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.
However, the material here is more than odds and ends, since a good understanding of the general equilibrium foundations of economic growth and the welfare theorems is necessary for what is to come in Part 3 below and later.The most important take-away messages from this chapter are as follows. First, the set of models 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) and which results depend on the further simplifying assumptions. In this respect, the First and the 195
Second Welfare Theorems are essential. They show that provided that all product and factor markets are competitive and that there are no externalities in production or consumption (and under some relatively mild technical assumptions), dynamic competitive equilibrium will be Pareto optimal and any Pareto optimal allocation can be decentralized as a dynamic competitive equilibrium. These results will be relevant especially in Part 3, where the focus will be on competitive economies. Importantly, these results will not directly apply in our analysis of technological change, where product markets will be monopolistic, or in our study 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.
In addition, this chapter introduced the first formulation of the optimal growth problems in discrete and in continuous time. These will be used as examples in the next two chapters.
5.11.