Sensitivity analysis of multisector optimal economic dynamics

Abstract

This paper develops several comparative dynamics results for Ramsey-type multidimensional dynamic optimization problems in economics. We provide sufficient conditions for the value function to be monotone and supermodular, and for the extremal optimal policies to be monotone in the state and in other parameters. These results are natural extensions of the one-dimensional case when the varying parameters are endogenous (state variables), but are rather restrictive for exogenous parameters (discount rate and length of horizon). The analysis relies mostly on the fundamental results in lattice programming.