Economics 1860, Spring 2012
The Theory of General Equilibrium
Tue., Thu. 9-10:20 a.m., Sayles Hall 205

Textbook
G. Debreu, (1959), Theory of Value, Yale University Press, New York.

Prerequisites
Econ 1110 or Econ 1130; Applied Math 0330 and 0340 or Math 0180 and 0520 or Math 1010.

Course Overview
General Equilibrium Theory studies the allocation of resources resulting from the interaction of several economic agents (consumers and producers). The analysis considers all commodities and all agents simultaneously. In a free market economy, which is the main focus of the course, rational behavior of individual consumers and producers (utility maximization and profit maximization) takes place in the context of markets, and it is through the market prices that the agents (indirectly) interact with one another. In equilibrium, the prices are such that rational individual behavior of the agents results in all markets clearing. General equilibrium, in contrast to partial equilibrium, refers to a simultaneous clearing of all markets.
In equilibrium, the consumption and production decisions of all the agents constitute a particular allocation on the economy’s resources. The big questions relate to the properties of an equilibrium: Does the market mechanism lead to an efficient allocation of resources under certain conditions? Does it do so in an equitable manner? What conditions are sufficient for an equilibrium to exist? Under what conditions is it unique? While economists have long speculated on answers to these questions, it was not until a systematic application of appropriate mathematical techniques in the 1950s and 1960s that a coherent theory emerged. This theory now forms the foundations of modern economics.
Chapter 1 of the textbook contains almost all of the mathematics that we will use in this course.

Grading
There will be one mid-term exam (30% of the grade), one in-class presentation (30%) and one final exam (40%).

Schedule
No class on Thu. February 2 and on Tue. February 14
Mid-Term Exam, 9 a.m., Tue. March 20
Last class (during reading period), May 1
Final Exam, 2 p.m., May 15

Background Reading

Debreu, G., (1991), The Mathematization of Economic Theory, American Economic Review, 1-7.

Introduction (slides)

First Welfare Theorem (slides)

Homework #2

Notes on General Equilibrium

Course Outline

I. Walrasian Equilibrium: Existence
I.1 Mathematical preliminaries; introduction to the Arrow-Debreu model.
Textbook, Chapter 1
Mathematical Appendices in Equilibrium Analysis by W. Hildenbrand, A. Kirman, (1988), North-Holland, Amsterdam.
I.2. Existence of Equilibrium
Textbook, Chapters 3, 4, 5.
Notes

II. Pareto Efficiency
The First and Second Welfare Theorems
Textbook, Chapter 6
Notes

III. The Core
Relationship of the Core to Walrasian equilibria and Core Convergence
Hildenbrand and Kirman, Chapter 5.1, 5.2.

IV. Papers for Class Presentation

Core Convergence
Debreu, G.  and H. Scarf, (1963), A Limit Theorem on the Core of an Economy, International Economic Review, 235-246.
Aumann, R.J., (1964), Markets with a contiinuum of Traders, Econometrica, 32, 39-50.
Anderson, R.M. (1978), An Elementary Core Equivalence Theorem, Econometrica, 46, 1483-1487.

Economies with Non-Ordered Preferences
Shafer, W.,  and H. Sonnenschein, (1975), Equilibrium in Abstract Economies without Ordered Preferences, Journal of Mathematical Economics, 345-348.

Economies with Public Goods
Foley, D., Lindahl's Solution and the Core of an Economy, (1970), Econometrica, 66-72.

Economies with Increasing Returns
Brown, D. J., (1991), Equilibrium Analysis with Non-Convex Technologies, in: W. Hildenbrand & H. Sonnenschein (ed.), Handbook of Mathematical Economics, vol. 4, 1963-1995, North-Holland, Amsterdam.

Uncertainty
Cass, D. and K. Shell, (1983), Do Sunspots Matter?, Journal of Political Economy, 9, 193-227.

Aggregate Demand Functions
Shafer, W. and H. Sonnenschein (1982), Market Demand and Excess Demand Functions, in K.J. Arrow and M.D. Intrilligator, Handbook of Mathematical Economics, vol. 2, 671 - 693, North-Holland, Amsterdam.

Fixed Point Theorems in Game Theory
Nash, J., (1951), Non-Cooperative Games, Annals of Mathematics, 54, 286-295.
Related reading, Nash, J. (1950), Equilibrium Points in n-Person Games, Proceedings of the National Academy of Science, 23, 48-49. Reprinted in Classics in Game Theory,, Ed. H.W. Kuhn, Princeton University Press, 1997.

Shapley, L. and R. Vohra, (1991), On Kakutani's Fixed Point Theorem, the K-K-M-S Theorem and the Core of a Balanced Game, Economic Theory, 107-116.