KC Border's notes on selected topics in mathematical economics
Colleagues and students:
In the previous millennium, 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 remaining errors.
However, many of them are incomplete. Feel free to use them in your
courses or studies, but do so at your own risk. Or as Ronald Reagan
was fond of saying, “Trust, but verify.”
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
November of 2015, I began to update the first pages to reflect
the new Caltech Identity Project's recommendations on the use of the new
logo, so almost all file modification dates are 2015 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
Rational choice and demand theory

Rational choice.
233K,
20161107

Introductory notes on stochastic
rationality.
109K,
20160412

Preference relations,
and conditions that guarantee the equivalence of preference maximization
and expenditure minimization.
329K,
20170221

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.
253K,
20151111

Neoclassical demand theory, as
you might find in Samuelson's Foundations, but with
slightly more modern notation.
79K,
20160114

Duality and demand theory.
45K,
20151111

The weak axiom of revealed
preference implies negative semidefiniteness of the Slutsky
matrix.
78K,
20160115

Partial notes on Hurwicz and Uzawa's approach to the
integrability
problem.
207K,
20161109

Review of demand theory.
A crib sheet for qualifying exams.
59K,
20160115

Worked examples
of deriving demand functions, indirect utilities, and
expenditure functions from utility functions in the full
ngood case. Includes Cobb–Douglas (logarithmic and
exponential versions), linear, Leontief, quasilinear
Cobb–Douglas; with accurate pictures of indifference
curves.
97K,
20161104
Cost and production
Arrow–Debreu–McKenzie–Nikaidô Model

Introduction to the Arrow–Debreu–McKenzie–Nikaidô
Model.
86K,
20160204

Notes on boundedness of the set of
allocations.
66K,
20151111

Statement and proof of the
First Welfare Theorem.
52K,
20160119

Statement and proof of the
Second Welfare Theorem.
80K,
20160126

Hurwicz's approach to the
Second Welfare Theorem via Saddlepoints.
50K,
20151111

Notes on the
core of an economy,
based on Debreu and Scarf and Richter.
86K,
20170328

(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.
129K,
20160204

Worked examples of computing Walrasian equilibria for
Robinson Crusoe economies.
49K,
20151111
Decision under uncertainty

Desultory notes on
Decision Theory
including Dutch book arguments.
183K,
20160504

Note on the de Finetti–Arrow–Pratt coefficient of
risk aversion.
164K,
20161208
Financial economics
Search
Miscellany
Mathematics
Calculus

The firstorder linear differential equation
and its economic interpretation.
61K,
20161208

Maximization of a function of one variable.
165K,
20160927

Maximization
of a function of several variables.
158K,
20161021 Including the Lagrange
Multiplier Theorem.

Implicit Function Theorem.
161K,
20160115

Envelope theorem.
117K,
20151111

Comparative statics.
68K,
20160504

Increasing differences and comparative statics.
59K,
20160115

Euler's theorem on homogeneous functions.
58K,
20151111

Leibniz' rule for differentiating an integral.
793K,
20161225

Advanced integration by parts.
A bit sloppy in places.
90K,
20160115
Linear algebra
Convex analysis

Separating Hyperplane Theorems.
287K,
20161208

Supergradients and subgradients.
147K,
20160613

Theorem of the Alternative.
232K,
20151120

Saddlepoints
and constrained maximization.
89K,
20161021

Notes on the theory of
Linear Programming and saddlepoints.
99K,
20160115

Notes on the
Simplex Algorithm
and how to use it.
238K,
20160115

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.
76K,
20151111
Metric spaces and topology

What you should remember about
metric spaces.
154K,
20170220 A list of terms
and results with almost no proofs.

Introduction to the basic concepts of pointset topology.
105K,
20160613

Correspondences.
162K,
20160911
Probability
Miscellany
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This page created and maintained by KC Border. Last updated
20160504