KC Border's notes on selected topics in mathematical economics
Colleagues and students:
In the previous millenium, I began to put my course
“handouts” on the web instead of handing them out. Here
is an index of them. I offer no warranty as to the correctness of
these notes, but I am not aware of any errors. However, many of them
are incomplete. Feel free to use them in your courses or studies, but
do so at your own risk.
I add to this list as I have time. The file sizes and dates
reflect the latest uploads. The revision date in the text reflects
only major revisions. If I find typos, reformat a few equations, or
simply play around with different fonts, I may upload the new version
without changing the revision date in the text. Sorry, but I'm just
not compulsive enough to assign version numbers and keep them up to
date. (I am now adding a time stamp that indicates the
last time the file was converted to pdf from LaTeX. This is usually an
indication that something has changed, even if only the format.)
I'd appreciate it if you let me
know if you find any mistakes, or if you just find something too
obscure. Corrections are also greatly appreciated.
— KCB
Mathematical Economics
Cost and production
-
Notes on support functions, or profit and cost functions.
118K,
August 21, 2009.
- Traditional
approach to cost minimization.
120K,
November 25, 2008.
-
The Cobb--Douglas Production
Function.
64K,
May 6, 2008.
-
Production possibility frontier and
marginal costs.
157K,
September 13, 2011.
-
Worked examples.
176K,
May 14, 2011.
Rational choice and demand theory
-
Rational choice.
372K,
January 24, 2012.
-
Introductory notes on stochastic
rationality.
275K,
October 5, 2011.
-
Preference relations,
and conditions that guarantee the quivalence of prefernce maximization
and expenditure minimization.
577K,
October 25, 2011.
-
From the point of view of competitive demand theory,
local nonsatiation is
no more general than monotonicity. It took me thirty years
to notice this.
356K,
October 25, 2011.
-
Neoclassical demand theory, as
you might find in Samuelson's Foundations, but with
more slightly more modern notation.
279K,
October 5, 2011.
-
Duality and demand theory.
74K,
November 9, 2004.
-
The weak axiom of revealed
preference implies negative semidefiniteness of the Slutsky
matrix.
200K,
October 6, 2011.
-
Partial notes on Hurwicz and Uzawa's approach to the
integrability
problem.
375K,
October 25, 2011.
-
Review of demand theory.
A crib sheet for qualifying exams.
61K,
October 14, 2011.
-
Worked examples
of deriving demand functions, indirect utilityies, and
expenditure functions from utility functions in the full
n-good case. Includes Cobb–Douglas (logarithmic and
exponential versions), linear, Leontieff, quasi-linear
Cobb–Douglas; with accurate pictures of indifference
curves.
118K,
February 24, 2008.
Arrow–Debreu–McKenzie–Nikaidô Model
-
Introduction to the Arrow–Debreu–McKenzie–Nikaidô
Model.
209K,
October 19, 2010.
-
Notes on boundedness of the set of
allocations.
103K,
April 3, 2003.
-
Statement and proof of the
First Welfare Theorem.
78K,
February 25, 2009.
-
Statement and proof of the
Second Welfare Theorem.
115K,
May 3, 2005.
-
Hurwicz's approach to the
Second Welfare Theorem via Saddlepoints.
171K,
October 25, 2011.
-
Notes on the
core of an economy,
based on Debreu and Scarf and Richter.
206K,
January 31, 2011.
-
(Non-)Existence of Walrasian Equilibrium.
Examples of what can go wrong when standard assumptions are
violated, plus a sketch of an existence proof based on the
excess demand approach.
301K,
January 31, 2011.
-
Worked examples of computing Walrasian equilibria for
Robinson Crusoe economies.
123K,
November 17, 2011.
Decision under uncertainty
-
Desultory notes on
Decision Theory
including Dutch book arguments.
372K,
March 29, 2011.
-
Note on the de Finetti–Arrow–Pratt coefficient of
risk aversion.
320K,
December 3, 2009.
Financial economics
Search
Miscellany
Mathematics
Calculus
-
The first-order linear differential equation
and its economic interpretation.
107K,
October 30, 2007.
-
Maximization of a function of one variable.
214K,
September 29, 2008.
-
Maximization
of a function of several variables.
216K,
October 18, 2005.
-
Envelope theorem.
162K,
October 23, 2008.
-
Comparative statics.
85K,
September 29, 2010.
-
Increasing differences and comparative statics.
84K,
August 30, 2009.
-
Euler's theorem on homogeneous functions.
97K,
September 29, 2004.
-
Leibniz' rule for differentiating an integral.
12M,
June 5, 2009.
-
Advanced integration by parts.
A bit sloppy in places.
149K,
May 25, 2005.
Linear algebra
Convex analysis
-
Separating Hyperplane Theorems.
368K,
June 19, 2009.
-
Supergradients and subgradients.
217K,
June 23, 2009.
-
Theorem of the Alternative.
421K,
October 14, 2011.
-
Saddlepoints
and constrained maximization.
142K,
July 31, 2007.
-
Notes on the theory of
Linear Programming and saddlepoints.
138K,
February 25, 2009.
-
Notes on the
Simplex Algorithm
and how to use it.
296K,
February 25, 2009.
-
An example of a pointed, generating, finite cone in
R4 whose dual
cone has a different number of extreme rays, which I
prepared for Roko Aliprantis.
192K,
November 17, 2011.
Metric spaces and topology
-
What you should remember about
metric spaces.
326K,
October 26, 2011. A list of terms
and results with almost no proofs.
-
Correspondences.
280K,
October 26, 2011.
Probability
Miscellany
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This page created and maintained by KC Border. Last updated on
October 25, 2011.
