Two parameter equation of cardinal utility and the possibility of an empirical evaluation of its options

Theoretical bases of economics and management

The concept of rejecting the attempts to measure utility (the feeling of satisfaction from consuming goods), i.e., represent it numerically was first proposed by John Hicks in 1934 but has remained only theoretical up until the present time. As it became clear by the end of the 20th  century, it was counterproductive for the analysis of economic reality.  In accordance with modern concepts of representative theory of measurement, Hicks essentially suggested using an ordinal scale instead of the ratio scale for measuring utility. Pfanzagl later demonstrated that even the simplest mathematical operations are impossible with the results of measurements on a scale of order. This was what likely caused Hicks’s ordinal approach to be unproductive. Our work shows the possibility of measuring the feeling of satisfaction from consuming goods (utility) by the ratio scale. It is known that the entire arsenal of mathematical operations on the named values can be performed with the results of these measurements. We used the methodology of mathematical modeling by differential equations. It is based on a fundamental property of differentiable functions of many variables. The relationship between the differential of the function and the differentials of its arguments is always linear. Partial derivatives can be considered to be factors of proportionality between the differentials. With this approach, the task of constructing a mathematical model is reduced to the justification of the form factors of proportionality (partial) before the differentials of the arguments.  We have substantiated the differential equation of cardinal utility. Its solution, presented in view of the requirements of the correct recording of mathematical expressions with named variables, yields a two-parameter equation of cardinal utility. We discussed the economic meaning of its parameters and the possibility of an empirical evaluation of their numerical values.