The GFT Utility Function

  • R. L. Basmann
  • D. J. Slottje
  • K. Hayes
  • J. D. Johnson
  • D. J. Molina
Part of the Lecture Notes in Economics and Mathematical Systems book series (LNE, volume 316)


Samuelson, in his Foundations of Economic Analysis (1947), credits Walras with having shown many years before that it is possible to modify utility analysis so as to take account of the peculiar properties of money; (Samuelson, 1947b, p. 118).The first part of this chapter is adapted in part from Basmann, Molina and Slottje (1987). The latter exposition follows Basmann, Molina and Slottje (1984a). In response to Walras’ critics who feared “that there was something viciously circular in assuming the existence of prices and of a ‘value for money’ in the midst of the process by which that value was to be determined” Samuelson sought to clear up such misconceptions, by deriving the consumer’s demand function for holding of money from a utility function subject to a linear budget constraint in which the price of “gold”1 and the rate of interest, as well as commodity prices and total expenditure appear as parameters; (Samuelson, 1947b, pp. 119–121). Samuelson introduced commodity prices and the price of “gold” into the consumer’s ordinal direct utility function U(X; p) as parameters.2 Apart from the usual restrictions on fixed-preference utility functions, only homogeneity of degree zero in all prices was imposed. Even without an explicit form of a direct utility function that restriction is sufficient to imply the meaningful, refutable hypothesis that the demand for (holding) money has unitary own-price elasticity; (Samuelson, 1947b, p. 121).


Utility Function Budget Constraint Demand Function Total Expenditure Individual Consumer 
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  1. 1.
    “Of course no reader will think that I attach any particular importance to gold or any other metal; any conventional unit which serves as money will do.” (Samuelson, 1947b, p. 119).Google Scholar
  2. 3.
    E.g., precious stones, gold (possibly) have been considered as “conspicuous consumption” goods, the purchase of which acquire greater or less snob appeal accordingly as their prices increase or decrease. Thorstein Veblen (1899) is usually cited in this connection. Veblen (1899) put forward an explanatory theory of the utility of commodities that attempts to account for the formation and change of consumer preferences over time. Actually, the utility of commodities is viewed as a resultant of two kinds of utility, which compete with each other in affecting the consumers’ responses to changes in prices consumers must pay and to the consumers’ abilities to pay, i.e., the total expenditure of which a consumer is capable (Veblen, 1899, pp. 97–99). In the present connection it must be emphasized that Veblen considered this secondary utility of commodities to be pervasive rather than confined to a few unusual commodities (Veblen, 1899, p. 101). According to Veblen, consumption goods, even productive goods, generally possess and exhibit a mixture of primary and secondary utility. Later in the chapter “Pecuniary Cannons of Taste”, Veblen suggests that there are no goods supplied in any trade which do not have secondary utility in greater or less degree (Veblen, 1899, p. 157). According to Veblen’s theory, conspicuous consumption, or the consumption of goods and services that is motivated predominantly by secondary utility, is not confined to the leisure class but prevails over all the social and income classes from richest to poorest (Veblen, 1899, pp. 88–85, p. 103). This brief review of Veblen’s theory of the utility of commodities makes clear the practical motive for assuming that prices and total expenditures have some influence on the parameters of a direct utility function that is supposed to be mathematical description of the resultant effects of primary and secondary utility in Veblen’s sense.Google Scholar
  3. 4.
    In empirical demand analysis and predetermined variable, apart from prices p and total expenditure M as arguments, is ipso facto hypothesized to be a preference-changing parameter in relation to the underlying preference structure, e.g, time as a trend variable, or “dummy variables” to change intercepts (Basmann, 1956, p. 48).Google Scholar
  4. 5.
    For instance consider f(X) = exp(-1/X 2) at x ≠ 0, f(0) = 0. The function possesses continuous derivatives of all orders; consequently, the Taylor expansion exists. No matter to how many terms the Taylor expansion is carried, the remainder Rn is equal to the value of f(X) itself. cf. Franklin (1940), p. 150.Google Scholar
  5. 7.
    cf. Report of Kiel Meeting, Econometrica, Vol. 24, pp. 327–328.Google Scholar
  6. 8.
    On this, see Pollak’s (1978) quotation from Friedman’s textbook Friedman (1962).Google Scholar
  7. 10.
    Thurstone (1931, p. 141) states that motivation is equivalent to the economists “marginal utility.”Google Scholar
  8. 11.
    See Thurstone, 1931, pp. 142–143)Google Scholar
  9. 12.
    ibid. (p.147)Google Scholar
  10. 13.
    ibid. (p.142)Google Scholar
  11. 14.
    ibid. (p.141)Google Scholar
  12. 15.
    See Hicks, 1946, pp. 309–310Google Scholar
  13. 16.
    See Hicks, 1946, p. 309Google Scholar
  14. 17.
    It seems amusing that economists since, at the very least, the time of Smiths’ infamous invisible hand, have been receptive to the notion of the price vector as a market signal yet any readjustment of individual utility extraction technology over time has been a traditional faux pas. It is as if the organ which secretes the preferences has been amputated yet somehow still exists a grin without a cat. Maybe this is out of the fear of the “havoc it may wreak with the whole theory of choice,” as Scitovsky (1945, p. 100) stated.Google Scholar
  15. 18.
    Arrow (1961, p. 177) noted the emptiness of the definition of complementarity: “There is no room for specialized relations of complementarity or substitution among particular pairs of commodities.”Google Scholar
  16. 19.
    Diewert (1974) provides the generally accepted definition of a flexible functional form: a linearly homogeneous function is flexible if it can provide a second order approximation to an arbitrary twice continuously differentiate linearly homogeneous function.Google Scholar
  17. 21.
    The authors do not interpret (2.36–2.37) as affording a community preference field, although it may serve some function for which community preference fields are intended (cf. Gorman, 1963).Google Scholar

Copyright information

© Springer Science+Business Media New York 1988

Authors and Affiliations

  • R. L. Basmann
    • 1
  • D. J. Slottje
    • 2
  • K. Hayes
    • 2
  • J. D. Johnson
    • 4
  • D. J. Molina
    • 3
  1. 1.Department of EconomicsSUNY BinghamtonBinghamtonUSA
  2. 2.Department of EconomicsSouthern Methodist UniversityDallasUSA
  3. 3.Department of EconomicsUniversity of North TexasDentonUSA
  4. 4.Department of EconomicsUniversity of Mississippi UniversityUSA

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