TITLE:
Generalized Demand Densities for Retail Price Investigation
AUTHORS:
Philip Thomas, Alec Chrystal
KEYWORDS:
Demand Density; Probability Density; Demand Curve; Double Power Demand Density; Rectangular Demand Density; Kinked Demand Density
JOURNAL NAME:
American Journal of Industrial and Business Management,
Vol.3 No.3,
June
27,
2013
ABSTRACT:
The paper introduces generalized demand densities as a new and effective way of conceptualizing and analyzing retail demand. The demand density is demonstrated to contain the same information as the demand curve conventionally used in economic studies of consumer demand, but the fact that it is a probability density sets bounds on its possible behavior, a feature that may be exploited to allow near-exhaustive testing of possible demand scenarios using candidate demand densities. Four such demand densities are examined in detail. The Household Income demand density is based on the assumption that a person’s maximum acceptable price (MAP) for an item is proportional to his household after-tax income. The Double Power demand density allows the mode to be located anywhere in the range between zero and the highest MAP possessed by anyone in the target population. The two-parameter, Rectangular demand density, the simplest model that a retailer may employ, has the useful feature that it may be matched relatively easily to any unimodal demand density and hence may act as its approximate proxy. The Kinked demand density is derived from the kinked demand curve sometimes used as a relatively uncomplicated way of conceptualizing the effects of oligopoly. The central measures of each of these demand densities are derived: mean price, mode, median, optimal and, when appropriate, the mean of the matched Rectangular demand density. In a further result arising from the use of demand densities, it is shown that stable trading at the kink price will not occur if the demand curve is kinked and convex.