Consumer Response to Increased Variety in Demand and Inverse Demand Systems with Consistent Preferences

Current neoclassical microeconomic theory of rational consumer behavior affirms a unique consumer price-quantity relationship under conditions associated with monopolistic competition. Inverse demand will be just as own-price elastic as demand in the neighborhood of the limit state, while demand will always be more own-price elastic than inverse demand everywhere else. This study shows that these results require inconsistent preferences and irrational consumer behavior. When preferences are consistent, the unique price-quantity relationship for an individual consumer choosing among imperfect substitutes is actually quite rare, and is never found with increased variety in or near the limit state which generally is used to define monopolistic competition. Instead, inverse demand systems lead to a perfectly price elastic price-quantity relationship, while demand system price elasticities reflect the given degree of product differentiation in or near the limit state, so consumers will be more responsive to changes in quantities than prices. This result can extend significantly away from the limit state to very small product groups. Coincidence of demand and inverse demand systems is not ruled out, but with imperfect substitutes, occurs outside the limit state, and the distance between coincidence and the limit state increases with the degree of product differentiation. This means that a rational consumer should generally respond in two quite different ways to changes in prices as compared with changes in quantities with an identical utility function and consistent preferences across both systems in monopolistic competition settings. These results are general and hold regardless of the particular utility function employed to model consumer behavior, or of any special preference the consumer may have for increased breadth variety. These results are based on a two-dimensional concept of variety involving both the number of substitutes, and the ease of substitution among them. Consumer response is classified as breadth variety neutral/breadth variety diverse/breadth variety focused, as the ease of substitution is unaffected/increases/decreases with increased number of goods considered. Although it is possible to observe inverse demand that is less price elastic than demand as the number of goods approaches the limit state, this is restricted to strong breadth variety diverse/extreme breadth variety diverse consumer response in which variety in this two-dimensional sense actually is constant/decreasing. The validity of these results depends critically on the comparison of the consumer response ratio for demand systems with the consumer response ratio for inverse demand systems. Consistent preferences for this study require these to be equal. It is shown that when they are equal, the aggregated rescaled size of the cross-substitution effect relative to the size of the income effect in demand systems will equal the rescaled size of cross-complementarity effect relative to the size of the scale effect in inverse demand systems. Implications of this analysis are important for rethinking the meaning of rational consumer behavior, and its impact on developing reliable welfare comparisons of Cournot vs. Bertrand models of competition with imperfect substitutes, for reliable analysis of the economic impact of increased trade among nations, for econometric studies involving inverse demand systems, and much more