Topics in Mathematical Economics

Mr. Moody

The topic this semester is duality theory. We take duality
from its purely mathematical origins

to it's application in estimating econometric models. Consequently,
the prerequisites for this

topic are both Mathematical Economic (Econ 331) or Math 111-212, and Econometrics
(Econ 308).

1. Review

Matrix derivatives

Nonlinear programming (Kuhn-Tucker)

Linear programming

Minimizing costs subject to an output constraint

Second order conditions

2. Theory of the firm.

The envelope theorem

Cost and profit functions

Shephard's lemma

Hotelling's lemma

Varian, H.R. *Microeconomic Analysis.* New York:
W.W. Norton, 1978, Ch. 1.

Silberberg, E. *The Structure of Economics: A Mathematical
Analysis. *Second Edition, New

York: McGraw-Hill, 1990, ch. 7-9.

Toumanoff, P. and F. Nourzad. *A Mathematical Approach
to Economic Analysis*. Minneapolis:

West Publishing Co., 1994, ch. 11.

3. Consumer demand theory.

Indirect utility functions

Envelope theorem again

Roy's identity

Silberberg, ch. 10.

Varian p. 112

Baumol, W.J. *Economic Theory and Operations Analysis. *Fourth Edition.
Chapter 14,

"Towards Observability, Revealed Preference and Expenditure
and Cost Functions, pp. 353- 373.

4. Application to reality

Factor demand

Allen elasticities of substitution

Generalized Leontief cost function

Translog cost function

Demand for fuel by industry

Varian, ch. 4

Berndt, E.R. *The Practice of Econometrics: Classic and Contemporary*.
Reading: Addison- Wesley, 1991, ch. 9.

Baumol, pp. 370-373

Diewert, W.E. "An Application of the Shephard Duality Theorem: A Generalized
LeontiefProduction Function." *Journal of Political Economy, *79,
1971, 482-507.

Berndt, E.R. and D.O. Wood, "Technology, Prices, and
the Derived Demand for Energy."*Review of Economics and Statistics,*
52, 1975, 259-268.

Griffin, J.M. "The Econometrics of Joint Production: Another Approach."
*Review of Economics and Statistics, *59, 1977, 389-397.