Edited by the late Kenneth J. Arrow, formerly Joan Kenney Professor of Economics and Professor of Operations Research Emeritus, Stanford University, US and the late Gérard Debreu, former University Professor and Class of 1958 Professor of Economics and Mathematics Emeritus, University of California at Berkeley, US and European University Institute, Italy

• Contents:AcknowledgementsPrefaceMark BlaugPART IGENERAL EQUILIBRIUM 1. Erik Lindahl (1939/1970), ‘The Traditional Setting of the Pricing Problem’, ‘Perfect Foresight and Stationary Conditions’, ‘Perfect Foresight and Dynamic Conditions’, ‘Imperfect Foresight’ and ‘The Problem of Balancing the Budget’2. Karl Schlesinger (1934), ‘Über die Produktionsgleichungen der Ökonomischen Wertlehre’3. Abraham Wald (1951), ‘On Some Systems of Equations of Mathematical Economics’ [translation of ‘Über einige Gleichungssysteme der mathematischen Ökonomie]’4. J. v. Neumann (1946), ‘A Model of General Economic Equilibrium’ [translation of ‘Über ein Ökonomisches Gleichungssystem und eine Verallgemeinerung des Brouwerschen Fixpunktsatzes]’5. John F. Nash, Jr (1950), ‘Equilibrium Points in N-Person Games’6. K.J. Arrow (1964), ‘The Role of Securities in the Optimal Allocation of Risk-bearing’ [translation of ‘Le Rôle des Valeurs Boursières pour la Répartition la Meilleure des Risques]’7. Lionel McKenzie (1954), ‘On Equilibrium in Graham’s Model of World Trade and Other Competitive Systems’8. Kenneth J. Arrow and Gerard Debreu (1954), ‘Existence of an Equilibrium for a Competitive Economy’9. Herbert Scarf (1960), ‘Some Examples of Global Instability of the Competitive Equilibrium’10. Herbert Scarf (1962), ‘An Analysis of Markets with a Large Number of Participants’11. Gerard Debreu and Herbert Scarf (1963), ‘A Limit Theorem on the Core of an Economy’12. Robert J. Aumann (1964), ‘Markets with a Continuum of Traders’13. Herbert Scarf (1967), ‘On the Computation of Equilibrium Prices’14. Roy Radner (1968), ‘Competitive Equilibrium Under Uncertainty’15. Gerard Debreu (1970), ‘Economies with a Finite Set of Equilibria’16. Hugo Sonnenschein (1972), ‘Market Excess Demand Functions’17. Sanford J. Grossman and Joseph E. Stiglitz (1976), ‘Information and Competitive Price Systems’18. Sanford J. Grossman (1977), ‘A Characterization of the Optimality of Equilibrium in Incomplete Markets’19. Werner Hildenbrand (1983), ‘On the "Law of Demand”’20. Darrell Duffie and Wayne Shafer (1985), ‘Equilibrium in Incomplete Markets I: A Basic Model of Generic Existence’21. Darrell Duffie and Wayne Shafer (1986), ‘Equilibrium in Incomplete Markets II: Generic Existence in Stochastic Economies’22. John Geanakoplos and Andreu Mas-Colell (1989), ‘Real Indeterminacy with Financial Assets’PART IIWELFARE ECONOMICS 23. Harold Hotelling (1938), ‘The General Welfare in Relation to Problems of Taxation and of Railway and Utility Rates’24. Abram Burk (1938), ‘A Reformulation of Certain Aspects of Welfare Economics’25. Nicholas Kaldor (1939), ‘Welfare Propositions of Economics and Inter-personal Comparisons of Utility’26. Kenneth J. Arrow (1951), ‘An Extension of the Basic Theorems of Classical Welfare Economics’27. Tibor Scitovsky (1954), ‘Two Concepts of External Economies’PART IIISOCIAL CHOICE28. Howard R. Bowen (1944), ‘The Interpretation of Voting in the Allocation of Economic Resources’29. Duncan Black (1948), ‘On the Rationale of Group Decision-making’30. Amartya Sen and Prasanta K. Pattanaik (1969), ‘Necessary and Sufficient Conditions for Rational Choice under Majority Decision’31. S.Ch. Kolm (1969/2001), ‘The Optimal Production of Social Justice’32. M.V. Posner and H. Tulkens (1969), ‘Discussion of Mr Kolm’s Paper’33. Amartya Sen (1970), ‘The Impossibility of a Paretian Liberal’34. Douglas H. Blair, Georges Bordes, Jerry S. Kelly and Kotaro Suzumura (1976), ‘Impossibility Theorems without Collective Rationality’35. Peter J. Hammond (1976), ‘Equity, Arrow’s Conditions, and Rawls’ Difference Principle’36. Kevin W.S. Roberts (1980), ‘Possibility Theorems with Interpersonally Comparable Welfare Levels’Name Index

Edited by the late Kenneth J. Arrow, formerly Joan Kenney Professor of Economics and Professor of Operations Research Emeritus, Stanford University, US and the late Gérard Debreu, former University Professor and Class of 1958 Professor of Economics and Mathematics Emeritus, University of California at Berkeley, US and European University Institute, Italy

• Contents:AcknowledgementsPrefaceMark BlaugPART IGENERAL EQUILIBRIUM 1. Erik Lindahl (1939/1970), ‘The Traditional Setting of the Pricing Problem’, ‘Perfect Foresight and Stationary Conditions’, ‘Perfect Foresight and Dynamic Conditions’, ‘Imperfect Foresight’ and ‘The Problem of Balancing the Budget’2. Karl Schlesinger (1934), ‘Über die Produktionsgleichungen der Ökonomischen Wertlehre’3. Abraham Wald (1951), ‘On Some Systems of Equations of Mathematical Economics’ [translation of ‘Über einige Gleichungssysteme der mathematischen Ökonomie]’4. J. v. Neumann (1946), ‘A Model of General Economic Equilibrium’ [translation of ‘Über ein Ökonomisches Gleichungssystem und eine Verallgemeinerung des Brouwerschen Fixpunktsatzes]’5. John F. Nash, Jr (1950), ‘Equilibrium Points in N-Person Games’6. K.J. Arrow (1964), ‘The Role of Securities in the Optimal Allocation of Risk-bearing’ [translation of ‘Le Rôle des Valeurs Boursières pour la Répartition la Meilleure des Risques]’7. Lionel McKenzie (1954), ‘On Equilibrium in Graham’s Model of World Trade and Other Competitive Systems’8. Kenneth J. Arrow and Gerard Debreu (1954), ‘Existence of an Equilibrium for a Competitive Economy’9. Herbert Scarf (1960), ‘Some Examples of Global Instability of the Competitive Equilibrium’10. Herbert Scarf (1962), ‘An Analysis of Markets with a Large Number of Participants’11. Gerard Debreu and Herbert Scarf (1963), ‘A Limit Theorem on the Core of an Economy’12. Robert J. Aumann (1964), ‘Markets with a Continuum of Traders’13. Herbert Scarf (1967), ‘On the Computation of Equilibrium Prices’14. Roy Radner (1968), ‘Competitive Equilibrium Under Uncertainty’15. Gerard Debreu (1970), ‘Economies with a Finite Set of Equilibria’16. Hugo Sonnenschein (1972), ‘Market Excess Demand Functions’17. Sanford J. Grossman and Joseph E. Stiglitz (1976), ‘Information and Competitive Price Systems’18. Sanford J. Grossman (1977), ‘A Characterization of the Optimality of Equilibrium in Incomplete Markets’19. Werner Hildenbrand (1983), ‘On the "Law of Demand”’20. Darrell Duffie and Wayne Shafer (1985), ‘Equilibrium in Incomplete Markets I: A Basic Model of Generic Existence’21. Darrell Duffie and Wayne Shafer (1986), ‘Equilibrium in Incomplete Markets II: Generic Existence in Stochastic Economies’22. John Geanakoplos and Andreu Mas-Colell (1989), ‘Real Indeterminacy with Financial Assets’PART IIWELFARE ECONOMICS 23. Harold Hotelling (1938), ‘The General Welfare in Relation to Problems of Taxation and of Railway and Utility Rates’24. Abram Burk (1938), ‘A Reformulation of Certain Aspects of Welfare Economics’25. Nicholas Kaldor (1939), ‘Welfare Propositions of Economics and Inter-personal Comparisons of Utility’26. Kenneth J. Arrow (1951), ‘An Extension of the Basic Theorems of Classical Welfare Economics’27. Tibor Scitovsky (1954), ‘Two Concepts of External Economies’PART IIISOCIAL CHOICE28. Howard R. Bowen (1944), ‘The Interpretation of Voting in the Allocation of Economic Resources’29. Duncan Black (1948), ‘On the Rationale of Group Decision-making’30. Amartya Sen and Prasanta K. Pattanaik (1969), ‘Necessary and Sufficient Conditions for Rational Choice under Majority Decision’31. S.Ch. Kolm (1969/2001), ‘The Optimal Production of Social Justice’32. M.V. Posner and H. Tulkens (1969), ‘Discussion of Mr Kolm’s Paper’33. Amartya Sen (1970), ‘The Impossibility of a Paretian Liberal’34. Douglas H. Blair, Georges Bordes, Jerry S. Kelly and Kotaro Suzumura (1976), ‘Impossibility Theorems without Collective Rationality’35. Peter J. Hammond (1976), ‘Equity, Arrow’s Conditions, and Rawls’ Difference Principle’36. Kevin W.S. Roberts (1980), ‘Possibility Theorems with Interpersonally Comparable Welfare Levels’Name Index

Edited by the late Kenneth J. Arrow, formerly Joan Kenney Professor of Economics and Professor of Operations Research Emeritus, Stanford University, US and the late Gérard Debreu, former University Professor and Class of 1958 Professor of Economics and Mathematics Emeritus, University of California at Berkeley, US and European University Institute, Italy

• Contents:AcknowledgementsPrefaceMark BlaugPART IGENERAL EQUILIBRIUM 1. Erik Lindahl (1939/1970), ‘The Traditional Setting of the Pricing Problem’, ‘Perfect Foresight and Stationary Conditions’, ‘Perfect Foresight and Dynamic Conditions’, ‘Imperfect Foresight’ and ‘The Problem of Balancing the Budget’2. Karl Schlesinger (1934), ‘Über die Produktionsgleichungen der Ökonomischen Wertlehre’3. Abraham Wald (1951), ‘On Some Systems of Equations of Mathematical Economics’ [translation of ‘Über einige Gleichungssysteme der mathematischen Ökonomie]’4. J. v. Neumann (1946), ‘A Model of General Economic Equilibrium’ [translation of ‘Über ein Ökonomisches Gleichungssystem und eine Verallgemeinerung des Brouwerschen Fixpunktsatzes]’5. John F. Nash, Jr (1950), ‘Equilibrium Points in N-Person Games’6. K.J. Arrow (1964), ‘The Role of Securities in the Optimal Allocation of Risk-bearing’ [translation of ‘Le Rôle des Valeurs Boursières pour la Répartition la Meilleure des Risques]’7. Lionel McKenzie (1954), ‘On Equilibrium in Graham’s Model of World Trade and Other Competitive Systems’8. Kenneth J. Arrow and Gerard Debreu (1954), ‘Existence of an Equilibrium for a Competitive Economy’9. Herbert Scarf (1960), ‘Some Examples of Global Instability of the Competitive Equilibrium’10. Herbert Scarf (1962), ‘An Analysis of Markets with a Large Number of Participants’11. Gerard Debreu and Herbert Scarf (1963), ‘A Limit Theorem on the Core of an Economy’12. Robert J. Aumann (1964), ‘Markets with a Continuum of Traders’13. Herbert Scarf (1967), ‘On the Computation of Equilibrium Prices’14. Roy Radner (1968), ‘Competitive Equilibrium Under Uncertainty’15. Gerard Debreu (1970), ‘Economies with a Finite Set of Equilibria’16. Hugo Sonnenschein (1972), ‘Market Excess Demand Functions’17. Sanford J. Grossman and Joseph E. Stiglitz (1976), ‘Information and Competitive Price Systems’18. Sanford J. Grossman (1977), ‘A Characterization of the Optimality of Equilibrium in Incomplete Markets’19. Werner Hildenbrand (1983), ‘On the "Law of Demand”’20. Darrell Duffie and Wayne Shafer (1985), ‘Equilibrium in Incomplete Markets I: A Basic Model of Generic Existence’21. Darrell Duffie and Wayne Shafer (1986), ‘Equilibrium in Incomplete Markets II: Generic Existence in Stochastic Economies’22. John Geanakoplos and Andreu Mas-Colell (1989), ‘Real Indeterminacy with Financial Assets’PART IIWELFARE ECONOMICS 23. Harold Hotelling (1938), ‘The General Welfare in Relation to Problems of Taxation and of Railway and Utility Rates’24. Abram Burk (1938), ‘A Reformulation of Certain Aspects of Welfare Economics’25. Nicholas Kaldor (1939), ‘Welfare Propositions of Economics and Inter-personal Comparisons of Utility’26. Kenneth J. Arrow (1951), ‘An Extension of the Basic Theorems of Classical Welfare Economics’27. Tibor Scitovsky (1954), ‘Two Concepts of External Economies’PART IIISOCIAL CHOICE28. Howard R. Bowen (1944), ‘The Interpretation of Voting in the Allocation of Economic Resources’29. Duncan Black (1948), ‘On the Rationale of Group Decision-making’30. Amartya Sen and Prasanta K. Pattanaik (1969), ‘Necessary and Sufficient Conditions for Rational Choice under Majority Decision’31. S.Ch. Kolm (1969/2001), ‘The Optimal Production of Social Justice’32. M.V. Posner and H. Tulkens (1969), ‘Discussion of Mr Kolm’s Paper’33. Amartya Sen (1970), ‘The Impossibility of a Paretian Liberal’34. Douglas H. Blair, Georges Bordes, Jerry S. Kelly and Kotaro Suzumura (1976), ‘Impossibility Theorems without Collective Rationality’35. Peter J. Hammond (1976), ‘Equity, Arrow’s Conditions, and Rawls’ Difference Principle’36. Kevin W.S. Roberts (1980), ‘Possibility Theorems with Interpersonally Comparable Welfare Levels’Name Index