Retail Price Optimization from Sparse Demand Data

Abstract

It will be shown how the retailer can use economic theory to exploit the sparse information available to him to set the price of each item he is selling close to its profit-maximizing level. The variability of the maximum price acceptable to each customer is modeled using a probability density for demand, which provides an alternative to the conventional demand curve often employed. This alternative way of interpreting retail demand data provides insights into the optimal price as a central measure of a demand distribution. Modeling individuals ’ variability in their maximum acceptable price using a near-exhaustive set of “ demand densities ” , it will be established that the optimal price will be close both to the mean of the underlying demand density and to the mean of the Rectangular distribution fitted to the underlying distribution. An algorithm will then be derived that produces a near-optimal price, whatever the market conditions prevailing, monopoly, oligopoly, monopolistic competition or, in the limiting case, perfect competition, based on the minimum of market testing. The algorithm given for optimizing the retail price, even when demand data are sparse, is shown in worked examples to be accurate and thus of practical use to retail businesses.