Consumer Surplus Under Demand Uncertainty

Abstract

Traditionally, in the economics literature, the Consumer Surplus is mainly defined for the case where demand is a deterministic function of the price. However, in various operations management problems, demand is assumed to be stochastic, and hence stock-outs can occur. To measure consumer welfare in such settings, one needs an appropriate definition of the Consumer Surplus under demand uncertainty. We present a general extension of the Consumer Surplus for multiple products under stochastic demand with a general capacity allocation rule. We provide a graphical interpretation of this definition as well as its connection to the utility function of a representative consumer. We then use this definition to study the impact of demand uncertainty on consumers by comparing the expected Consumer Surplus under stochastic demand to the Consumer Surplus in a deterministic setting. We show that, in many cases, demand uncertainty hurts consumers. We then propose a sharing mechanism in which the supplier can share its excess capacity (or demand) among its different stores. Such a mechanism increases the expected Consumer Surplus. We also derive an analytical bound on the ratio of the Consumer Surplus relative to the deterministic setting for the special case of linear demand. Finally, we investigate how different levels of demand uncertainty information affect the Consumer Surplus.

Keywords: Consumer Surplus, Demand Uncertainty, Rationing Capacity, Resource Sharing