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 talked about why the
social planner problem may be a problem whose solution is
interesting. It is because it is the unique equilibrium of
the economy once we use the welfare (and other)
theorems. We construct 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 argue that we can then solve for Social
Planner problem sometimes, but that we do so using
recursive methods (dynamic programming). Why not then
always recursive methods? This is to define equilibria
recursively. I posed the sequence of markets equilibrium
using state contingent capital to be delivered BEFORE
production next period which, using the no-arbitrage
condition, puts constraints on the sum of the state
I show how to construct a Seq of Mark
equilibrium from an Arrow Debreu and viceversa, and how it
is important to transform the prices. We then defined
Recursive Competitive Equilibrium. We started with that of
arbitrary expectations and moved on to a rational
We reviewed RCE. We did it with a
version with leisure and no shocks. 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 went into many details of how to
characterize the RCE and what are its FOCs.
We then talked about a variety of
environments where the welfare theorems do not apply: the
existence of public goods, of consumption externalities
(concurrent and lagged). We then move on to consider
environments where a government taxes and produces the
public good. First, with a period by period budget
constraint with either lump sum taxes, labor, or total
income, or consumption 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
We discussed the use of RCE not when the
welfare theoremes fail, but when there are differnt
agents. We started with agents differing in wealth in a
model wihout leisure, and moved to having them differ in
wealth and efficient units of labor. We then started looking
at two countries and what does this mean.
We finished the discussion of two
countries. We started looking at the Lucas tree model. We
defined equilibrium and we also started to derive a formula
for share prices (that you should finish). We also talked
about how to pose the sale of state contingent shares and of
state contingent fruit.
We discussed finance. What is the price
of statate contingent goods and from there we used
arbitrage, to get formulae for interest rates and to price
shares, options, repos, the works. We then discussed the RCE
when firms own land an install capital and households own
firms via a stock market. Up to here is what goes to the
midterm. We started measure theory.
We had the midterm.
We continued the discussion of measure
theory, including measurable functions, transition functions
and updating operators. We started talking about the size
distribution of firms by posing the problem of a firm and
deriving an aggregate labor supply function given a measure
We discussed industry equilibrium in the Hopenhayn
model. For this we defined stationary equilibrium, with
exogenous death, then with endogenous death. We talked about
how measures describe well the size and type of firms.
We finished discussing Industry EQ theory. We looked at how
to compute statistics using measures (ratios, Ginis, and the
like). We also discussed adjustment costs and how the
problem of the firm changes because of this. We started
discussing growth. We went over the AK model and the model
with an externality in capital.
I asked a few homeworks meaning things that you should be
able to do. They include the definition of Industry eq with
adjustment costs, with emphasis on how to construct the
transition process for firms; the ability of computing
industry statistics using the equilibrium tools; the
calculation of the equilibrium and the solution to the
social planner in an economy with an externality in
production so that output is linear in capital.
I went briefly over the human capital
growth model. Then I went over the and especially I will review the Romer growth
model with an externality and an R&D sector. This involves
I went over search. Looking at environments
where a worker takes a job or not with a few tweaks. I
defined matching functions.
I discussed bargaining in abstract and in
the context of the search and matching labor model. I went
briefly over the conditions to get a stationary
equilibrium. I also discussed competitive search.
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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