KC Border's notes on selected topics in mathematical economics
Colleagues and students:
A few years ago, I began to put my course “handouts” on
the web instead of handing them out. Here is a list of some 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.
I will 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. (As I make revisions, 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.
96K,
November 4, 2003.
-
Worked examples.
103K,
October 14, 2004.
Rational choice and demand theory
-
Rational choice as I interpret Ket
Richter.
236K,
November 10, 2009.
-
Introductory notes on stochastic
rationality.
184K,
January 14, 2009.
-
Preference relations
and their properties.
179K,
October 2, 2008.
-
From the point of view of competitive demand theory,
local nonsatiation is no more general than monotonicity.
272K,
June 28, 2009.
-
Neoclassical demand theory, as
you might find in Samuelson's Foundations.
145K,
November 11, 2009.
-
Duality and demand theory.
74K,
November 9, 2004.
-
The weak axiom of revealed
preference implies negative semidefiniteness of the Slutsky
matrix.
97K,
November 29, 2001.
-
Partial notes on Hurwicz and Uzawa's approach to the
integrability
problem.
225K,
August 10, 2005.
-
Review of demand theory.
A crib sheet for qualifying exams.
70K,
October 31, 2009.
-
Worked examples
of deriving demand 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.
109K,
February 25, 2009.
-
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,
February 27, 2002.
-
Hurwicz's approach to the
Second Welfare Theorem via Saddlepoints.
111K,
November 5, 2004.
-
Notes on the
core of an economy,
based on Debreu and Scarf and Richter.
111K,
February 21, 2006.
-
(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.
197K,
April 28, 2009.
-
Worked examples of computing Walrasian equilibria for
Robinson Crusoe economies.
68K,
April 10, 2003.
Decision under undertainty
-
Desultory notes on
Decision Theory
including Dutch book arguments.
235K,
January 16, 2009.
-
Note on the de Finetti–Arrow–Pratt coefficient of
risk aversion.
228K,
November 12, 2003.
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.
229K,
October 14, 2004.
-
Envelope theorem.
161K,
October 23, 2008.
-
Comparative statics.
86K,
September 28, 2001.
-
Increasing differences and comparative statics.
92K,
October 12, 2001.
-
Euler's theorem on homogeneous functions.
96K,
September 28, 2004.
-
Leibniz' rule for differentiating an integral.
1.2M,
September 23, 2008.
-
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.
237K,
October 15, 2003.
-
Theorem of the Alternative.
261K,
September 25, 2008.
-
Saddlepoints
and constrained maximization.
155K,
October 16, 2005.
-
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 at the behest of Roko Aliprantis.
129K,
December 15, 2004.
Metric spaces and topology
Probability
Miscellany
·
Home page
·
Caltech Social Science Home Page
·
Caltech H&SS Home Page
·
Caltech Home Page
·
This page created and maintained by KC Border. Last updated on
October 30, 2009.