# SFB 303 Discussion Paper No. A - 246

**Author**: Jerison, David, and Michael Jerison

**Title**: Approximately Rational Consumer Demand and Ville Cycles

**Abstract**: Recent research has shown that small deviations from optimizing
behavior can have substantial effects on economic equilibria. Nonoptimizing
demand behavior is of particular importance since individual consumer
expenditure data often violate the strong axiom of revealed preference, and
since the demand of an entire consumption sector is often modeled as the
demand of a representative consumer even though it cannot generally be
derived from maximization of a single utility function. This paper describes
and compares various measures of the extent to which demand behavior
deviates from behavior derivable from utility maximization. If a demand
function satifies the weak but not the strong axiom of revealed preference,
then it is possible for real income to rise monotonically while nominal
income and prices follow a smooth path that returns to its starting point.
Such a path is called a Ville cycle. The extent of the deviation from
optimizing behavior can be measured by the rate at which real income can
rise along such a path. We show how this measure is related to alternative
measures such as the degree of asymmetry of the Slutsky matrix, and the
minimum distance between the given demand function and a function that is
derivable from utility maximization. The relationships among these measures
yield simple revealed preference interpretations for violations of Slutsky
symmetry while suggesting how to compare the sizes of revealed preference
inconsistencies.

**Keywords**:

**JEL-Classification-Number**:

**Creation-Date**: May 1989

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