absorbing and positive fixed points in resource consumption models

The effect of resource usage on economic growth has been studied in multiple models. However, the generic effect of improving resource usage efficacy through improved technical skills has not been studied in detail. We here analyze a model incorporating resource usage by capital and the parallel production of technical skill in order to study the effect of improving the efficacy of resources usage with advanced technologies. We show that a practically inevitable result of such a model is that improving the resource usage efficacy leads to a lower steady-state level of resources. A surprising conclusion from ordinary differential equations realization of the model is an extreme sensitivity to parameters, where a small parameter change can lead to an irreversible state through a hysteresis mechanism between a scenario of a collapse of the economy and a scenario of sustainable economy. This sensitivity is lost when spatial stochastic simulations are performed. In the stochastic regime the two scenarios coexist, with different fractions of the lattice residing in each state. Changing parameters smoothly changes the fraction of lattice sites in each state. The transition between the collapsed economy and the sustainable one is not symmetrical. Escape from the collapsed situation can only occur through diffusion from neighboring sustained lattice sites. On the other hand, the collapse can occur even in the absence of diffusion. This difference leads to diffusion dependent capital growth, where an optimal capital is obtained for middiffusion values. Such a transition may actually be generic phenomena in ecological and economic systems.