Department of Economics University of Minnesota
Phone-(612) 625-0941 4-101 Hanson Hall (off 4-179) Fed
Phone (612) 204-5528 1925 Fourth Street South Fax: (612)
624-0209 Minneapolis, MN 55455
Department of Economics, University of Minnesota,
Tue and 14:30-15:45 Hanson Hall 4-170. Off Hours:
Before and after class and by appointment.
Fax: (612) 624-0209
Fed Phone (612) 204-5528
I described the course. We discussed
what is the meaning of an equilibrium (a mapping from
environment to allocations). We then discussed why the
social planner problem may be a problem whose solution is
interesting. It is because it is the equilibrium of the
economy once we use the welfare (and other) theorems. We
constrect an Arrow Debreu Equilibrium for the
workhorse of macro, the growth model, using the welfare
theorems. We then saw how to build a sequence of markets
equilibrium out of an Arrow-Debreu equilibrium (and
viceversa). We started the definion of Recursive
equilibrium for arbitrary expectations.
We will continued with the definition
of Recursive equilibrium. We started with that of arbitrary
expectations and move on to a rational expectations
equilibria. I showed how to construct a Seq of Mark
equilibrium from a recursive equilibrium and I hinted what
are the troubles for going in the opposite direction. We
then talked about a variety of environments where the
welfare theorems do not apply. We started with one where
there is an externality in consumption. We moved on to
consider environments where a government taxes and produces
a publich good. First with a period by period budget
constraint with either lump sum taxes, labor or capital
income taxes. Finally we considered a government that
issues debt and we viewed the equilibrium conditions
including the no Ponzi scheme on the part of the government.
We looked at economies with two types of
agents. They differed in labor earnings and/or wealth and
could also differ on other things. We also looked at two
countries and carefully assessed how to model the equality
of rates of return.
We looked at economies with aggregate
shocks. We went from the secial planner problem to RCE (via
the A-D Eq, the sequence of markets equilibrium). We put
special emphasis in ensuring that we had complete markets
(we discussed the first welfare theorem in this respect).
We looked to a growth model
where the firm faces a dynamic problem by redefining labor
in the growth model as land. We then looked at the Lucas
tree. We argued its logic, we showed how to pose the problem
recursively and we got a formula for the prices of the tree
and for the prices of one and two period options.
We reviewed briefly the Lucas tree. We
then talked about the OLG model. We reviewed how to define
equilibrium in sequence of markets and the nature of the
trouble that leads to the existence of money. Then I
discussed why the notion of monetary equilibria maybe iffy,
and I proposed an alternative allocation (which is an
organizational equilibrium). Finally, and more importantly,
I addressed how to write a RCE with life cycle households
on top of a growth model, the modern use of OLG models.
We discussed measure theory.
April 19 Class 1
We went over Industry Equilibria.
April 19 Class 2
We went over various models of
Growth. The AK model, the externality in K, and the ability
to accummulate human capital via goods not time.
We went go over the Romer (1990) growth
model. It has an R&D sector as well as monopolistic
competition and an externality in learning.
search, (you can use
these notes for help). We posed the basic model of
what job to take in both discrete and continuous time. We
also talked about unemployment, and
We talked about on the job search, and posed
the matching function and wage setting via Nash
bargaining. Then we discussed the ingredients of a
stationary equilibria with endogenous vacancy creation by
posing free entry of firms.
We went over competitive search in some detail.
We had the test.
This course complements 8105-8107. In my view, the ultimate
goal of this course is to learn to use a variety of models
that can be used to give quantitative answers to
economic questions. The models can generate artificial data of
both allocations and prices that can be meaningfully related
to actual data. In this course most (if not all) of the
material will be studied from the strict point of view of the
theory, so we will not look at data in any serious manner nor
at solving the models with the computer. The emphasis is
on economic rigor, i.e. the target is to learn tools
that will be useful later. The course, then, is not a survey
of topics in macroeconomics. When some specific topic is
addressed the objective is not to give a review of known
results but rather to give an example of how an issue is
addressed and of how tools are used.
There will be recitations once a week. These will be used
either to introduce some mathematical apparatus that we need,
to solve homeworks, or to explore issues related to those
presented in class. The material covered in recitations
constitutes part of the required curriculum.
Homeworks and Grades
In the context of the course, I will assign some
homeworks: usually I will ask you to prove something during a
lecture, sometimes they will be posted in the homepage. These
problems are not required but will give you an idea of what is
expected for the exams, and especially for the prelim. The
grades will be based 30% on a midterm, 60% on a final that
will take place the last day of class and 10% on class
participation. Bernabe will give you feedback regarding the
He may post them on the web as well as post answers to it at a
later day. Or he may not. We will see about it.
Textbooks and papers
No special textbooks. There are notes from
previous years and Bernabe may post class notes of this year's
class. It never hurts to have the usual suspects, but I do not
dwell on them. Besides those used and recommended by my
colleagues, there is a good little book (out of print
actually) that is useful,
. The papers that I cite (in a very incomplete form
below) are not to be read in general, although some students
may find them useful. First year is to learn tools, not to
Preliminary List of Material to Cover
This list is of material that I
want to go over. The first few items you have seen in a very
similar way, so I will go very fast over it, but I find it
very useful to go over them again.
Competitive equilibrium in the
growth model. Taking advantage of the welfare theorems.
Stokey and Lucas,
, Chapters 15 and 16; Harris, , Chapters 3 and
4; Cooley and Prescott,
A stochastic version of the
growth model. What are complete markets? What are one
period ahead Arrow-securities? How to define Competitive
equilibrium in stochastic growth model.
COOLEY, T. F., AND E. C. PRESCOTT (1995): "Economic Growth
and Business Cycles," in Frontiers of Business Cycle Research, ed. by
T. F. Cooley, chap. 1. Princeton University Press, Princeton.
HARRIS, M. (1987): Dynamic Economic Analysis. Oxford
LUCAS, R. E. (1988): "On the Mechanics of Economic Development,"
ROGERSON, R., R. SHIMER, AND R. WRIGHT (2005):
"Search-Theoretic Models of the Labor Market: A Survey," Journal of
Economic Literature, 43, 959-988.
ROMER, P. M. (1986): "Increasing Return and Long-run Growth," 94,
(1990): "Endogenous Technological Change," 98, S71-S102.
STOKEY, N. L., AND E. C. LUCAS, R. E. WITH PRESCOTT
(1989): Recursive Methods in Economic Dynamics. Harvard University
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