Consumer Surplus Under Demand Uncertainty

48 Pages Posted: 14 Sep 2017 Last revised: 18 Oct 2018

See all articles by Maxime Cohen

Maxime Cohen

New York University (NYU) - Leonard N. Stern School of Business

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

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

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)

New York University (NYU) - Leonard N. Stern School of Business ( email )

44 West 4th Street
Suite 9-160
New York, NY NY 10012
United States

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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