SEPARATION OF VARIABLES FOR UTILITY FUNCTIONS

Back to Page Authors: Alexander F. Mironychev

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Keywords: utility function, generating function, mathematical model, separation of variables

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Abstract: The current paper investigates the problem of construction of the utility function for a given demand function in small dimensional consumer models. The method of separation of variables is used for the utility function and for the demand function. It turns out it is possible to find the differential equation for the special generating function which allows constructing the indirect utility function for the given Marshallian demand function and initial conditions. Afterward, it is also possible to find the direct utility function and the Hicksian demand function. Some examples are demonstrated as the application of the method. The mathematical model for only two consumer goods is considered.

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