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 many 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 on occasion. The file sizes and dates below
reflect the latest uploads. The revision date in the handout 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. I am now adding a
time stamp to the handouts 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. In fact, in the late
summer of 2012, I began standardizing on the Latin Modern fonts and
utf8 encoding and adding hyperlinks, so almost all file modification
dates are 2012 or later, despite the fact that some of these notes
date back to the early 1980s and were converted from troff
.
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
Rational choice and demand theory

Rational choice.
211K,
20141111

Introductory notes on stochastic
rationality.
89K,
20131011

Preference relations,
and conditions that guarantee the quivalence of prefernce maximization
and expenditure minimization.
316K,
20141024

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.
241K,
20130821

Neoclassical demand theory, as
you might find in Samuelson's Foundations, but with
slightly more modern notation.
72K,
20120828

Duality and demand theory.
36K,
20120827

The weak axiom of revealed
preference implies negative semidefiniteness of the Slutsky
matrix.
65K,
20131011

Partial notes on Hurwicz and Uzawa's approach to the
integrability
problem.
187K,
20141120

Review of demand theory.
A crib sheet for qualifying exams.
50K,
20131022

Worked examples
of deriving demand functions, indirect utilityies, and
expenditure functions from utility functions in the full
ngood case. Includes Cobb–Douglas (logarithmic and
exponential versions), linear, Leontieff, quasilinear
Cobb–Douglas; with accurate pictures of indifference
curves.
78K,
20131115
Arrow–Debreu–McKenzie–Nikaidô Model

Introduction to the Arrow–Debreu–McKenzie–Nikaidô
Model.
64K,
20120828

Notes on boundedness of the set of
allocations.
52K,
20120828

Statement and proof of the
First Welfare Theorem.
39K,
20120828

Statement and proof of the
Second Welfare Theorem.
66K,
20131115

Hurwicz's approach to the
Second Welfare Theorem via Saddlepoints.
42K,
20131024

Notes on the
core of an economy,
based on Debreu and Scarf and Richter.
59K,
20140305

(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.
106K,
20121030

Worked examples of computing Walrasian equilibria for
Robinson Crusoe economies.
37K,
20120828
Decision under uncertainty

Desultory notes on
Decision Theory
including Dutch book arguments.
155K,
20131118

Note on the de Finetti–Arrow–Pratt coefficient of
risk aversion.
130K,
20120915
Financial economics
Search
Miscellany
Mathematics
Calculus

The firstorder linear differential equation
and its economic interpretation.
49K,
20120824

Maximization of a function of one variable.
146K,
20120915

Maximization
of a function of several variables.
138K,
20140129

Implicit Function Theorem.
143K,
20130827

Envelope theorem.
106K,
20120827

Comparative statics.
56K,
20121031

Increasing differences and comparative statics.
48K,
20120827

Euler's theorem on homogeneous functions.
45K,
20120827

Leibniz' rule for differentiating an integral.
11M,
20130925

Advanced integration by parts.
A bit sloppy in places.
149K,
20050525
Linear algebra
Convex analysis

Separating Hyperplane Theorems.
274K,
20120915

Supergradients and subgradients.
128K,
20130925

Theorem of the Alternative.
204K,
20141211

Saddlepoints
and constrained maximization.
75K,
20120915

Notes on the theory of
Linear Programming and saddlepoints.
83K,
20120828

Notes on the
Simplex Algorithm
and how to use it.
176K,
20130904

An example of a pointed, generating, finite cone in
R^{4} whose dual
cone has a different number of extreme rays, which I
prepared for Roko Aliprantis.
61K,
20130925
Metric spaces and topology

What you should remember about
metric spaces.
129K,
20141030 A list of terms
and results with almost no proofs.

Introduction to the basic concepts of pointset topology.
89K,
20131022

Correspondences.
146K,
20141113
Probability
Miscellany
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This page created and maintained by KC Border. Last updated
20140721