Optimal Growth. Continuous Time Analysis

Abstract

Maintaining the same structure of the neoclassical growth model of Solow and Swan we have reviewed in the previous chapter, Cass [18] and Koopmans [52] characterized the optimal rate of capital accumulation in order to maximize some social welfare criterion. That amounts to specifying the optimal distribution of output between consumption and savings each period, taking into account the fact that savings decisions provide resources for gross investment, thereby conditioning future production possibilities and growth. We are still in a one-good economy, where the single commodity is produced and can either be consumed or used as an input for future production. The stock of the commodity being used in production is physical capital, which is not reversible. It is subject to some constant rate of depreciation, δ, but it cannot be converted back into consumption.