Requirements/prerequisites: 211 is an essential prerequisite, 221 and 251 are strongly
recommended and 212 would be useful, but not essential. Students
would also benefit by simultaneously taking Course 412 - Probability.
Duration: Michaelmas, Hilary and Trinity
Number of lectures per week:
Assessment: Problem sets will be assigned regularly throughout the course
and will be discussed in tutorials
Course 381, first offered in 1993-94, is a course in mathematical economics (including a substantial component on mathematical finance) taught by Dr Patrick Waldron (Economics Department). It is a compulsory mathematics course for Junior Sophister TSM students in mathematics and economics and may also be chosen by the following:
Senior Sophister TSM students in mathematics whose other subject is not economics
Senior Sophister TSM students in mathematics and economics who have
not already taken course 3.08 (Mathematical economics) as a Junior
Sophister economics option.
(In 1995-96, these courses will be taught separately, although about half of the course material is common to the two courses).
There will be two lectures per week and tutorials will be arranged
from week 3 of Michaelmas term. Some tutorials will be based on a
collection of Mathematica notebooks accompanying the textbook by
The objective of this course is to introduce students of mathematics
to a few of the countless applications of mathematics in modern
economics and finance. Much of the mathematics will be familiar, and
the emphasis will be on applying it in economics.
The course will be broken down into the following topics:
Convexity and Concavity
Equality Constrained Optimisation and Lagrange Multipliers
Inequality Constrained Optimisation and the Kuhn-Tucker Theorem
Consumer Choice Theory
General Equilibrium Theory
The Welfare Theorems
Equilibrium with Arrow-Debreu Securities
Choice under Uncertainty and the Expected Utility Paradigm
The Single-period Portfolio Choice Problem
Mathematics of the Portfolio Frontier
Market Equilibrium: The Capital Asset Pricing Model
Arbitrage and the Pricing of Derivative Securities
Multi-period and Continuous Time Investment Problems
 Arrow, K.J. & Hahn, F.H. (1971), General Competitive Analysis,
Holden-Day, San Francisco.
 Debreu, G. (1959), Theory of Value: An Axiomatic Analysis of Economic
Equilibrium, Yale University Press, New Haven.
 Dixit, A.K. (1990), Optimization in Economic Theory, 2nd edition,
Oxford University Press, Oxford.
 Hildenbrand, W. & Kirman, A.P. (1988), Equilibrium Analysis:
Variations on themes by Edgeworth and Walras, North-Holland,
 Huang, C.-F. & Litzenberger, R.H. (1988), Foundations for Financial
 Kreps, D.M. (1990), A Course in Microeconomic Theory, Harvester
Wheatsheaf, New York.
 Madden, P. (1986), Concavity and Optimization in Microeconomics, Basil
 Mendelson, B. (1975), Introduction to Topology, 3rd edition, Allyn and
 Merton, R.C. (1972), ``An analytic derivation of the efficient portfolio
frontier", Journal of Financial and Quantitative Analysis 7,
 Roberts, A.W. & Varberg, D.E. (1973), Convex Functions, Academic
Press, New York.
 Rockafellar, R.T. (1970), Convex Analysis, Princeton University Press,
 Roll, R. (1977), ``A critique of the asset pricing theory's tests -
Part I: On past and potential testability of the theory", Journal of
Financial Economics 4, 129-176.
 Silberberg, E. (1978), The Structure of Economics: A Mathematical
Analysis, McGraw-Hill, New York.
 Simon, C.P. & Blume, L. (1994), Mathematics for Economists, Norton,
 Takayama, A. (1994), Analytical Methods in Economics, Harvester
Wheatsheaf, New York.
 Varian, H.R. (1992), Microeconomic Analysis, 3rd edition, Norton, New
For the first eight topics, the primary text, insofar as there is one, is Varian. For the last seven topics, it is Huang and Litzenberger. Students should also get the errata for Varian's book. Reference will occasionally be made to particular topics covered in the other sources listed here.
Jun 10, 1998