Taking Stock

This chapter introduced the preliminaries necessary for an in-depth study of equilibrium and optimal growth theory. At some level it can be thought of as an “odds and ends” chapter, introducing the reader to the notions of representative household, dynamic optimization, welfare theorems and optimal growth.

The most important take-away messages from this chapter are as follows. First, the set of models we study in this book are examples of more general dynamic general equilibrium models. It is therefore important to understand which features of the growth models are gen­eral (in the sense that they do not depend on the specific simplifying assumptions we make) and which results depend on the further simplifying assumptions we adopt. In this respect, the First and the Second Welfare Theorems are essential. They show that provided that all product and factor markets are competitive and there are no externalities in production or consumption (and under some relatively mild technical assumptions), dynamic competitive equilibrium will be Pareto optimal and that any Pareto optimal allocation can be decentral­ized as a dynamic competitive equilibrium. These results will be relevant for the first part of the book, where our focus will be on competitive economies. They will not be as relevant (at least if used in their current form), when we turn to models of technological change, where product markets will be monopolistic or when we study certain classes of models of economic development, where various market imperfections will play an important role.

Second, the most general class of dynamic general equilibrium models will not be tractable enough for us to derive sharp results about the process of economic growth. For this reason, we we will often adopt a range of simplifying assumptions. The most important of those is the representative household assumption, which enables us to model the demand side of the economy as if it were generated by the optimizing behavior of a single household. We saw how this assumption is generally not satisfied, but also how a certain class of preferences, the Gorman preferences, enable us to model economies as if they admit a representative household. We also discussed how typical general equilibrium economies can be modeled as if they admit a representative firm.

In addition, in this chapter we introduced the first formulation of the optimal growth problems in discrete and in continuous time, which will be useful as examples in the next two chapters where we discuss the tools necessary for the study of dynamic optimization problems.

5.12.