General Equilibrium

Syllabus

Textbook: Debreu, Gerard. Theory of value: An axiomatic analysis of economic equilibrium. Vol. 17. Yale University Press, 1959.

Part I: Classical General Equilibrium Theory - Debreu's Theory of Value

August 16th Basics of Sets, Preorderings, Set topology in Euclidean space

Reading: Section 1.2, 1.4, 1.5, 1.6 (a-h)

August 23rd Set topology in Euclidean space, continuity of functions

Reading: Section 1.3, 1.6 (i-u), 1.7

August 30th Continuity of Correspondence, Convexity, Separating hyperplane, Sum of Sets, Production

Reading: Section 1.8, 1.9, 2, 3.1, 3.2, 3.3 (i - f')

September 6th Production, Consumption

Reading: Section 3.3 - 3.5, 4.1 - 4.6

Student Presentation: No-arbitrage theorem and Separating hyperplane theorem ( Reference )

September 13th Preference and Economy

Reading: Section 4.6 - 4.10, 5.1-5.6

Student Presentation: Economy with public goods (Reference)

September 20th Gale-Debreu-Nikaido Lemma and the existence proof

Reading: Section 5.6, 5.7

Student Presentations:

Non-free disposal (Reference)

Gramham's trade model in a general equilibrium framework (Reference)

September 27th Pareto Optimality: the existence and its relation to the competitive equilibrium

Reading: Section 1.9 ((5)-(8)), Section 4.9, Section 6

Part II: Topics in General Equilibrium Theory

October 11th Time and Uncertainty: Arrow-Debreu Economy and the Spot Market

Reading: Section 7, notes

Student Presentations:

Non-convexity of production set with the cost of information (Reference)

Radner's model of the sequential market (Reference)

October 18th Free Market and the Price-Taking Assumption

Reading: Debreu-Scarf (1963), notes

Additional Readings: Aumann (1964), Bewley (1973)

Student Presentations:

Core with indivisibility (Reference)

Core with indivisibility and some power relation (Reference)

October 25th Learning from Radner: Turnpike Theory and Economics of Teams

Readings: Radner (1961) , Arrow-Radner (1979), notes

Additional Readings:

On Turnpike Theory: Mckenzie (1976), Nikaido (1964), Bewley (1980)

On Economics of Teams: Marschak-Radner (1972)

November 1st Matching: Allocation of Indivisible Resources

Readings: Koopmans-Beckmann (1957), notes

Student Presentations:

Two-sided market and the role of price

From an optimal transportation view

November 8th Indeterminacy and Stability

Readings: notes, MWG 17.CDEFH

Student Presentations:

The stability problem via the Debreu-Mantel-Sonnenschein Theorem

Brown-Matzkin Theorem on the testability of equilibrium

November 15th General Equilibrium with Incomplete Markets (Part I)

Readings: notes

Student Presentations:

Economy with non-rational preferences

Economy under a given trading graph

An application of Scarf's computational algorithm for finding equilibria

November 29th General Equilibrium with Incomplete Markets (Part II)

Readings: notes

Student Presentations:

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Collateral

Leverage Cycle