# The Theory of Value

• R. G. D. Allen

## Abstract

An individual consumer is considered. There are n consumer goods (X1, X2, …Xn) so that the individual’s consumption is shown by the vector :
$$x = \left( {{x_1},{x_2}, \ldots {x_n}} \right)$$
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 :
$$u = u\left( {{x_1},{x_2}, \ldots {x_n}} \right)$$
(1)
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 :
$$utility = \phi \left( u \right)$$
(2)
where ϕ is any function such that ϕ′(u)>0. For example :
$$au + b;\quad a{u^2};\quad a\,\log \,u\quad \left( {a > 0} \right)$$
are all possible functions to represent ordinal utility.

## Keywords

Utility Function Utility Level Indifference Curve Consumption Activity Substitution Effect
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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