Optimal growth in a two-sector economy facing an expected random shock
This article deals with an optimal growth in the two-sector model with two kind of technologies (``clean'' and ``dirty''). The growth of each sector is described by the system of linear differential equations. It is assumed that in some random time the parameters of the equation change while the moment of the change has an exponential distribution. The problem of optimizing the social welfare function is stated as the optimal control problem and solved using Pontryagin's maximum principle. The authors give a characterization of the solutions for all possible cases (relations of the values of parameters). The analysis is performed by the qualitative analysis of differential equations: phase diagrams and checking vector fields generated by the system.
scientific article; zbMATH DE number 6345324
scientific article