Optimal Growth. Discrete Time Analysis

Abstract

In this chapter we present the discrete time version of some of the issues discussed in the previous chapter. We introduce a government in the economy, and define and characterize the competitive equilibrium. The intertemporal government budget constraint, the relationship between the competitive equilibrium allocation and that of the benevolent planner mechanism, and the Ricardian doctrine, can be all analyzed in discrete-time in a similar fashion as we have done in the continuous time version of the model. Dealing with all the details of the discrete time version of the Cass–Koopmans economy is very instructive in order to be able to formulate alternative, more complex growth models, as well as to perform policy analysis, as we do towards the end of the chapter. It is particularly important to get familiar with the formulation and use of the transversality condition and with the characterization of stability conditions. As we will see below, stability conditions are crucial to generate a numerical solution for this model in the form of a set of time series for the endogenous variables.