Theory and Decision

, Volume 43, Issue 2, pp 139–166 | Cite as

Discount-neutral utility models for denumerable time streams

  • Peter Fishburn
  • Ward Edwards


This paper formulates and axiomatizes utility models for denumerable time streams that make no commitment in regard to discounting future outcomes. The models address decision under certainty and decision under risk. Independence assumptions in both contexts lead to additive or multiplicative utilities over time periods that allow unambiguous comparisons of the relative importance of different periods. The models accommodate all patterns of future valuation. This discount-neutral feature is attained by restricting preference comparisons to outcome streams or probability distributions on outcome streams that differ in at most a finite number of periods.

Time preference denumerable time streams discount-neutral models 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Algoet, P.H.: 1994, ‘The strong law of large numbers for sequential decisions under uncertainty’, IEEE Transactions on Information Theory 40, 609–633.Google Scholar
  2. Bailey, S.: 1825, A Critical Dissertation on the Nature, Measure, and Causes of Value, New York: Augustus M. Kelly (1967).Google Scholar
  3. Balintfy, J.L., Duffy, W.J. and Sinha, P.: 1974, ‘Modeling food preferences over time’, Operations Research 22, 711–727.Google Scholar
  4. Baumol, W.J.: 1958, ‘On the social rate of discount’, American Economic Review 58, 788–802.Google Scholar
  5. Becker, R.A., Boyd, J.H. and Sung, B.Y.: 1989, ‘Recursive utility and optimal capital accumulation. I. Existence’, Journal of Economic Theory 47, 76–100.Google Scholar
  6. Bernoulli, D.: 1738, ‘Specimen theoriae novae de mensura sortis’, Commentarii Academiae Scientiarum Imperialis Petropolitanae 5, 175–192. Translated by L. Sommer: 1954, ‘Exposition of a new theory on the measurement of risk’, Econometrica 22, 23–36.Google Scholar
  7. Blackwell, D.: 1965, ‘Discounted dynamic programming’, Annals of Mathematical Statistics 36, 226–235.Google Scholar
  8. Blackwell, D. and Girshick, M.A.: 1954, Theory of Games and Statistical Decisions, New York: Wiley.Google Scholar
  9. Bleichrodt, H. and Gafni, A.: 1994, ‘Time preference, the discounted utility model and health’, preprint.Google Scholar
  10. Böhm-Bawerk, E. von: 1889, Positive Theorie des Kapitals, Vol. II, 4th edn., translated by I.D. Huncke: 1959, Capital and Interest, Vol. II, Positive Theory of Capital, Book IV, Section I, pp. 257–289, South Holland, IL: Libertarian Press.Google Scholar
  11. Brown, D.J. and Lewis, L.M.: 1981, ‘Myopic economic agents’, Econometrica 49, 359–368.Google Scholar
  12. Chow, Y.S. and Robbins, H.: 1963, ‘On optimal stopping rules’, Zeitschrift für Wahrscheinlichkeitstheorie und verwandte Gebiete 2, 33–49.Google Scholar
  13. Cowen, T. and High J.: 1988, ‘Time, bounded utility, and the St. Petersburg paradox’, Theory and Decision 25, 219–223.Google Scholar
  14. Dana, R.A. and Le Van, C.: 1991, ‘Equilibria of a stationary economy with recursive preferences’, Journal of Optimization Theory and Applications 71, 289–313.Google Scholar
  15. Debreu, G.: 1960, ‘Topological methods in cardinal utility theory’, in Mathematical Methods in the Social Sciences, 1959, K.J. Arrow, S. Karlin and P. Suppes, (ed.) pp. 16–26, Stanford: Stanford University Press.Google Scholar
  16. Diamond, P.A.: 1965, ‘The evaluation of infinite utilitystreams’, Econometrica 33, 170–177.Google Scholar
  17. Duffie, D., Epstein, L.G. and Skiadas, C.: 1992, ‘Stochastic differential utility’, Econometrica 60, 353–394.Google Scholar
  18. Epstein, L.G. and Wang, T.: 1994, ‘Intertemporal asset pricing under Knightian uncertainty’, Econometrica 62, 283–322.Google Scholar
  19. Epstein, L. and Zin, S.: 1989, ‘Substitution, risk aversion and the temporal behavior of consumption and asset returns: A theoretical framework’, Econometrica 57, 937–969.Google Scholar
  20. Fetter, F.A.: 1915, Economic Principles, Vol. I, New York: The Century Co.Google Scholar
  21. Fetter, F.A.: 1977, Capital, Interest, and Rent: Essays in the Theory of Distribution, ed. by M. Rothbard, Kansas City: Sheed Andrews and McMeel.Google Scholar
  22. Fishburn, P.C.: 1965a, ‘Independence in utility theory with whole product sets’, Operations Research 13, 28–45.Google Scholar
  23. Fishburn, P.C.: 1965b, ‘Markovian dependence in utility theory with whole product sets’, Operations Research 13, 238–257.Google Scholar
  24. Fishburn, P.C.: 1966, ‘Additivity in utility theory with denumerable product sets’, Econometrica 34, 500–503.Google Scholar
  25. Fishburn, P.C.: 1970, Utility Theory for Decision Making, New York: Wiley.Google Scholar
  26. Fishburn, P.C.: 1990, ‘Continuous nontransitive additive conjoint measurement’, Mathematical Social Sciences 20, 165–193.Google Scholar
  27. Fisher, I.: 1892, ‘Mathematical investigations in the theory of values and prices’, Transactions of the Connecticut Academy of Arts and Sciences 9, 1–124.Google Scholar
  28. Fisher, I.: 1930, The Theory of Interest, New York: Macmillan.Google Scholar
  29. Gilboa, I.: 1989, ‘Expectation and variation in multi-period decisions’, Econometrica 57, 1153–1169.Google Scholar
  30. Gordon, B.: 1975, Economic Analysis Before Adam Smith: Hesiod to Lessius, New York: Barnes and Noble.Google Scholar
  31. Hammond, P.J.: 1976, ‘Changing tastes and coherent dynamic choice’, Review of Economic Studies 43, 159–173.Google Scholar
  32. Harvey, C.M.: 1988, ‘Utility functions for infinite-period planning’, Management Science 34, 645–665.Google Scholar
  33. Harvey, C.M.: 1994, ‘The reasonableness of non-constant discounting’, Journal of Public Economics 53, 31–51.Google Scholar
  34. Harvey, C.M.: 1995, ‘Proportional discounting of future costs and benefits’, Mathematics of Operations Research 20, 381–399.Google Scholar
  35. Jensen, N.E.: 1967, ‘An introduction to Bernoullian utility theorem. I. Utility functions’, Swedish Journal of Economics 69, 163–183.Google Scholar
  36. Kauder, E.: 1965, A History of Marginal Utility Theory, Princeton: Princeton University Press.Google Scholar
  37. Keeney, R.L.: 1968, ‘Quasi-separable utility functions’, Naval Research Logistics Quarterly 15, 551–565.Google Scholar
  38. Keeney, R.L. and Raiffa, H.: 1976, Decisions with Multiple Objectives: Preferences and Value Tradeoffs, New York: Wiley.Google Scholar
  39. Kohn, M.G. and Shavell, S.: 1974, ‘The theory of search’, Journal of Economic Theory 9, 93–123.Google Scholar
  40. Koopmans, T.C.: 1960, ‘Stationary ordinal utility and impatience’, Econometrica 28, 287–309.Google Scholar
  41. Koopmans, T.C.: 1972, ‘Representation of preference orderings over time’, in Decision and Organization, ed. by C.B. McGuire and R. Radner, pp. 79–100, Amsterdam: North-Holland.Google Scholar
  42. Krantz, D.H., Luce, R.D., Suppes, P. and Tversky, A.: 1971, Foundations of Measurement, Vol. I, New York: Academic Press.Google Scholar
  43. Kreps, D.M. and Porteus, E.L.: 1977, ‘On the optimality of structured policies in countable stage decision processes. II: Positive and negative problems’, SIAM Journal on Applied Mathematics 32, 457–466.Google Scholar
  44. Kreps, D.M. and Porteus, E.L.: 1978, ‘Temporal resolution of uncertainty and dynamic choice theory’, Econometrica 46, 185–200.Google Scholar
  45. Kreps, D.M. and Porteus, E.L.: 1979, ‘Dynamic choice theory and dynamic programming’, Econometrica 47, 91–100.Google Scholar
  46. Loewenstein, G.: 1987, ‘Anticipation and the valuation of delayed consumption’, Economic Journal 97, 666–684.Google Scholar
  47. Loewenstein, G. and Elster, J.: 1992, Choice over Time, New York: Russell Sage Foundation.Google Scholar
  48. Loewenstein, G. and Prelec, D.: 1991, ‘Negative time preference’, AEA Papers and Proceedings 81, 347–352.Google Scholar
  49. Loewenstein, G. and Thaler, R.: 1989, ‘Anomalies: Intertemporal choice’, Journal of Economic Perspectives 3, 181–193.Google Scholar
  50. Lucas, R. and Stokey, N.: 1984, ‘Optimal growth with many consumers’, Journal of Economic Theory 32, 139–171.Google Scholar
  51. Menger, K.: 1934, ‘Das Unsicherheitsmoment in der Wertlehre’, Zeitschrift für Nationaloekonomie 5, 459–485. Translated by W. Schoellkopf: 1967, ‘The role of uncertainty in economics’, in Essays in Mathematical Economics, ed. M. Shubik, pp. 211–231, Princeton: Princeton University Press.Google Scholar
  52. Nairay, A.: 1984, ‘Asymptotic behavior and optimal properties of a consumptioninvestment model with variable time preference’, Journal of Economics and Dynamic Control 7, 283–313.Google Scholar
  53. Olson, M. and Bailey, M.J.: 1981, ‘Positive time preference’, Journal of Political Economy 89, 1–25.Google Scholar
  54. Pauly, M.V.: 1970, ‘Risk and the social rate of discount’, American Economic Review 60, 195–198.Google Scholar
  55. Peleg, B. and Yaari, M.E.: 1973, ‘On the existence of a consistent course of action when tastes are changing’, Review of Economic Studies 40, 391–401.Google Scholar
  56. Pollak, R.A.: 1967, ‘Additive von Neumann-Morgenstern utility functions’, Econometrica 35, 485–494.Google Scholar
  57. Ramsey, F.P.: 1928, ‘A mathematical theory of saving’, Economic Journal 38, 543–559.Google Scholar
  58. Rothbard, M.N.: 1990, ‘Time preference’, in The New Palgrave: Utility and Probability, ed. by J. Eatwell, M. Milgate and P. Newman, pp. 270–275, London: Macmillan.Google Scholar
  59. Samuelson, P.A.: 1977, ‘St. Petersburg paradoxes: Defanged, dissected, and historically described’, Journal of Economic Literature 15, 24–55.Google Scholar
  60. Savage, L.J.: 1954, The Foundations of Statistics, New York: Wiley.Google Scholar
  61. Shafer, G.: 1988, ‘The St. Petersburg paradox’, in Encyclopedia of Statistical Sciences, Vol. 8, ed. by S. Kotz and N.L. Johnson, pp. 865–870, New York: Wiley.Google Scholar
  62. Streufert, P.A.: 1993, ‘Abstract recursive utility’, Journal of Mathematical Analysis and Applications 175, 169–185.Google Scholar
  63. Suppes, P. and Zinnes, J.L.: 1963, ‘Basic measurement theory’, in Handbook of Mathematical Psychology, I, ed. by R.D. Luce, R.R. Bush, and E. Galanter, New York: Wiley.Google Scholar
  64. Toulet, C.: 1986, ‘An axiomatic model of unbounded utility functions’, Mathematics of Operations Research 11, 81–94.Google Scholar
  65. Uzawa, H.: 1968, ‘Time preference, the consumption function, and optimum asset holdings’, in Value, Capital and Growth: Papers in Honour of Sir John Hicks, ed. by J.N. Wolfe, Edinburgh: Edinburgh University Press.Google Scholar
  66. von Mises, L.: 1949, Human Action: A Treatise on Economics, third revised edn. (1966), Chicago: Regnery.Google Scholar
  67. Wakker, P.P.: 1989, Additive Representations of Preferences, Dordrecht: Kluwer Academic.Google Scholar
  68. Wakker, P.P.: 1993, ‘Unbounded utility for Savage's ‘Foundations of Statistics’ and other models’, Mathematics of Operations Research 18, 446–485.Google Scholar
  69. Weibull, J.W.: 1985, ‘Discounted-value representationsof temporal preferences’, Mathematics of Operations Research 10, 244–250.Google Scholar
  70. Yahav, J.A.: 1966, ‘On optimal stopping’, Annals of Mathematical Statistics 37, 30–35.Google Scholar

Copyright information

© Kluwer Academic Publishers 1997

Authors and Affiliations

  • Peter Fishburn
    • 1
  • Ward Edwards
    • 2
  1. 1.AT&T Bell LaboratoriesMurray HillU.S.A
  2. 2.University of Southern CaliforniaLos AngelesU.S.A

Personalised recommendations