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# Mathematical Economics

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Mathematical Economics is an authoritative collection of the most influential contributions essential to an understanding of this important area of economic science.

Three volume set

Extent: 1,648 pp

Mathematical Economics is an authoritative collection of the most influential contributions essential to an understanding of this important area of economic science. These seminal papers illustrate the development of the field from its inception in the 19th century up to the present, and exhibit the power of mathematics to lead to new thinking which can illuminate the scientific structures underlying economic arguments. Many of these papers started new fields of economics, influencing deeply the way economists think about their world. They illustrate the extensive range of topics to which mathematics has been applied productively, and show the areas of mathematics which have proved valuable, including functional analysis, linear algebra, algebraic and differential topology, stochastic processes and dynamical systems. They also show the extent to which today’s policy analysis rests on yesterday’s mathematical economics. Anyone with an interest in economics as a science will find this collection indispensable. The collection is an essential part of any course using mathematical economics.

62 articles, dating from 1928 to 1997

Contributors include: G.B. Antonelli, K. Arrow, Y. Baryshnikov, G. Debreu, L. Lauwers, P. Pattanik, F. Ramsey, D.M. Topkis, J. von Neumann

Contributors include: G.B. Antonelli, K. Arrow, Y. Baryshnikov, G. Debreu, L. Lauwers, P. Pattanik, F. Ramsey, D.M. Topkis, J. von Neumann

Contents:

Volume I:

Acknowledgements • Introduction Graciela Chichilnisky

Preferences and Public Choice

1. Giovanni Battista Antonelli (1971), ‘On the Mathematical Theory of Political Economy’

2. Kenneth J. Arrow (1950), ‘A Difficulty in the Concept of Social Welfare’

3. Yuliy M. Baryshinikov (1993), ‘Unifying Impossibility Theorems: A Topological Approach’

4. Graciela Chichilnisky (1980), ‘Social Choice and the Topology of Spaces of Preferences’

5. Duncan K. Foley (1976), ‘Resource Allocation and the Public Sector’

6. Paul Milgrom (1981), ‘An Axiomatic Characterization of Common Knowledge’

7. Graciela Chichilnisky and Geoffrey Heal (1983), ‘Necessary and Sufficient Conditions for a Resolution of the Social Choice Paradox’

8. G. Chichilnisky and G.M. Heal (1997), ‘The Geometry of Implementation: A Necessary and Sufficient Condition for Straightforward Games’

9. Gerard Debreu (1976), ‘Smooth Preferences: A Corrigendum’

10. Allan Gibbard (1973), ‘Manipulation of Voting Schemes: A General Result’

11. Theodore Groves and John Ledyard (1977), ‘Optimal Allocation of Public Goods: A Solution to the “Free Rider” Problem’

12. Ehud Kalai and Eitan Muller (1977), ‘Characterization of Domains Admitting Nondictatorial Social Welfare Functions and Nonmanipulable Voting Procedures’

13. M. Ali Khan and Ye Neng Sun (1990), ‘On Complete Regularity of Spaces of Economic Agents Endowed with the Order Topology’

14. L. Lauwers (1995), ‘Social Choice with Infinite Populations’

15. Amartya Sen and Prasanta K. Pattanaik (1969), ‘Necessary and Sufficient Conditions for Rational Choice Under Majority Decision’

16. Dieter Sondermann (1975), ‘Smoothing Demand by Aggregation’

17. Donald M. Topkis (1978), ‘Minimizing a Submodular Function on a Lattice’

Name Index

Volume II:

Acknowledgements

Part I: Savings and Growth

1. F.H. Hahn (1966), ‘Equilibrium Dynamics with Heterogeneous Capital Goods’

2. Harold Hotelling (1931), ‘The Economics of Exhaustible Resources’

3. Graciela Chichilnisky (1996), ‘An Axiomatic Approach to Sustainable Development’

4. Walter Perrin Heller (1971), ‘Disequilibrium Dynamics of Competitive Growth Paths’

5. Tjalling C. Koopmans (1965), ‘On the Concept of Optimal Economic Growth’

6. F.P. Ramsey (1928), ‘A Mathematical Theory of Saving’

7. J. V. Neumann (1945), ‘A Model of General Economic Equilibrium’

8. Roy Radner (1961), ‘Paths of Economic Growth that are Optimal with Regard Only to Final States: A Turnpike Theorem’

9. Harl E. Ryder, Jr. and Geoffrey M. Heal (1973), ‘Optimal Growth with Intertemporally Dependent Preferences’

10. G. Chichilnisky and P.J. Kalman (1980), ‘Application of Functional Analysis to Models of Efficient Allocation of Economic Resources’

11. Graciela Chichilnisky (1977), ‘Nonlinear Functional Analysis and Optimal Economic Growth’

Part II: General Equilibrium

12. Donald J. Brown, Geoffrey M. Heal, M. Ali Khan and Rajiv Vohra (1986), ‘On a General Existence Theorem for Marginal Cost Pricing Equilibria’

13. Egbert and Hildegard Dierker (1972), ‘The Local Uniqueness of Equilibria’

14. Yves Balasko (1979), ‘A Geometric Approach to Equilibrium Analysis’

15. Donald J. Brown and Geoffrey Heal (1979), ‘Equity, Efficiency and Increasing Returns’

16. Graciela Chichilnisky and Yuqing Zhou (1996), ‘Smooth Infinite Economies’

17. Duncan K. Foley (1994), ‘A Statistical Equilibrium Theory of Markets’

18. John F. Nash, Jr. (1950), ‘Equilibrium Points in N-Person Games’

19. Gerard Debreu (1975), ‘The Rate of Convergence of the Core of an Economy’

20. Graciela Chichilnisky (1996), ‘A Unified Perspective on Resource Allocation: Limited Arbitrage is Necessary and Sufficient for the Existence of a Competitive Equilibrium, the Core and Social Choice’

21. Allan M. Feldman (1973), ‘Bilateral Trading Processes, Pairwise Optimality, and Pareto Optimality’

22. John Geanakoplos and Geoffrey Heal (1983), ‘A Geometric Explanation of the Transfer Paradox in a Stable Economy’

23. Roger Guesnerie (1975), ‘Pareto Optimality in Non-Convex Economies’

24. Graciela Chichilnisky (1986), ‘A General Equilibrium Theory of North–South Trade’

25. Yuqing Zhou (1997), ‘Genericity Analysis on the Pseudo-Equilibrium Manifold’

Name Index

Volume III:

Acknowledgements

Part I: Uncertainty and Financial Markets

1. Kenneth J. Arrow (1963), ‘Uncertainty and the Welfare Economics of Medical Care’

2. Louis Bachelier (1900), ‘Theory of Speculation’

3. Graciela Chichilnisky (1985), ‘Von Neumann–Morgenstern Utilities and Cardinal Preferences’

4. I.N. Herstein and John Milnor (1953), ‘An Axiomatic Approach to Measurable Utility’

5. Mark J. Machina (1982), ‘“Expected Utility” Analysis without the Independence Axiom’

6. E. Malinvaud (1973), ‘Markets for an Exchange Economy with Individual Risks’

7. Bruno de Finetti (1937), ‘Foresight: Its Logical Laws, Its Subjective Sources’

8. Kenneth J. Arrow (1970), ‘Exposition of the Theory of Choice under Uncertainty’

9. Graciela Chichilnisky (1996), ‘Markets with Endogenous Uncertainty: Theory and Policy’

10. Nicholas C. Yannelis (1991), ‘The Core of an Economy with Differential Information’

11. Graciela Chichilnisky and Geoffrey Heal (1996), ‘On the Existence and the Structure of the Pseudo-Equilibrium Manifold’

12. Darrell Duffie and Wayne Shafer (1985), ‘Equilibrium in Incomplete Markets: I: A Basic Model of Generic Existence’

13. Fischer Black and Myron Scholes (1973), ‘The Pricing of Options and Corporate Liabilities’

14. Leonard J. Savage (1971), ‘Elicitation of Personal Probabilities and Expectations’

Part II: Stability and Computation

15. Richard H. Day and Giulio Pianigiani (1991), ‘Statistical Dynamics and Economics’

16. B. Curtis Eaves and Herbert Scarf (1976), ‘The Solution of Systems of Piecewise Linear Equations’

17. Morris W. Hirsch and Stephen Smale (1979), ‘On Algorithms for Solving f(x) = 0’

18. Steve Smale (1983), ‘On the Average Number of Steps of the Simplex Method of Linear Programming’

19. Paul A. Samuelson (1949), ‘Market Mechanisms and Maximization’

20. Geoffrey Heal and Darryl McLeod (1984), ‘Gains from Trade, Stability and Profits: A Comment on Chichilnisky’s “Terms of Trade and Domestic Distribution: Export-led Growth with Abundant Labour”’

Name Index

Volume I:

Acknowledgements • Introduction Graciela Chichilnisky

Preferences and Public Choice

1. Giovanni Battista Antonelli (1971), ‘On the Mathematical Theory of Political Economy’

2. Kenneth J. Arrow (1950), ‘A Difficulty in the Concept of Social Welfare’

3. Yuliy M. Baryshinikov (1993), ‘Unifying Impossibility Theorems: A Topological Approach’

4. Graciela Chichilnisky (1980), ‘Social Choice and the Topology of Spaces of Preferences’

5. Duncan K. Foley (1976), ‘Resource Allocation and the Public Sector’

6. Paul Milgrom (1981), ‘An Axiomatic Characterization of Common Knowledge’

7. Graciela Chichilnisky and Geoffrey Heal (1983), ‘Necessary and Sufficient Conditions for a Resolution of the Social Choice Paradox’

8. G. Chichilnisky and G.M. Heal (1997), ‘The Geometry of Implementation: A Necessary and Sufficient Condition for Straightforward Games’

9. Gerard Debreu (1976), ‘Smooth Preferences: A Corrigendum’

10. Allan Gibbard (1973), ‘Manipulation of Voting Schemes: A General Result’

11. Theodore Groves and John Ledyard (1977), ‘Optimal Allocation of Public Goods: A Solution to the “Free Rider” Problem’

12. Ehud Kalai and Eitan Muller (1977), ‘Characterization of Domains Admitting Nondictatorial Social Welfare Functions and Nonmanipulable Voting Procedures’

13. M. Ali Khan and Ye Neng Sun (1990), ‘On Complete Regularity of Spaces of Economic Agents Endowed with the Order Topology’

14. L. Lauwers (1995), ‘Social Choice with Infinite Populations’

15. Amartya Sen and Prasanta K. Pattanaik (1969), ‘Necessary and Sufficient Conditions for Rational Choice Under Majority Decision’

16. Dieter Sondermann (1975), ‘Smoothing Demand by Aggregation’

17. Donald M. Topkis (1978), ‘Minimizing a Submodular Function on a Lattice’

Name Index

Volume II:

Acknowledgements

Part I: Savings and Growth

1. F.H. Hahn (1966), ‘Equilibrium Dynamics with Heterogeneous Capital Goods’

2. Harold Hotelling (1931), ‘The Economics of Exhaustible Resources’

3. Graciela Chichilnisky (1996), ‘An Axiomatic Approach to Sustainable Development’

4. Walter Perrin Heller (1971), ‘Disequilibrium Dynamics of Competitive Growth Paths’

5. Tjalling C. Koopmans (1965), ‘On the Concept of Optimal Economic Growth’

6. F.P. Ramsey (1928), ‘A Mathematical Theory of Saving’

7. J. V. Neumann (1945), ‘A Model of General Economic Equilibrium’

8. Roy Radner (1961), ‘Paths of Economic Growth that are Optimal with Regard Only to Final States: A Turnpike Theorem’

9. Harl E. Ryder, Jr. and Geoffrey M. Heal (1973), ‘Optimal Growth with Intertemporally Dependent Preferences’

10. G. Chichilnisky and P.J. Kalman (1980), ‘Application of Functional Analysis to Models of Efficient Allocation of Economic Resources’

11. Graciela Chichilnisky (1977), ‘Nonlinear Functional Analysis and Optimal Economic Growth’

Part II: General Equilibrium

12. Donald J. Brown, Geoffrey M. Heal, M. Ali Khan and Rajiv Vohra (1986), ‘On a General Existence Theorem for Marginal Cost Pricing Equilibria’

13. Egbert and Hildegard Dierker (1972), ‘The Local Uniqueness of Equilibria’

14. Yves Balasko (1979), ‘A Geometric Approach to Equilibrium Analysis’

15. Donald J. Brown and Geoffrey Heal (1979), ‘Equity, Efficiency and Increasing Returns’

16. Graciela Chichilnisky and Yuqing Zhou (1996), ‘Smooth Infinite Economies’

17. Duncan K. Foley (1994), ‘A Statistical Equilibrium Theory of Markets’

18. John F. Nash, Jr. (1950), ‘Equilibrium Points in N-Person Games’

19. Gerard Debreu (1975), ‘The Rate of Convergence of the Core of an Economy’

20. Graciela Chichilnisky (1996), ‘A Unified Perspective on Resource Allocation: Limited Arbitrage is Necessary and Sufficient for the Existence of a Competitive Equilibrium, the Core and Social Choice’

21. Allan M. Feldman (1973), ‘Bilateral Trading Processes, Pairwise Optimality, and Pareto Optimality’

22. John Geanakoplos and Geoffrey Heal (1983), ‘A Geometric Explanation of the Transfer Paradox in a Stable Economy’

23. Roger Guesnerie (1975), ‘Pareto Optimality in Non-Convex Economies’

24. Graciela Chichilnisky (1986), ‘A General Equilibrium Theory of North–South Trade’

25. Yuqing Zhou (1997), ‘Genericity Analysis on the Pseudo-Equilibrium Manifold’

Name Index

Volume III:

Acknowledgements

Part I: Uncertainty and Financial Markets

1. Kenneth J. Arrow (1963), ‘Uncertainty and the Welfare Economics of Medical Care’

2. Louis Bachelier (1900), ‘Theory of Speculation’

3. Graciela Chichilnisky (1985), ‘Von Neumann–Morgenstern Utilities and Cardinal Preferences’

4. I.N. Herstein and John Milnor (1953), ‘An Axiomatic Approach to Measurable Utility’

5. Mark J. Machina (1982), ‘“Expected Utility” Analysis without the Independence Axiom’

6. E. Malinvaud (1973), ‘Markets for an Exchange Economy with Individual Risks’

7. Bruno de Finetti (1937), ‘Foresight: Its Logical Laws, Its Subjective Sources’

8. Kenneth J. Arrow (1970), ‘Exposition of the Theory of Choice under Uncertainty’

9. Graciela Chichilnisky (1996), ‘Markets with Endogenous Uncertainty: Theory and Policy’

10. Nicholas C. Yannelis (1991), ‘The Core of an Economy with Differential Information’

11. Graciela Chichilnisky and Geoffrey Heal (1996), ‘On the Existence and the Structure of the Pseudo-Equilibrium Manifold’

12. Darrell Duffie and Wayne Shafer (1985), ‘Equilibrium in Incomplete Markets: I: A Basic Model of Generic Existence’

13. Fischer Black and Myron Scholes (1973), ‘The Pricing of Options and Corporate Liabilities’

14. Leonard J. Savage (1971), ‘Elicitation of Personal Probabilities and Expectations’

Part II: Stability and Computation

15. Richard H. Day and Giulio Pianigiani (1991), ‘Statistical Dynamics and Economics’

16. B. Curtis Eaves and Herbert Scarf (1976), ‘The Solution of Systems of Piecewise Linear Equations’

17. Morris W. Hirsch and Stephen Smale (1979), ‘On Algorithms for Solving f(x) = 0’

18. Steve Smale (1983), ‘On the Average Number of Steps of the Simplex Method of Linear Programming’

19. Paul A. Samuelson (1949), ‘Market Mechanisms and Maximization’

20. Geoffrey Heal and Darryl McLeod (1984), ‘Gains from Trade, Stability and Profits: A Comment on Chichilnisky’s “Terms of Trade and Domestic Distribution: Export-led Growth with Abundant Labour”’

Name Index