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Lecture notes for Macroeconomics I, 2004

Per Krusell

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Chapter 1
These lecture notes cover a one-semester course. The overriding goal of the course is
to begin provide methodological tools for advanced research in macroeconomics. The
emphasis is on theory, although data guidesthe theoretical explorations. We build entirely on models with microfoundations, i.e., models where behavior is derived from basic
assumptions on consumers’ preferences, production technologies, information, and so on.
Behavior is always assumed to be rational: given the restrictions imposed by the primitives, all actors in the economic models are assumed to maximize their objectives.Macroeconomic studies emphasize decisions with a time dimension, such as various
forms of investments. Moreover, it is often useful to assume that the time horizon is
infinite. This makes dynamic optimization a necessary part of the tools we need to
cover, and the first significant fraction of the course goes through, in turn, sequential
maximization and dynamic programming. We assume throughout that timeis discrete,
since it leads to simpler and more intuitive mathematics.
The baseline macroeconomic model we use is based on the assumption of perfect competition. Current research often departs from this assumption in various ways, but it is
important to understand the baseline in order to fully understand the extensions. Therefore, we also spend significant time on the concepts of dynamiccompetitive equilibrium,
both expressed in the sequence form and recursively (using dynamic programming). In
this context, the welfare properties of our dynamic equilibria are studied.
Infinite-horizon models can employ different assumptions about the time horizon of
each economic actor. We study two extreme cases: (i) all consumers (really, dynasties) live
forever - the infinitely-lived agent model -and (ii) consumers have finite and deterministic
lifetimes but there are consumers of different generations living at any point in time the overlapping-generations model. These two cases share many features but also have
important differences. Most of the course material is built on infinitely-lived agents, but
we also study the overlapping-generations model in some depth.
Finally, manymacroeconomic issues involve uncertainty. Therefore, we spend some
time on how to introduce it into our models, both mathematically and in terms of economic concepts.
The second part of the course notes goes over some important macroeconomic topics.
These involve growth and business cycle analysis, asset pricing, fiscal policy, monetary
economics, unemployment, and inequality. Here, few new tools areintroduced; we instead
simply apply the tools from the first part of the course.


Chapter 2
Motivation: Solow’s growth model
Most modern dynamic models of macroeconomics build on the framework described in
Solow’s (1956) paper.1 To motivate what is to follow, we start with a brief description of
the Solow model. This model was set up to study a closed economy, and we will assumethat there is a constant population.


The model

The model consists of some simple equations:
Ct + It = Yt = F (Kt, L)


It = Kt+1 − (1 − δ ) Kt


It = sF (Kt , L) .


The equalities in (2.1) are accounting identities, saying that total resources are either
consumed or invested, and that total resources are given by the output of a production
function withcapital and labor as inputs. We take labor input to be constant at this point,
whereas the other variables are allowed to vary over time. The accounting identity can also
be interpreted in terms of technology: this is a one-good, or one-sector, economy, where
the only good can be used both for consumption and as capital (investment). Equation
(2.2) describes capital accumulation: the output...
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