Consumer Surplus Under Demand Uncertainty

49 Pages Posted: 14 Sep 2017 Last revised: 9 Jul 2019

See all articles by Maxime Cohen

Maxime Cohen

Desautels Faculty of Management, McGill University

Georgia Perakis

Massachusetts Institute of Technology (MIT) - Sloan School of Management

Charles Thraves

Massachusetts Institute of Technology (MIT) - Operations Research Center; University of Chile - Industrial Engineering

Date Written: September 12, 2017

Abstract

In the economics literature, the Consumer Surplus is traditionally defined for the case where demand is a deterministic function of the price. However, in most 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 in several special cases (additive versus multiplicative demand noise). 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 under linear demand. Finally, we investigate how different levels of demand uncertainty information affect the Consumer Surplus.

Keywords: Consumer Surplus, Demand Uncertainty, OM-Economics Interface, Rationing Capacity, Resource Sharing

Suggested Citation

Cohen, Maxime and Perakis, Georgia and Thraves, Charles, Consumer Surplus Under Demand Uncertainty (September 12, 2017). Available at SSRN: https://ssrn.com/abstract=3035992 or http://dx.doi.org/10.2139/ssrn.3035992

Maxime Cohen (Contact Author)

Desautels Faculty of Management, McGill University ( email )

1001 Sherbrooke St. W
Montreal, Quebec H3A 1G5
Canada

Georgia Perakis

Massachusetts Institute of Technology (MIT) - Sloan School of Management ( email )

100 Main Street
E62-565
Cambridge, MA 02142
United States

Charles Thraves

Massachusetts Institute of Technology (MIT) - Operations Research Center ( email )

77 Massachusetts Avenue
Bldg. E 40-149
Cambridge, MA 02139
United States

University of Chile - Industrial Engineering ( email )

Rep├║blica 701, Santiago
Chile

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