Numerical search for the global solution in the two-regime model with exhaustible resources

Current paper is focused on the numerical search for the equilibrium trajectory in the two-sector model of economic growth (production and energy sectors). There is a possibility in the energy sector to use oil resources from limited reserves. The distribution of resources between sectors depends on the operating regime of economy (with or without oil). It is necessary to find transition path which delivers economy to the long term equilibrium. In this paper we propose to apply shooting algorithm with the analogue of Newton method to update the starting point of recursive process. We discuss some aspects of applying this approach to such type of economic problems: features of the phase trajectory map, convenient step and stopping criterion ensures result comparable with the scale of economy.