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# Accession Number:

## ADA197135

# Title:

## Deriving a Utility Function For the U.S. Economy

# Descriptive Note:

## Technical rept.

# Corporate Author:

## STANFORD UNIV CA SYSTEMS OPTIMIZATION LAB

# Report Date:

## 1988-04-01

# Pagination or Media Count:

##
73.0

# Abstract:

## Given a general dynamic equilibrium formulation of a time staged model, this document seeks conditions on the distribution of utility functions of individuals which imply the model is equivalent to a mathematical program. Gorman and others long ago have observed that Engel curves of average consumption as a function of income at fixed prices are remarkably linear over a broad range of income of interest with tapers off at both ends of this range. The authors reproduce this phenomenon by assuming that a general polynomial of the second degree has enough parameters coefficients to globally represent the utility functions of individual consumers, and the distribution of utility functions that individuals have is independent of the income they happen to have. They achieve the latter by assigning values to the parameters of the utility functions by a random drawing with replacement from a population urn containing a representative sets of the parameters. They then derive the functional form of the per capita demand function and necessary and sufficient conditions for its integrability. Finally, the document shows in the context of the time staged model, that when the population is not too polarized as to its tastes at fixed income levels, a concave objective function always exists, which maximized subject to the physical flow constraints, implies the equilibrium conditions. Keywords Economic models, Mathematical models.

# Distribution Statement:

## APPROVED FOR PUBLIC RELEASE

#