Product Quality and the Law of Demand: An Example of early $2.5 Gold Coins

This article suggests that the Slutsky analysis should be extended so that quality is included in the consumer's utility function as a continuous variable. When quality is included in the consumer's utility function, the consumer is conceived to maximize his/her utility subject to his/her budget constraint by trading off quantity, quality, and price for various products in his market basket. Also, this article suggests that the revised consumer demand theory does not require automatically that the substitution effect is negative (SE < 0). Empirical demand analysis can find that price and quantity are related directly without violating our extended consumer demand theory or without relying on the theory of conspicuous consumption. In other words, the sign of SE is an empirical question which cannot be answered by a theoretical analysis as previously suggested by Slutsky and others. After testing this theory with the numismatic demand for early U.S. $2.5 gold coins, the Slutsky results do not obtain. In this market, the consumer’s quality substitution effect QSE is positive and the consumer’s quantity substitution effect SE is negative; however the magnitude of the parameter for the QSE significantly out weights this parameter for the SE. Hence, the determination of the sign and magnitude of the SE and QSE for this particular consumer and product appear to be an empirical question only answerable through statistical analysis. If these results can be replicated for this and or other products and consumers, then the traditional law of demand may have to be significantly modified when product or service quality are important variables to the consumer. INTRODUCTION Although economists are aware that consumer demand is influenced by product quality as well as by price and income, product quality generally is excluded in most partial equilibrium analysis of consumer behavior. The economist’s theory of consumer behavior began with Adam Smith; however, F. Slutsky in 1905 first PRODUCT QUALITY AND THE LAW OF DEMAND 3 modeled this behavior mathematically. From this time on, the consumer has been thought to treat price and quantity as continuous variables, while quality almost always has remained a constant. In traditional analysis, the consumer is thought to accept product quality as a predetermined variable. Economists felt consumers might substitute products of different quality for one another as they determined that they better satisfied their needs. However, each of these consumers would view quality differently, and quality as a continuous variable never directly entered his/her utility function. This article expands the traditional partial equilibrium analysis by introducing quality directly into the consumer's utility function as a continuous variable at least over a given range. Although the introduction of quality into the consumer's utility function requires some important and limiting assumptions, the ultimate results seem to be worth the effort. While there are many products which possess more than one quality attribute, this article treats only products possessing one quality attribute for simplicity. The ultimate objective of the article is to introduce quality into the consumer's utility function and to reconstruct and analyze the law of demand. After analyzing the substitution effect of the reconstructed law of demand, the author shows that the sign of this effect may not always be negative. This revised theory is tested using the numismatic demand for early U.S. $2.5 gold pieces.