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Advanced Price Theory II: General Equilirium

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/

It is arguable that general equilibrium thinking is what makes economists economists. Recognizing the interdependence of markets and applying tools developed to represent and analyze that interdependence is an essential weapon in the applied economist’s arsenal. At the same time, the complexity of these tools requires that we understand clearly their limits. This course provides an overview of equilibrium analysis for competitive markets. We begin with an overview of the general problem of general equilibrium modeling. Then we review the basic results of pure theory that underlie our applied work: existence and finiteness of equilibria, and the existence of comparative statics. From there we move on to applied general equilibrium modeling. That is, we develop simple, tractable models that allow us to analyze specific policy questions. We will consider both standard perfectly competitive models as well as models characterized by unemployment, imperfect competition, and firm heterogeneity. We conclude with an overview of welfare analysis. That is, we consider the nature, and limits, of normative conclusions that can be based on the sorts of model developed in the first part of the course.

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]

Ross Starr (2011). *General Equilibrium Theory: An Introduction*. (2^{nd} edition) Cambridge: CUP.

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.

Richard Tresch (2015). *Public Finance: A Normative Theory*. San Diego: Academic Press. [Tresch]

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.

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

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

Truman F.</span Bewley (2007). *General Equilibrium, Overlapping Generations Models, and Optimal Growth Theory*. Cambridge, Mass.: Harvard University Press.

At a more advanced level, the following are excellent:

Gerard Debreu (1959). *The Theory of Value*. New York: Wiley.

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

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

James C. Moore (2006). *General Equilibrium and Welfare Economics: An Introduction*. New York: Springer.

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.

Yves Balasko (2009). *The Equilibrium Manifold: Postmodern Developments in the Theory of General Economic Equilibrium*. Cambridge: MIT 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). i>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.

Gareth Myles (1995). *Public Economics*. 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.

On the application to finance:

Yvan Lengwiler (2004). *Microfoundations of Financial Economics: An Introduction to General Equilibrium Asset Pricing*. Princeton: Princeton University Press.

Michael Magill and Martine Quinzii (2002). *Theory of Incomplete Markets, Vol. 1*. 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. Several sets of exercises will be assigned as homeowork. 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.

Policy on examinations. The midterm exam will be given on 10 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: 4 May, 1:00-5:00 (there will be no exceptions so do not make travel plans that conflict with this). Exams must be written in blue books, which you must supply.

Honor code: All students are responsible for knowing and adhering to Tulane University’s Honor Code, available at http://www.tulane.edu/~jruscher/dept/Honor.Code.html .

SACS-Related Material

I am aware that PhD students at Tulane are able to read a standard university syllabus and determine the content of the course and its relation to the major and the individual student’s course of study. However, the administration of Tulane University, along with the Southern Association of Colleges and Schools (SACS–which “accredits” primary and secondary schools as well as all varieties of 2 and 4 year undergraduate programs [with very little in the way of adjustment in rubrics, metrics, etc.]), has determined that you require additional information. I collect this material in a separate section so that you can refer to it, or discard it, as you consider appropriate.

Relevant Program Outcomes Addressed in this Course:

I. Understand and apply the tools of general equilibrium modeling.

II. Understand the limits of equilibrium analysis in terms of existence and finiteness of equilibrium.

III. Understand and apply applied general equilibrium models under perfect and imperfect competition.

IV. Understand mainstream welfare economics.

Learning Objectives–Upon completion of this course you should have developed a practical knowledge of:

Pure general equilibrium theory;

Applied general equilibrium theory; and

Welfare economics.

Topic I. Introduction to GE Thinking

Topic II. Visualizing GE

● The Endowment Model: Edgeworth Boxes & Their Generalization

■ MWG, Chapter 15, sections a-b, 18b

■ Varian, Chapter 17 and section 21.1.

○ Starr, Chapter 3

■ 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.

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

● Production in Simple GE Models

■ MWG, Chapter 15, section C & D.

■ Varian, Chapter 18.

○ Starr, Chapters 2 and 4.

○ 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 III. The Fruits of Abstract GE

● Model Structure & Existence

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

○ Starr Chapters 9-14.

○ Arrow and Debreu. (1954). “Existence of an Equilibrium for a Competitive Economy.” *Econometrica*, V.22-#3, 265-90.

○ McKenzie, Lionel W. (1959). “On the Existence of General Equilibrium for a Competitive Market.” *Econometrica*, V.27-#1, 54-71.

○ McKenzie, Lionel W. (1981). “The Classical Theorem on Existence of Competitive Equilibrium.” *Econometrica*, V.49-#4, 819-41.

○ 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.

○ Richter and Rubinstein. (2015). “Back to Fundamentals: Equilibrium in Abstract Economies.” *American Economic Review*, V.105-#8, 2570-94.

● Problems/Extensions: Nonconvexities (Optional)

○ 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.

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

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

○ Coles and 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 and Incomplete Markets (optional)

○ Varian, Chapter 20.

○ MWG, Chapter 19

○ Starr, Chapter 20

○ Arrow (1953/1964). “The Role of Securities in the Optimal Allocation of Risk-Bearing.” *The Review of Economic Studies*, V.31-#2, 91-96.

○ Debreu (1959). “Uncertainty”. Chapter 7 of *Theory of Value*. New Haven: Yale University Press, pp. 98-102.

○ Radner (1972). “Existence of Equilibrium of Plans, Prices and Price Expectations in a Sequence of Markets”. *Econometrica*; 40-#2, pp. 289-304.

○ Hart (1975). “On the Optimality of Equilibrium When the Market Structure Is Incomplete.” *Journal of Economic Theory*, V.11-#3, 418-43.

○ Duffie and Shafer (1985). “Equilibrium in Incomplete Markets I: Basic Model of Generic Existence”. *Journal of Mathematical Economics*; V.14-#3, pp. 285-300.

○ Geanakoplos and Polemarchakis (1986). “Existence, Regularity, and Constrained Suboptimality of Competitive Allocations when the Asset Market Is Incomplete” in W. Heller, R. Starr, and D. Starrett (eds.), *Essays in Honor of Kenneth Arrow, Vol. 3*. Cambridge University Press, pp. 65-95

○ Geanakoplos (1990). “An Introduction to General Equilibrium with Incomplete Asset Markets.” *Journal of Mathematical Economics*, V.19-#1-2, 1-38.

○ Geanakoplos and Shubik. (1990). “The Capital Asset Pricing Model as a General Equilibrium with Incomplete Markets.” *The GENEVA Papers on Risk and Insurance – Theory*, V.15-#1, 55-71.

○ Varian (1987). “The Arbitrage Principle in Financial Economics.” *The Journal of Economic Perspectives*, V.1-#2, 55-72.

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

● Going Deeper: Finiteness, Comparative Statics

■ MWG, Chapter 17, sections E, F & G

○ Debreu (1970). “Economies with a Finite Set of Equilibria.” *Econometrica*, V.38-#3, 387-92.

○ Dierker (1972). “Two Remarks on the Number of Equilibria of an Economy.” *Econometrica*, V.40-#5, 951-53.

○ Varian (1975). “A Third Remark on the Number of Equilibria of an Economy.” *Econometrica*, V.43-#5/6, 985-86.

○ Nishimura (1978). “A Further Remark on the Number of Equilibria of an Economy.” *International Economic Review*, V.19-#3, 679-85.

○ Smale (1974). “Global Analysis and Economics IV: Finiteness and Stability of Equilibria with General Consumption Sets and Production.” *Journal of Mathematical Economics*, V.1-#2, 119-27.

○ Kehoe (1980). “An Index Theorem for General Equilibrium Models with Production.” *Econometrica*, V.48-#5, 1211-32.

○ 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.

○ Debreu. (1974). “Excess Demand Functions.” *Journal of Mathematical Economics*, V.1-#1, 15-21.

○ Mantel. (1976). “Homothetic Preferences and Community Excess Demand Functions.” *Journal of Economic Theory*, V.12-#2, 197- 201.

■ 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.

○ 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]

○ Kehoe (1985). “Multiplicity of Equilibria and Comparative Statics.” *The Quarterly Journal of Economics*, V.100-#1, 119-47.

○ Brown and Matzkin. (1996). “Testable Restrictions on the Equilibrium Manifold.” *Econometrica*, V.64-#6, 1249-62.

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

Topic IV. Applied General Equilibrium Theory: Positive Analysis

● Introduction to Production for Applied GE

■ Johnson (1971). *The Two-Sector Model of General Equilibrium*. Chicago: Aldine. (Chapter 1 & 2)

■ Melvin (1968). “Production and Trade with Two Factors and Three Goods.” *American Economic Review*, V.58-#5, 1249-68.

■ Lerner (1952). “Factor Prices and International Trade.” *Economica-New Series*, V.19-#73, 1-15.

■ Findlay and Grubert (1959). “Factor Intensities, Technological Progress, and the Terms of Trade.” *Oxford Economic Papers*, V.11-#1, 111-21.

■ Neary (1978). “Short-Run Capital Specificity and Pure Theory of International Trade.” *Economic Journal*, V.88-#351, 488-510.

○ Savosnick (1958). “The Box Diagram and the Production Possibility Curve.” *Ekonomisk Tidskrift*, V.60-#3, 183-97.

○ Krauss & Johnson (1974). *General Equilibrium Analysis*. Chicago: Aldine.

○ Scarth and Warne (1973). “The Elasticity of Substitution and the Shape of the Transformation Curve.” *Economica*, V.40-#159, 299-304.

○ Manning and Melvin (1992). “The Geometric Construction of Production Functions That Are Consistent with an Arbitrary Production-Possibility Frontier.” *Canadian Journal of Economics*, V.25-#2, 485-92.

● Duality Theory for GE: Simple Graphical Analytics

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

■ Woodland (1977). “A Dual Approach to Equilibrium in the Production Sector in International Trade Theory.” *Canadian Journal of Economics*, V.10-#1, 50-68.

■ Cornes (1979). “Further Applications of the Dual Approach to Equilibrium in the Production Sector.” *Canadian Journal of Economics*, V.12-#3, 511-17.

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

○ Jones (1965). “Duality in International Trade: A Geometrical Note.” *The Canadian Journal of Economics and Political Science*, V.31-#3, 390-93.

○ Ikema, Makoto. (1978). “On the Factor-Price Frontier in the Pure Theory of International Trade.” *Hitotsubashi Journal of Economics*, V.18-#2, 62-75.

○ Darrough and Southey. (1977). “Duality in Consumer Theory Made Simple: The Revealing of Roy’s Identity.” *Canadian Journal of Economics*, V.10-#2, 307-17.

○ Weymark (1980). “Duality Results in Demand Theory.” *European Economic Review*, V.14-#3, 377-95.

○ Cornes (1992). *Duality and Modern Economics*. Cambridge: Cambridge University Press.

● Introduction to Comparative Statics for Applied GE

■ Silberberg and Suen, Chapter 18. [Blackboard]

■ MWG, Chapter 15, section d

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

○ Tresch (2014). “A General Equilibrium Model for Public Sector Analysis”. Chapter 2 Tresch, pp. 21-36.

○ 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.

● Comparative Static Example: Factor Market Distortions/Tax Incidence

■ Jones (1971). “Distortions in Factor Markets and General Equilibrium Model of Production.” *Journal of Political Economy*, V.79-#3, 437-59.

■ McLure (1975). “General Equilibrium Incidence Analysis: The Harberger Model after Ten Years.” *Journal of Public Economics*, V.4-#2, 125-61.

○ Whalley (1994). “Operationalizing Walras: Experience with Recent Applied General Equilibrium Tax Models,” in T. Bewley ed. *Advances in Econometrics. *Cambridge: Cambridge University Press, 231-59.

○ Fullerton and Melcalf (2002). “Tax Incidence”. *Handbook of Public Economics, V.4*. Amsterdam: Elsevier, pp. 1787-1872.

○ Myles, Chapter 8.

○ Tresch (2014). “The Theory and Measurement of Tax Incidence”. Chapter 16, pp. 271-296.

○ Harberger (1962). “The Incidence of the Corporation Income Tax”. *Journal of Political Economy*; V.70-#3, pp. 215-240.

● 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. [Blackboard]

■ Woodland (1982). “Intermediate Inputs and Joint Outputs”. Chapter 5 of *International Trade and Resource Allocation*.

Amsterdam: North-Holland, pp. 105-146. [Blackboard]

● 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.

○ 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.

● Applied GE theory: Unemployment in GE

■ Davidson, Martin and Matusz (1988). “The Structure of Simple General Equilibrium-Models with Frictional Unemployment.” *Journal of Political Economy*, V.96-#6, 1267-93.

○ Davidson, Martin and Matusz (1994). “Jobs and Chocolate: Samuelsonian Surpluses in Dynamic Models of Unemployment.” *Review of Economic Studies*, V.61-#1, 173-92.

○ Davidson, Martin and Matusz (1999). “Trade and Search Generated Unemployment.” *Journal of International Economics*, V.48-#2, 271-99.

■ Hosios (1990). “Factor Market Search and the Structure of Simple General Equilibrium Models.” *Journal of Political Economy*, V.98-#2, 325-55.

■ Agell and Lundborg. (1992). “Fair Wages, Involuntary Unemployment and Tax Policies in the Simple General Equilibrium Model.” *Journal of Public Economics*, V.47-#3, 299-320.

■ Kreickemeier and Nelson (2006). “Fair Wages, Unemployment and Technological Change in a Global Economy.” *Journal of International Economics*, V.70-#2, 451-69.

● Applied GE Theory: Monopolistic Competition

■ Dixit and Stiglitz (1977). “Monopolistic Competition and Optimum Product Diversity.” *American Economic Review*, V.67-#3, 297-308.

■ Ethier (1982). “National and International Returns to Scale in the Modern Theory of International Trade.” *American Economic Review*, V.72-#3, 389-405.

■ Francois and Nelson. (2002). “A Geometry of Specialisation.” *Economic Journal*, V.112-#481, 649-78.

■ Neary (2001). “Of Hype and Hyperbolas: Introducing the New Economic Geography.” *Journal of Economic Literature*, V.39-#2, 536-61.

○ Romer, Paul M. (1987). “Growth Based on Increasing Returns Due to Specialization.” *The American Economic Review*, V.77-#2, 56-62.

○ Matusz (1996). “International Trade, the Division of Labor, and Unemployment.” *International Economic Review*, V.37-#1, 71-84.

○ Altenburg and Brenken. (2008). “Effort, Trade, and Unemployment.” *The Canadian Journal of Economics*, V.41-#3, 864-93.

● Applied GE Theory: Continuum Economies

■ Dornbusch, Fischer and Samuelson. (1977). “Comparative Advantage, Trade, and Payments in a Ricardian Model with a Continuum of Goods.” *The American Economic Review*, V.67-#5, 823-39.

○ Wilson (1980). “On the General Structure of Ricardian Models with a Continuum of Goods: Applications to Growth, Tariff Theory, and Technical Change.” *Econometrica*, V.48-#7, 1675-702.

■ Eaton, Jonathan and Samuel Kortum. (2002). “Technology, Geography, and Trade.” *Econometrica*, V.70-#5, 1741-79.

■ Alvarez and Lucas. (2007). “General Equilibrium Analysis of the Eaton–Kortum Model of International Trade.” *Journal of Monetary Economics*, V.54-#6, 1726-68.

■ Caliendo, Parro;, Rossi-Hansberg and Sarte (2014). “The Impact of Regional and Sectoral Productivity Changes on the US Economy,”* NBER Working Paper*, #20168.

○ Neary (2015). “International Trade in General Oligopolistic Equilibrium,”* University of Oxford, Department of Economics Discussion Paper*, #769.

● Applied GE Theory: Firm Heterogeneity

■ Melitz (2003). “The Impact of Trade on Intra-Industry Reallocations and Aggregate Industry Productivity.” *Econometrica*, V.71-#6, 1695-725.

■ Bernard, Redding and Schott. (2007). “Comparative Advantage and Heterogeneous Firms.” *Review of Economic Studies*, V.74-#1, 31-66.

■ Melitz and Ottaviano. (2008). “Market Size, Trade, and Productivity.” *Review of Economic Studies*, V.75-#1, 295-316.

■ Yeaple (2005). “A Simple Model of Firm Heterogeneity, International Trade, and Wages.” *Journal of International Economics*, V.65-#1, 1-20.

■ Bernard, Jensen, Redding & Schott (forth.). “Global Firms”. *Journal of Economic Literature*.

○ Egger and Kreickemeier. (2009). “Firm Heterogeneity and the Labor Market Effects of Trade Liberalization.” *International Economic Review*, V.50-#1, 187-216.

○ Helpman, Itskhoki and Redding. (2010). “Inequality and Unemployment in a Global Economy.” *Econometrica*, V.78-#4, 1239-83.

Topic V. Applied Welfare Economics

● What Do We Want from Welfare Economics & Can We Have It?

■ Robbins (1938). “Interpersonal Comparisons of Utility: A Comment.” *The Economic Journal*, V.48-#192, 635-41.

■ Kaldor (1939). “Welfare Propositions of Economics and Interpersonal Comparisons of Utility.” *The Economic Journal*, V.49-#195, 549-52.

■ Hicks (1939). “The Foundations of Welfare Economics.” *The Economic Journal*, V.49-#196, 696-712.

○ Bergson (1938). “A Reformulation of Certain Aspects of Welfare Economics.” *The Quarterly Journal of Economics*, V.52-#2, 310-34.

■ Samuelson (1947). “Welfare Economics”. Chapter 8, *Foundations of Economic Analysis*. Cambridge: Harvard University Press.

○ Samuelson (1950). “Evaluation of Real National Income.” *Oxford Economic Papers*, V.2-#1, 1-29.

○ Baldwin (1953). “A Comparison of Welfare Criteria.” *The Review of Economic Studies*, V.21-#2, 154-61.

○ Samuelson (1956). “Social Indifference Curves.” *The Quarterly Journal of Economics*, V.70-#1, 1-22.

○ Samuelson (1981). “Bergsonian Welfare Economics,” in S. Rosefielde ed *Economic Welfare and the Economics of Soviet Socialism: Essays in Honor of Abram Bergson. *Cambridge: Cambridge University Press, 223-66.

○ Bator (1957). “The Simple Analytics of Welfare Maximization.” *The American Economic Review*, V.47-#1, 22-59.

■ Chipman and Moore (1978). “The New Welfare Economics 1939-1974.” *International Economic Review*, V.19-#3, 547-84.

■ Cooter and Rappoport. (1984). “Were the Ordinalists Wrong About Welfare Economics?” *Journal of Economic Literature*, V.22-#2, 507-30.

● Fundamental Theorems of Welfare Economics

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

■ MWG, Chapter 16

■ Arrow (1951). “An Extension of the Basic Theorems of Classical Welfare Economics”. *Second Berkeley Symposium on Mathematical Statistics and Probability*. Berkeley: University of California Press, pp. 507-532.

■ 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. [Blackboard]

■ Piccione and Rubinstein. (2007). “Equilibrium in the Jungle.” *The Economic Journal*, V.117-#522, 883-96.

● Applied Welfare Economics,1: Welfare Measurement

■ MWG, Chapter 10 e.

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

○ Hicks, J. R. (1941). “The Rehabilitation of Consumers’ Surplus.” *The Review of Economic Studies*, V.8-#2, 108-16.

○ Harberger (1971). “Three Basic Postulates for Applied Welfare Economics: An Interpretive Essay.” *Journal of Economic Literature*, V.9-#3, 785-97.

○ Silberberg (1972). “Duality and the Many Consumer’s Surpluses.” *The American Economic Review*, V.62-#5, 942-52.

○ Willig (1976). “Consumer’s Surplus without Apology.” *The American Economic Review*, V.66-#4, 589-97.

○ Smith and Banzhaf. (2004). “A Diagrammatic Exposition of Weak Complementarity and the Willig Condition.” *American Journal of Agricultural Economics*, V.86-#2, 455-66.

○ Martin and Alston. (1997). “Producer Surplus without Apology? Evaluating Investments in RD.” *Economic Record*, V.73-#221, 146-58.

○ Chipman and Moore. (1980). “Compensating Variation, Consumer’s Surplus, and Welfare.” *The American Economic Review*, V.70-#5, 933-49.

○ Hausman, Jerry A. (1981). “Exact Consumer’s Surplus and Deadweight Loss.” *The American Economic Review*, V.71-#4, 662-76.

■ 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. [covers one person theory]

● Applied Welfare Economics, 2: Distortions, Second-best, and Policy

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

■ MWG, Chapter 22, sections a-d

○ Myles, Chapter 10. [Blackboard]

○ Tresch, Chapter 12

○ 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.

○ Lipsey and Lancaster. (1956). “The General Theory of Second Best.” *The Review of Economic Studies*, V.24-#1, 11-32.

○ Davis and Whinston. (1965). “Welfare Economics and the Theory of Second Best.” *The Review of Economic Studies*, V.32-#1, 1-14.

○ McManus (1967). “Private and Social Costs in the Theory of Second Best.” *The Review of Economic Studies*, V.34-#3, 317-21.

○ Davis and Whinston (1967). “Piecemeal Policy in the Theory of Second Best.” *The Review of Economic Studies*, V.34-#3, 323-31.

○ McFadden (1969). “A Simple Remark on the Second Best Pareto Optimality of Market Equilibria.” *Journal of Economic Theory*, V.1-#1, 26-38.

○ Foster and Sonnenschein. (1970). “Price Distortion and Economic Welfare.” *Econometrica*, V.38-#2, 281-97.

○ Sontheimer (1971). “An Existence Theorem for the Second Best.” *Journal of Economic Theory*, V.3-#1, 1-22.

○ Kawamata (1974). “Price Distortion and Potential Welfare.” *Econometrica*, V.42-#3, 435-60.

○ Rader (1976). “The Welfare Loss from Price Distortions.” *Econometrica*, V.44-#6, 1253-57.

○ Roberts (1992). “When Does a Decrease in a Distortion Increase Welfare?” *Economics Letters*, V.39-#1, 37-42.

○ Dixit (1975). “Welfare Effects of Tax and Price Changes.” *Journal of Public Economics*, V.4-#2, 103-23. [Dixit & Munk, correction, 1977, *JPubE*, V.8-#1, pp. 103-107]

○ Kawamata (1977). “Price Distortion and the Second Best Optimum.” *The Review of Economic Studies*, V.44-#1, 23-29.

○ Hatta (1977). “A Theory of Piecemeal Policy Recommendations.” *The Review of Economic Studies*, V.44-#1, 1-21.

○ Turunen-Red (1990). “On the Hatta Normality Condition and Tax Reforms.” *Journal of Public Economics*, V.43-#2, 253-62.

■ Coase (1960). “The Problem of Social Cost”. *Journal of Law and Economics*, V.3-#, pp. 1-44.

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

● Applied Welfare Economics, 3: Optimal Taxation

■ Myles, Chapter 4. [Blackboard]

○ Tresch (2014). Chapters 13 & 14

○ 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.

■ 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.

○ Diewert (1978). “Optimal Tax Perturbations.” *Journal of Public Economics*, V.10-#2, 139-77.

○ Guesnerie (1977). “On the Direction of Tax Reform.” *Journal of Public Economics*, V.7-#2, 179-202.

○ Weymark (1979). “A Reconciliation of Recent Results in Optimal Taxation Theory.” *Journal of Public Economics*, V.12-#2, 171-89.

○ Weymark (1981). “Undominated Directions of Tax Reform.” *Journal of Public Economics*, V.16-#3, 343-69.

○ Dixit (1979). “Price Changes and Optimum Taxation in a Many-Consumer Economy.” *Journal of Public Economics*, V.11-#2, 143-57.

○ Tirole and Guesnerie. (1981). “Tax Reform from the Gradient Projection Viewpoint.” *Journal of Public Economics*, V.15-#3, 275-93.

● Applied Welfare Economics, 4: Collectivist Planning and GE (Optional Topic)

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

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

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

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

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

○ Makowski and 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 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 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 1994. *Whither Socialism?* Cambridge: MIT Press.

● Social Choice Theory: A (Very) Brief Introduction

■ MWG, Chapter 21

○ Arrow (1963). *Social Choice and Individual Values*. New York: Wiley.

○ Kelly (1988). *Social Choice Theory: An Introduction*. Berlin: Springer-Verlag.

■ Geanakoplos (2005). “Three Brief Proofs of Arrow’s Impossibility Theorem.” *Economic Theory*, V.26-#1, 211-15.

■ Reny (2001). “Arrow’s Theorem and the Gibbard-Satterthwaite Theorem: A Unified Approach.” *Economics Letters*, V.70-#1, 99-105.

■ Fleurbaey, Marc and Philippe Mongin. (2005). “The News of the Death of Welfare Economics Is Greatly Exaggerated.” *Social Choice and Welfare*, V.25-#2-3, 381-418.

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