Advertisement

Approximate Quasi-linearity for Large Incomes

  • Mamoru KanekoEmail author
Chapter
Part of the Indian Statistical Institute Series book series (INSIS)

Abstract

Quasi-linear utility functions are widely used in economics and game theory as convenient tools. Quasi-linearity ignores income effects on individual evaluations of alternative choices; indeed, it is captured by a condition of no-income effects on such evaluations. However, income effects are non-negligible relative to agents’ economic activities in many social/economic problems such as in housing markets. In this chapter, we consider how quasi-linearity holds for large incomes for agents. We employ an axiomatic approach to this problem and study its implications and applications to some economic and game theoretic problems.

Keywords

Quasi-linear utility function Approximate quasi-linearity Normality Lindahl-ratio equilibrium 

References

  1. 1.
    Aumann, R.J.: Linearity of unrestricted transferable utilities. Naval Res. Logist. Q. 7, 281–284 (1960)CrossRefGoogle Scholar
  2. 2.
    Fishburn, P.: The Foundations of Expected Utility. Springer-Science-Bussiness Media, Dordrecht (1982)CrossRefGoogle Scholar
  3. 3.
    Herstein, I.N., Milnor, J.: An axiomatic approach to measurable utility. Econometrica 21, 291–297 (1953)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Hicks, J.R.: A Value and Capital. Oxford University Press, Oxford (1939)Google Scholar
  5. 5.
    Hicks, J.R.: A Revision of Demand Theory. Clarendon Press, Oxford (1956)Google Scholar
  6. 6.
    Kaneko, M.: Note on transferable utility. Int. J. Game Theory 6, 183–185 (1976)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Kaneko, M.: The ratio equilibrium and a voting game in a public goods economy. J. Economic Theory 16, 123–136 (1977)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Kaneko, M.: Housing market with indivisibilities. J. Urban Econ. 13, 22–50 (1983)CrossRefGoogle Scholar
  9. 9.
    Kaneko, M., Wooders, M.H.: Utility Theories in Cooperative Games. Handbook of Utility Theory, vol. 2, pp. 1065–1098. Kluwer Academic Press, Dordrecht (2004)CrossRefGoogle Scholar
  10. 10.
    Kaneko, M., Ito, T.: An equilibrium-econometric analysis of rental housing markets with indivisibilities. In: Lina Mallozzi, L., Pardalos, P. (eds.) Spatial Interaction Models: Facility Location using Game Theory, pp. 193–223. Springer (2017)Google Scholar
  11. 11.
    Miyake, M.:Asymptotically quasi-linear utility function. TERGN Working Paper No. 154, Tohoku University (2000)Google Scholar
  12. 12.
    Miyake, M.: On the applicability of Marshallian partial-equilibrium analysis. Math. Soc. Sci. 52, 176–196 (2006)MathSciNetCrossRefGoogle Scholar
  13. 13.
    Miyake, M.: Convergence theorems of willingness-to-pay and willingness-to-accept for nonmaket goods. Soc. Choice Welf. 34, 549–570 (2010)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Maschler, M., Solan, E., Zamir, S.: Game Theory. Cambridge University Press, Cambridge (2013)Google Scholar
  15. 15.
    Mas-Collel, A., Whinston, M., Green, J.: Microeconomic Theory. Oxford University Press, Oxford (1995)Google Scholar
  16. 16.
    Negishi, T.: Welfare economics and existence of an equilibrium for a competitive economy. Metroeconomica 12, 92–97 (1960)CrossRefGoogle Scholar
  17. 17.
    Osborne, M.J., Rubinstein, A.: A Course in Game Theory. The MIT Press, London (1994)Google Scholar
  18. 18.
    Royden, H.L., Fitzpatrick, P.M.: Real Analysis, Prentice Hall, Upper Saddle River (2010)Google Scholar
  19. 19.
    Shapley, L.S., Shubik, M.: Competitive outcomes in the cores of market games. Int. J. Game Theory 4, 229–237 (1975)MathSciNetCrossRefGoogle Scholar
  20. 20.
    van den Nouweland, A., Tijs, S., Wooders, M.H.: Axiomatization of ratio equilibria in public good economies. Soc. Choice Welf. 19, 627–6363 (2002)MathSciNetCrossRefGoogle Scholar
  21. 21.
    van den Nouweland, A.: Lindahl and equilibrium. In: Binder, C. et al. (ed.) Individual and Collective Choice and Social Welfare, pp. 335–362. Springer (2015)Google Scholar
  22. 22.
    Vives, X.: Small income effects: a Marshallian theory of consumer surplus and downward sloping demand. Rev. Econ. Stud. 54, 87–103 (1987)CrossRefGoogle Scholar

Copyright information

© Springer Nature Singapore Pte Ltd. 2018

Authors and Affiliations

  1. 1.Faculty of Political Science and EconomicsWaseda UniversityTokyoJapan

Personalised recommendations