Dynamic Optimization and Control

Abstract

Dynamic optimization is most fundamental to our understanding of economic behavior analyzed through economic models. This is so for several reasons. For one thing, it includes static optimization as a special case, since a dynamic model in its steady-state equilibrium may represent a static equilibrium model. Second, many economic decisions e.g. investment decisions have long run consequences, so that a policy which is optimal in the sense of maximizing short run profits for a firm may not be optimal in the long run, since it may invite more entry and thereby reduce long run profits. This apparent inconsistency between the short-run or myopic policy and the long run policy may lead to various adjustments in firm behavior, particularly when the future is only incompletely known or imperfectly forecast. Third, the understanding of dynamic or intertemporal or moving equilibrium as an optimum concept, whenever such an interpretation is meaningful in economic models, provides us with a normative yardstick against which actual realized behavior can be compared and tested for correspondence. This is particularly important for differential game models, which are increasingly applied in recent literature, where two or more players seek to reach an intertemporal equilibrium or optimum by appropriately choosing their own strategies over time. Lastly, dynamically optimal policies are most important for applying econometric models over time, since updating of policy may be performed as more data become available over time.