Dynamic optimisation

Abstract

In Chapter 3 we developed the theory of optimisation, arguing that it provided the basis for a wide variety of economic models. The type of model analysed in that chapter involved agents making choices concerning the values of a variable at an instant in time. Many choices, however, involve the time-paths of variables from now, when the choice is made, until some time in the future. We might model firms, for example, as choosing current output to maximise current profits. Evidently, however, firms plan output levels for several time periods ahead, and are interested in future as well as current profits. Installing new machinery in period one may entail huge losses in period one but enhanced profits in the future: investment decisions must surely balance future profits against current losses. According to the life-cycle hypothesis of household saving, households are supposed to plan the future paths of their consumption and savings in the light of expected future incomes.