Randomized pricing of a storable good in the presence of consumer stockpiling

Abstract

In a retail setting with a storable product and customers that are heterogeneous in their product valuations and stockpile-up-to levels, intertemporal price discrimination is a key revenue driver. This study considers price randomization as an intertemporal price discrimination scheme that can bring in revenues comparable to those of the third-degree price discrimination. A mathematical model that captures the retailer's expected revenue maximization problem in a two-segment setting over an infinite horizon is developed. We show that when product valuations are uniformly distributed, price randomization generates at least 89\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\frac{8}{9}$$\end{document} of the revenue the retailer can achieve with the third-degree price discrimination strategy. The computational analysis indicates that price randomization can be an effective price discrimination option in the presence of segments having similar sizes and marked differences in product valuations. Moreover, the computational analysis illustrates that price randomization can recover a significant portion of the revenue that the retailer could achieve through deterministic cyclic policies with two price levels. We describe how a retailer should optimally design its price randomization strategy and identify market structures where randomized pricing can be an effective option.