Professor: Douglas Nelson

Office: Tilton 108 (Murphy Institute), Phone: 865-5317

Office Hours: Tuesday and Thursday, 3:30-5:30

Phone: 865-5317

email: dnelson@tulane.edu

Webpage: http://www.tulane.edu/~dnelson/

This course provides an overview of equilibrium analysis for competitive markets. The course is organized in four sections. An introductory section illustrates the main themes of the course in simple partial and general equilibrium environments. The second part of the course develops the main positive results from abstract general equilibrium theory. The third and fourth part of the course introduces students to the analysis of general equilibrium systems. Specifically, part III introduces positive analysis in terms of comparative statics, while part IV introduces students to welfare economics.

Evaluation: Your performance in this course will be evaluated on the basis of two examinations (worth 100 points each); and a number of problem sets (worth a total of 100 points). All students are expected to do all the expected reading, complete all problem sets, and actively participate in all classes.

Readings and exercises for the course will be drawn from the following core texts:

Andreu Mas-Colell, Michael Whinston, and Jerry Green (1995). *Microeconomic Theory*.
New York: Oxford University Press. [MWG]

Hal Varian (1992). *Microeconomic Analysis*. New York: Norton. [Varian]

Eugene Silberberg and Wing Suen (2001). *The Structure of Economics: A Mathematical
Analysis*. Boston: Irwin/McGraw Hill. [Silberberg and Suen]

Alan Woodland (1982). *International Trade and Resource Allocation*. Amsterdam: North
Holland.

Gareth Myles (1995). *Public Economics*. Cambridge: Cambridge University Press.

In addition, there will be a large number of articles available electronically.

The main substantive material of this course has been covered in a number of excellent texts. On pure general equilibrium theory, at a relatively elementary level the following are excellent:

Peter Newman (1965). *The Theory of Exchange*. Englewood Cliffs: Prentice-Hall.

James Quirk and Rubin Saposnik (1968). *Introduction to General Equilibrium Theory
and Welfare Economics*. New York: McGraw Hill.

Werner Hildenbrand and Alan Kirman (1988). *Equilibrium Analysis: Variations on
Themes by Edgeworth and Walras*. Amsterdam: North-Holland.

Ross Starr (1997). *General Equilibrium Theory: An Introduction*. Cambridge: CUP.

Bryan Ellickson (1993). *Competitive Equilibrium: Theory and Applications*. Cambridge:
CUP.

Alan Kirman, ed. (1998). *Elements of General Equilibrium Analysis*. Oxford: Blackwell.

At a more advanced level, the following are excellent:

Kenneth Arrow and Frank Hahn (1971). *General Competitive Analysis*. Amsterdam:
North-Holland.

Lionel McKenzie (2002). *Classical General Equilibrium Theory*. Cambridge: MIT Press.

Andreu Mas-Colell (1985). *The Theory of General Equilibrium: A Differentiable
Approach*. Cambridge: CUP/Econometric Society.

Yves Balasko (1988). *Foundations of the Theory of General Equilibrium*. San Diego:
Academic Press.

C. Aliprantis, D. Brown, and O. Burkinshaw (1990). *Existence and Optimality of
Competitive Equilibrium*. Berlin: Springer-Verlag.

On the application to public economics, texts emphasizing modern general equilibrium methods include:

David Starrett (1988). *Foundations of Public Economics*. Cambridge: Cambridge
University Press.

Jean-Jacques Laffont (1988). *Fundamentals of Public Economics*. Cambridge: MIT Press.

Roger Guesnerie (1995). *A Contribution to the Pure Theory of Taxation*. Cambridge:
Cambridge University Press.

On the application to trade:

Avinash Dixit and Victor Norman (1980). *Theory of International Trade*. Cambridge:
Cambridge University Press.

Kar-yiu Wong (1995). *International Trade in Goods and Factor Mobility*. Cambridge:
MIT Press.

Those interested in computational methods of general equilibrium analysis may want to consult:

John Shoven and John Whalley (1992). *Applying General Equilibrium*. Cambridge:
Cambridge University Press.

Victor Ginsburgh and Michiel Keyzer (1997). *The Structure of Applied General
Equilibrium Models*. Cambridge: MIT Press.

Joseph Francois and Kenneth Reinert, eds. (1997). *Applied Methods for Trade Policy
Analysis: A Handbook*. Cambridge: Cambridge University Press.

Finally, for those with an interest in the historical and philosophical background to general equilibrium theory, the place to start is a series of excellent books by E. Roy Weintraub:

E.R. Weintraub (1979). *Microfoundations*. Cambridge: CUP.

E.R. Weintraub (1986). *General Equilibrium Analysis: Essays in Appraisal*. Cambridge:
CUP.

E.R. Weintraub (1991). *Stabilizing Dynamics: Constructing Economic Knowledge*.
Cambridge: CUP.

E.R. Weintraub (2002). *How Economics Became a Mathematical Science*. Durham: Duke
University Press.

Homework. The syllabus that follows this course description lists the reading that you are expected to have done for the lecture on the listed date. For each date, in addition to the reading, the syllabus lists several homework problems. Homework is due on or before the first class in which that material is discussed. Late homework will not be accepted, and will receive a score of 0. The percent of total available homework credit will be taken as your homework score. For example, if you answer 90% of the homework questions correctly, your homework score is 90.

Examination format. Both exams will have the following format: about 40% short answer questions and about 60% essays. In general there will be more questions of both types than must be answered, so you will have some choice (though there is often one mandatory question which everyone must answer). Exams must be written in blue books, which you must supply.

Policy on examinations. The midterm exam will be given on 9 March. Unless you have a standard university accepted excuse for missing the exam (e.g. health with standard university form), you must take the exams at their scheduled time. The final examination will only be given on the scheduled date: 10 May, 8:00-12:00 (there will be no exceptions so do not make travel plans that conflict with this).

Topic I. Introduction

● Partial Equilibrium Analysis of Competitive Equilibrium

■ Varian, Chapter 13.

■ MWG, Chapter 10 a-d and f.

● General Equilibrium: Applying Microeconomic Tools to Macroeconomic Questions, Pure Exchange

■ MWG, Chapter 15, sections a-b

■ Varian, Chapter 17 and section 21.1.

■ Shapley and Shubik (1977). “An Example of a Trading Economy
with Three Competitive Equilibria”. *Journal of Political Economy*;
V.85-#4, pp. 873-875.

■ Debreu and Scarf (1963). “A Limit Theorem on the Core of an
Economy”. *International Economic Review*; V.4-#3, pp. 235-246.

■ Aumann (1964). “Markets with a Continuum of Traders”.
*Econometrica*; V.32-#1/2, pp. 39-50.

■ Shubik (1984). “Two-Sided Markets: The Edgeworth Game”.
Chapter 10 of *A Game Theoretic Approach to Political Economy*.
Cambridge: MIT Press, pp. 252-285. [optional]

■ Hildenbrand and Kirman (1988). “Introduction”. In *Equilibrium
Analysis*. Amsterdam: North-Holland, pp. 1-49. [optional]

● General Equilibrium: Applying Microeconomic Tools to Macroeconomic Questions, Simple Economies with Production

■ MWG, Chapter 15, section c.

■ Varian, Chapter 18.

■ Koopmans (1957). “Allocation of Resources and the Price System”.
Essay 1 of *Three Essays on the State of Economic Science*. New
York: McGraw Hill, pp. 3-126. [especially pp. 1-66.]

Topic II. Pure General Equilibrium Theory

● Fundamental Theorems of Welfare Economics

■ Silberberg and Suen, Chapter 19, sections 1-3. [ERes]

■ MWG, Chapter 16

■ Hammond (1998). “The Efficiency Theorems and Market Failure”.
Chapter 6 in A.P. Kirman, ed., *Elements of General Equilibrium
Analysis*. Oxford: Basil Blackwell, pp. 211-240. [ERes]

● Characterizing Equilibrium and Proving Existence

■ MWG, Chapter 17, sections a-d and f, appendix B.

■ Geanakoplos (2003). “Nash and Walras Equilibrium via Brouwer”.
*Economic Theory*; V.21-#2/3, pp. 585-603.

■ Debreu (1998). “Existence”. Chapter 2 in A.P. Kirman, ed.,
*Elements of General Equilibrium Analysis*. Oxford: Basil Blackwell,
pp. 10-37. [optional]

● Collectivist Planning and GE (Optional Topic)

■ Lerner, Abba P. (1934). “Economic Theory and the Socialist
Economy”. *Review of Economic Studies*; V.2-# , pp. 51-61.

■ Lange, Oskar (1936). “On the Economic Theory of Socialism: Part
One.” *The Review of Economic Studies*, 4(1), 53-71.

■ Lange, Oskar. 1937. “On the Economic Theory of Socialism: Part
Two.” *The Review of Economic Studies*, 4(2), 123-42.

■ Hayek, Friedrich (1945). “The Use of Knowledge in Society.”
*American Economic Review*, V.35-#4, 519-30.

■ Hurwicz, Leonid (1973). “The Design of Resource Allocation
Mechanisms.” *American Economic Review*, V.63-#2, 1-30.

■ Makowski, Louis and Joseph M. Ostroy. 1993. “General
Equilibrium and Market Socialism: Clarifying the Logic of
Competitive Markets,” in P. K. Bardhan and J. E. Roemer eds,
*Market Socialism: The Current Debate. *New York: Oxford
University Press, 69-88.

■ Stiglitz, Joseph E. 1993. “Market Socialism and Neoclassical
Economics,” in P. K. Bardhan and J. E. Roemer eds, *Market
Socialism: The Current Debate. *New York: Oxford University Press,
21-41.

■ Kornai, Janos. 1993. “Market Socialism Revisited,” in P. K.
Bardhan and J. E. Roemer eds, *Market Socialism: The Current
Debate. *New York: Oxford University Press, 42-68.

■ Stiglitz, Joseph E. 1994. *Whither Socialism?* Cambridge: MIT
Press.

● Problems/Extensions: Nonconvexities

■ MWG, Chapter 17, section I

■ Chipman (1970). “External Economies of Scale and Competitive
Equilibrium”. *Quarterly Journal of Economics*; V.84-#3, pp. 347-363.

■ Mayer (1974). “Homothetic Production Functions and the Shape of
the Production Possibility Locus”. *Journal of Economic Theory*; V.8-#2, pp. 101-110. [ERes]

■ Starrett (1971). “Fundamental Non-Convexities in the Theory of
Externalities”. *Journal of Economic Theory*; V.4-#2, pp. 180-199.
[ERes]

■ Cornes (1980). “External Effects: An Alternative Formulation”.
*European Economic Review*; V.14-#?, pp. 307-321. [optional]

■ Coles, Jeffrey L. and Peter J. Hammond. 1995. “Walrasian
Equilibrium without Survival: Equilibrium, Efficiency, and Remedial
Policy,” in K. Basu, P. Pattanaik and K. Suzumura eds, *Welfare and
Development: A Festschrift in Honour of Amartya K. Sen. *Oxford:
Oxford University Press, 32-64.

● Problems/Extensions: Uncertainty

■ Varian, Chapter 20.

■ MWG, Chapter 19

■ Hens (1998). “Incomplete Markets”. Chapter 5 in A.P. Kirman, ed.,
*Elements of General Equilibrium Analysis*. Oxford: Basil Blackwell,
pp. 139-210. [optional]

● General Equilibrium Comparative Statics?: The Sonnenschein-Debreu-Mantel Result

■ MWG, Chapter 17, section d-f.

■ Saari (1995). “The Mathematical Complexity of Simple
Economies”. *Notices of the American Mathematical Society*; V.42-#2,
pp. 222-230.

■ Kirman (1989). “The Intrinsic Limits of Modern Economic Theory:
The Emperor Has No Clothes”. *Economic Journal*; V.99-#395, pp.
126-139.

■ Sonnenschein (1973). “Do Walras' Indentity and Continuity
Characterize the Class of Community Excess Demand Functions?”.
*Journal of Economic Theory*; V.6-#4, pp. 345-354. [ERes]

■ Kemp and Shimomura (2002). “The Sonnenschein-Debreu-Mantel
Proposition and the Theory of International Trade”. *Review of
International Economics*; V.10-#4, pp. 671-679. [optional]

■ Nachbar (2002). “General Equilibrium Comparative Statics”.
*Econometrica**; V.70-#5, pp. 2065-2974. [optional]*

No Class: Thursday, 11 March

Topic III. Applied General Equilibrium Theory: Positive Analysis

● Introduction to Comparative Statics for Applied GE

■ Silberberg and Suen, Chapter 18. [ERes]

■ Woodland (1982). “The Production Sector”. Chapter 3 of
*International Trade and Resource Allocation*. Amsterdam: North-Holland, pp. 39-65. [ERes]

■ MWG, Chapter 15, section d

■ Jones (1965). “The Structure of Simple General Equilibrium
Models”. *Journal of Political Economy*; V.73-#6, pp. 557-572.
[optional]

■ Mussa (1979). “The Two Sector Model in Terms of Its Dual: A
Geometric Exposition”. *Journal of International Economics*; V.9-#4,
pp. 513-526. [optional]

■ Hale, Lady, Maybee, and Quirk (1999). “The Competitive
Equilibrium: Comparative Statics”. Chapter 7 in *Nonparametric
Comparative Statics and Stability*. Princeton: Princeton University
Press, pp. 170-205. [optional]

● Maximum Value Functions and Comparative Statics for General Equilibrium Analysis

■ MWG, Chapter 17, section g

■ Woodland (1982). “Comparative Statics of the Production Sector”.
Chapter 4 of *International Trade and Resource Allocation*.
Amsterdam: North-Holland, pp. 67-103. [ERes]

■ Woodland (1982). “Intermediate Inputs and Joint Outputs”.
Chapter 5 of *International Trade and Resource Allocation*.
Amsterdam: North-Holland, pp. 105-146. [ERes]

● Applied General Equilibrium Theory: The Stolper-Samuelson
Theorem, from 2 × 2 to *m* × *n*.

■ Chipman (1969). “Factor Price Equalization and the Stolper-Samuelson Theorem”. *International Economic Review*; V.10-#3, pp.
399-406.

■ Jones and Scheinkman (1977). “The Relevance of the Two-Sector
Production Model in Trade Theory”. *Journal of Political Economy*;
V.85-#5, pp. 909-935.

■ Ethier (1982). “The General Role of Factor Intensity in the
Theorems of International Trade”. *Economics Letters*; V.10-#3/4, pp.
337-342. [ERes]

■ Ethier (1984). “Higher Dimensional Issues in Trade Theory”. in R.
Jones and P. Kenen, eds. *Handbook of International Economics--Vol.
1*. Amsterdam: North-Holland, 131-184. [optional]

Topic IV. Applied Welfare Economics

● Applied Welfare Economics,1: Introduction

■ MWG, Chapter 10 e.

■ Silberberg and Suen, Chapter 19, section 7. [ERes]

■ Blackorby and Donaldson (1985). “Consumers’ Surpluses and
Consistent Cost-Benefit Tests”. *Social Choice and Welfare*; V.1-#4,
pp. 251-262. [optional]

■ Blackorby and Donaldson (1990). “The Case Against the Use of
the Sum of Compensating Variations in Cost-Benefit Analysis”.
*Canadian Journal of Economics*; V.23-#3, pp. 471-494.

■ Blackorby and Donaldson (1999). “Market Demand Curves and
Dupuit-Marshall Consumers’ Surpluses: A General Equilibrium
Analysis”. *Mathematical Social Sciences*; V37-#2, pp. 139-163.

■ Ahlheim (1998). “Measures of Economic Welfare”. In Barberà,
Hammond, and Seidl, eds. *Handbook of Utility Theory*. Dordrecht:
Kluwer, pp. 483-568. [Optional: covers one person theory]

● Applied Welfare Economics, 2: Commodity Taxation

■ Myles, Chapter 4. [ERes]

■ Diamond and Mirrlees (1971). “Optimal Taxation and Public
Production, I: Production Efficiency”. *American Economic Review*;
V.61-#1, pp. 8-27. [optional]

■ Diamond and Mirrlees (1971). “Optimal Taxation and Public
Production, II: Tax Rules”. *American Economic Review*; V.61-#3, pp.
261-278. [optional]

■ Diamond and McFadden (1974). “Some Uses of the Expenditure
Function in Public Finance”. *Journal of Public Economics*; V.3-#1,
pp. 3-21. [ERes]

■ Greenberg and Denzau (1988). “Profit and Expenditure Functions
in Basic Public Finance: An Expository Note”. *Economic Inquiry**;
V.26-#1, pp. 145-158.*

■ Deaton (1981). “Optimal Taxes and the Structure of Preferences”.
*Econometrica*; V.49-#5, pp. 1245-1260.

■ Stern (1986). “A Note on Commodity Taxation: The Choice of
Variable and the Slutsky, Hessian and Antonelli Matrices (SHAM)”.
*Review of Economic Studies*; V.53-#2, pp. 293-299.

● Applied Welfare Economics, 3: Distortions, Second-best, and Policy

■ Silberberg and Suen, Chapter 19, sections 5 and 6. [ERes]

■ MWG, Chapter 22, sections a-d

■ Myles, Chapter 10. [ERes]

■ Hammond (1998). “The Efficiency Theorems and Market Failure”.
Chapter 6 in A.P. Kirman, ed., *Elements of General Equilibrium
Analysis*. Oxford: Basil Blackwell, pp. 240-260. [ERes]

■ Hurwicz (1999). “Revisiting Externalities”. *Journal of Public
Economics Theory*; V.1-#2, pp. 225-245.

● Social Choice Theory: A (Very) Brief Introduction

■ MWG, Chapter 21

■ Mongin and d’Aspermont (1998). “Utility Theory and Ethics”. In
Barberà, Hammond, and Seidl, eds. *Handbook of Utility Theory*.
Dordrecht: Kluwer, pp. 371-481. [optional]