Economic growth and economic development 261

Introduction to Modern Economic Growth
subject to
(5.22)

k˙ (t) = f (k (t)) − c (t) − δk (t)

k (t) ≥ 0 and given k (0). The objective function (5.21) is the direct continuous-time

analogue of (5.18), and (5.22) gives the resource constraint of the economy, similar
to (5.19) in discrete time.

Once again, this problem lacks one boundary condition which will come from
the transversality condition.
The most convenient way of characterizing the solution to this problem is via
optimal control theory. Dynamic programming and optimal control theory will be
discussed briefly in the next two chapters.
5.10. 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,
what we have seen is more than odds and ends, since a good understanding of
the general equilibrium foundations on economic growth and the welfare theorems
should enable the reader to better understand and appreciate the material that will
be introduced in Part 3 below.
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
247