Abstract
An individual consumer is considered. There are n consumer goods (X 1, X 2, …X n) so that the individual’s consumption is shown by the vector :
and hence by a point P in commodity space of n dimensions. Assume that the individual’s level of satisfaction or utility is a function of his consumption :
where u is taken to vary continuously, and with continuous derivatives of the first and second order. However, the relation of the utility level u to consumption x is taken in the ordinal sense, i.e. u(x1, x2, … xn) is only one of many functions which can represent utility, and any other function which orders consumption in the same way will serve. This means that u is determined only up to an increasing (monotonie) transformation :
where ϕ is any function such that ϕ′(u)>0. For example :
are all possible functions to represent ordinal utility.
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© 1959 R. G. D. Allen
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Allen, R.G.D. (1959). The Theory of Value. In: Mathematical Economics. Palgrave Macmillan, London. https://doi.org/10.1007/978-1-349-81547-0_19
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