The mordukhovich normal cone and the foundations of welfare economics

Journal of Public Economic Theory

Volumn 1, Issue 3, 1999, Pages 309-338

  Ali Khan, M ^a  

^a JOHNS HOPKINS UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

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EID: 0002145762     PISSN: 10973923     EISSN: 14679779     Source Type: Journal    
DOI: 10.1111/1097-3923.00014     Document Type: Article

References (60)

1. ALLAIS, M. (1943) A la Recherche d'une Discipline Economique, vol. 1. Paris: Ateliers Industria. (2nd ed. published as Traité d'Economie Pure, Paris: Impremeria Nationale, 1953.)
2. ARROW, K.J. (1951) An extension of the basic theorems of classical welfare economics; in Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability, J. NEYMAN, ed., pp. 507-532. Berkeley: The University of California Press. Reprinted in Readings in Mathematical Economics, vol. 1, P. NEWMAN, ed., Baltimore: The Johns Hopkins University Press, pp. 365-390.
3. ARROW, K.J., and A. ENTHOVEN (1961) Quasiconcave programming, Econometrica 29, 779-800.
4. BONNISSEAU, J.M., and B. CORNET (1988) Valuation equilibrium and Pareto optimum, Journal of Mathematical Economics 17, 293-308.( Originally circulated as CORE discussion paper no. 8636, November 1986.)
5. BOULIGAND, G. (1932) Introduction à la Geometrie Infinitesimale Directe. Paris: Vuibert.
6. BROWN, D.J. (1991) Equilibrium analysis with nonconvex technologies; in Handbook of Mathematical Economics, vol. 4, H. SONNENSCHEIN and W. HILDENBRAND, eds. Amsterdam: North Holland.
7. BROWN, D.J., G. HEAL, M.A. KHAN, and R. VOHRA (1986) On a general existence theorem for marginal cost pricing equilibria, Journal of Economic Theory 38, 371-379.
8. CLARKE, F. (1975) Generalized gradients and applications, Transactions of the American Mathematical Society 205, 247-262.
9. CLARKE, F. (1976) A new approach to Lagrange multipliers, Mathematics of Operations Research 1, 165-174.
10. CLARKE, F. (1983) Optimization and Nonsmooth Analysis. New York: John Wiley.
11. CORNET, B. (1982) Existence of equilibria in economies with increasing returns, Berkeley working paper no. IP-311.
12. CORNET, B. (1986) The second welfare theorem in nonconvex economies, CORE discussion paper no. 8630.
13. CORNET, B. (1988) General equilibrium theory and increasing returns: Presentation, Journal of Mathematical Economics 17, 103-118.
14. CORNET, B. (1990) Marginal cost pricing and Pareto optimality; in Essays in Honor of Edmond Malinvaud, vol. 1, P. CHAMPSAUR, ed. Cambridge: MIT Press.
15. DEBREU, G. (1951) The coefficient of resource utilization, Econometrica 19, 273- 292.
16. DEBREU, G. (1954) Valuation equilibrium and Pareto optimum, Proceedings of the National Academy of Sciences, U.S.A. 40, 588-592.
17. DRÉZE, J.H. (1980) Public goods with exclusion, Journal of Public Economics 13, 5-24.
18. DRÉZE, J.H. (1989) Maurice Allais and the French Marginalist School, The Scandinavian Journal of Economics 91, 5-16.
19. EATWELL, J., M. MILGATE, and P.K. NEWMAN, eds. (1987) The New Palgrave. London: MacMillan.
20. FABRE-SENDER, F. (1969) Biens Collectifs et Biens à Qualité Variable. Paris: CEPREMAP.
21. FOLEY, D. (1967) Resource allocation and the public sector, Yale Economic Essays 7, 43-98.
22. FOLEY, D. (1970) Lindahl's solution and the core of an economy with public goods, Econometrica 38, 66-72.
23. GRAAF, J. de V. (1957) Theoretical Welfare Economics. Cambridge: Cambridge University Press.
24. GRANDMONT, J.-M. (1989) Report on Maurice Allais' scientific work, The Scandinavian Journal of Economics 91, 17-28.
25. GUESNERIE, R. (1975) Pareto optimality in non-convex economies, Econometrica 43, 1-29.
26. HAMANO, T. (1989) On the non-existence of the marginal cost pricing equilibrium and the Ioffe normal cone, Zeitschrift für Nationalökonomie 50, 47-53.
27. HICKS, J.R. (1939) The foundations of welfare economics, Economic Journal 49, 696-712. Also: Prefatory note to 1984 reprint in Wealth and Welfare: Collected Essays on Economic Theory, vol. 1, Oxford: Basil Blackwell.
28. IOFFE, A.D. (1981a) Sous-differentielles approchées de fonctions numérique, Comptes Rendus Academie de Sciences Paris Séries A-B 292, 675-678.
29. IOFFE, A.D. (1981b) Nonsmooth analysis: Differential calculus of nondifferential mappings, Transactions of the American Mathematical Society 266, 1-56.
30. IOFFE, A.D. (1984) Approximate subdifferentials and applications 1. The finite dimensional theory, Transactions of the American Mathematical Society 281, 389-416. Erratum in the same journal (1985) 288, 429.
31. IOFFE, A.D. (1986) On the theory of subdifferential; in Fermat Days 1985: Mathematics in Optimization, J.-B. HIRIAT-URRUTY, ed., pp. 183-200. Amsterdam: North Holland.
32. IOFFE, A.D. (1988) Nonconvex subdifferentials; in Nonsmooth Optimization and Related Topics, F.H. CLARKE, V.F. DEM'YANOV, and F. GIANNESSI, eds., pp. 241-253. London: Plenum Press.
33. JOUINI, E. (1988) A remark on Clarke's normal cone and the marginal cost pricing rule, Journal of Mathematical Economics 17, 309-315.
34. KHAN, M. ALI (1988) Ioffe's normal cone and the foundations of welfare economics: An example, Economics Letters 28, 15-19.
35. KHAN, M. ALI (1991) Ioffe's normal cone and the foundations of welfare economics: The infinite dimensional theory, Journal of Mathematical Analysis and Applications 161, 284-298. (Originally circulated as BEBR Faculty working paper no. 1391, November 1987.)
36. KHAN, M. ALI, and R. VOHRA (1987a) An extension of the second welfare theorem to economies with non-convexities and public goods, Quarterly Journal of Economics 102, 223-245. (Originally circulated as Brown University working paper no. 84-27.)
37. KHAN, M. ALI, and R. VOHRA (1987b) Lindahl-Hotelling equilibria, Journal of Public Economics 34, 143-158.
38. KHAN, M. ALI, and R. VOHRA (1988) Pareto optimal allocations of nonconvex economies in locally convex spaces, Nonlinear Analysis 12, 943-950. (Originally circulated as Brown University working paper no. 85-03, and presented at the Yale Conference on Increasing Returns, August 1985.)
39. KRUGER, A.Y., and B.Sh. MORDUKHOVICH (1980) Generalized normals and derivatives, and necessary optimality conditions in nondifferential programming, Part 1: Depon. VINITI, no. 408-80, Part II: Depon. VINITI, no. 494- 80, Moscow (Russian).
40. LANGE, O. (1942) The foundations of welfare economics, Econometrica 10, 215- 228. Reprinted in Readings in Welfare Economics, K.J. ARROW and T. SCITOVSKY, eds., London: Allen-Unwin, 1969.
41. MILLERON, J.-C. (1972) Theory of value with public goods: A survey article, Journal of Economic Theory 5, 419-477.
42. MISHAN, E.J. (1960) A survey of welfare economics, 1939-1959, Economic Journal 70, 197-265.
43. MORDUKHOVICH, B.Sh. (1976) Maximum principle in the optimal time control problem with nonsmooth constraints, Prikl. Matem. Mekh. 40, 1014- 1023. English translation in Journal of Applied Mathematics and Mechanics (1976), 40, 960-969.
44. MORDUKHOVICH, B.Sh. (1980) Metric approximations and necessary optimality conditions for general classes of non-smooth extremum problems, Doklady Akad. Nauk. SSR 254, 1072-1076. English translation in Soviet Math. Doklady (1980), 22, 526-530.
45. MORDUKHOVICH, B.Sh. (1985) On necessary conditions for an extremum in nonsmooth optimization, Doklady Akad. Nauk. SSR 283, 816-821. English translation in Soviet Math. Doklady (1985), 32, 215-220.
46. MORDUKHOVICH, B.Sh. (1988) Approximation Methods in Problems of Optimization and Control. Nauka, Moscow (Russian; English translation to appear in Wiley-Interscience).
47. NEWMAN, P., Ed. (1968) Readings in Mathematical Economics, vol. 1. Baltimore: The Johns Hopkins University Press.
48. OTANI, Y., and J. SICILIAN (1977) Externalities and problems of non-convexity and overhead costs in welfare economics, Journal of Economic Theory 14, 239-251.
49. QUINZII, M. (1986) Rendements croissants et equilibre général, Ph.D. dissertation, Université de Paris II.
50. QUINZII, M. (1992) Increasing Returns and Efficiency. Oxford: Oxford University Press.
51. ROCKAFELLER, R.T. (1980) Generalized directional derivatives and subgradients of nonconvex functions, Canadian Journal of Mathematics 32, 257-280.
52. ROCKAFELLER, R.T. (1981) The Theory of Subgradients and its Application to Optimization.
53. SAMUELSON, P.A. (1943) Further commentary on welfare economics, American Economic Review 33, 605-607.
54. SAMUELSON, P.A. (1947) Foundations of Economic Analysis. Cambridge: Harvard University Press.
55. SAMUELSON, P.A. (1954) The pure theory of public expenditures, Review of Economics and Statistics 36, 387-389.
56. SAMUELSON, P.A. (1958) Book review of J. de V. Graaf, Theoretical Welfare Economics, Economic Journal 68, 539-541.
57. UZAWA, H. (1958) The Kuhn-Tucker Theorem in concave programming; in Studies in Linear and Non-linear Programming, K.J. ARROW, L. HURWICZ, and H. UZAWA, eds. Stanford: Stanford University Press.
58. VILLAR, A. (1996) General equilibrium with increasing returns, Lecture Notes in Economics and Mathematical Systems No. 438. Berlin: Springer-Verlag.
59. YUN, K.K. (1985) Pareto optimality in non-convex economies and marginal cost pricing equilibria, Korean Economic Review 1, 1-13. (Paper presented in 1984 at the First National Conference of Korean Economists.)
60. YUN, K.K. (1995) The Dubovickii-Miljutin lemma and characterizations of optimal allocations in non-smooth economies, Journal of Mathematical Economics 24, 435-460.