Economics 435
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

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.