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A Foundation for Logarithmic Utility Function of Money

Author

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  • Francisco J. Navarro-González

    (Department of Applied Mathematics, University of Alicante, 03690 Alicante, Spain)

  • Yolanda Villacampa

    (Department of Applied Mathematics, University of Alicante, 03690 Alicante, Spain)

Abstract

This paper presents a study on the optimization problem of a consumer’s choice constrained to a single time interval. In this problem, the choice is made over a set of perishable goods such that they do not retain value at the end of the period. Money has been introduced as the only means available to store that value for the future. Thus, consumer utility is measured on the possible combinations of goods consumed during the period and money held at the end of the period. Additionally, a set of simple conditions are assumed to the utility functions for goods and money given by: (1) Existence of a total utility that is additively separable with respect to the components of goods and money; (2) continuity of the derivatives of the utility functions of money and goods up to the second degree; and (3) non-uniqueness of the matrix obtained by differentiating the system of equations obtained by the condition of optimum. The article shows how the requirement of homogeneity conditions limits the possible expressions for the utility function of money. One of them is the frequently used logarithmic function.

Suggested Citation

  • Francisco J. Navarro-González & Yolanda Villacampa, 2021. "A Foundation for Logarithmic Utility Function of Money," Mathematics, MDPI, vol. 9(6), pages 1-8, March.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:6:p:665-:d:521215
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    References listed on IDEAS

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    1. Veronica Rappoport & Enrichetta Ravina & Daniel Paravisini, 2010. "Risk Aversion and Wealth: Evidence from Person-to-Person Lending Portfolios," 2010 Meeting Papers 664, Society for Economic Dynamics.
    2. Paul A. Samuelson, 1958. "An Exact Consumption-Loan Model of Interest with or without the Social Contrivance of Money," Journal of Political Economy, University of Chicago Press, vol. 66(6), pages 467-467.
    3. Fukuda, Shin-ichi, 1997. "The Role of Monetary Policy in Eliminating Nonconvergent Dynamic Paths," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 38(1), pages 249-261, February.
    4. Feenstra, Robert C., 1986. "Functional equivalence between liquidity costs and the utility of money," Journal of Monetary Economics, Elsevier, vol. 17(2), pages 271-291, March.
    5. Charles A. Holt & Susan K. Laury, 2002. "Risk Aversion and Incentive Effects," American Economic Review, American Economic Association, vol. 92(5), pages 1644-1655, December.
    6. Mahmud Yesuf & Randall A. Bluffstone, 2009. "Poverty, Risk Aversion, and Path Dependence in Low-Income Countries: Experimental Evidence from Ethiopia," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 91(4), pages 1022-1037.
    7. David R. Just & Hope C. Michelson, 2007. "Wealth as Welfare: Are Wealth Thresholds behind Persistent Poverty?," Review of Agricultural Economics, Agricultural and Applied Economics Association, vol. 29(3), pages 419-426.
    8. Lucas, Robert E, Jr & Stokey, Nancy L, 1987. "Money and Interest in a Cash-in-Advance Economy," Econometrica, Econometric Society, vol. 55(3), pages 491-513, May.
    9. Lucas, Robert E, Jr, 1980. "Equilibrium in a Pure Currency Economy," Economic Inquiry, Western Economic Association International, vol. 18(2), pages 203-220, April.
    10. Cesar Antunez Irgoin, 2010. "Modelo Money In Utility Function (Miu)," Contribuciones a la Economía, Servicios Académicos Intercontinentales SL, issue 2010-06, June.
    11. Daniel Paravisini & Veronica Rappoport & Enrichetta Ravina, 2017. "Risk Aversion and Wealth: Evidence from Person-to-Person Lending Portfolios," Management Science, INFORMS, vol. 63(2), pages 279-297, February.
    12. Bosch-Domenech, Antoni & Silvestre, Joaquim, 1999. "Does risk aversion or attraction depend on income? An experiment," Economics Letters, Elsevier, vol. 65(3), pages 265-273, December.
    13. Lucas, Robert Jr., 1972. "Expectations and the neutrality of money," Journal of Economic Theory, Elsevier, vol. 4(2), pages 103-124, April.
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    Cited by:

    1. Fabrizio Maturo & Pierpaolo Angelini, 2023. "Aggregate Bound Choices about Random and Nonrandom Goods Studied via a Nonlinear Analysis," Mathematics, MDPI, vol. 11(11), pages 1-30, May.

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