Approximately rational consumer demand and ville cycles
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.