On optimal pollution and consumption control in a macroeconomic system

A two sector macroeconomic growth model is used to determine optimal policies of consumption and investment in the two sectors of the economy. The first sector produces a general economic good and the second sector produces an activity of depollution. The performance criterion is defined by weighting the consumption and the pollution cost. An optimal control problem with singular extremals must be solved. Emphasis is given to the study of the rest point which may be reached by the economy. Numerical computations give an illustration of the usefullness of this model.