S-Shaped Incentive Schemes and Pay Caps

41 Pages Posted: 5 Apr 2011

See all articles by Tony Haitao Cui

Tony Haitao Cui

University of Minnesota - Twin Cities

Jagmohan S. Raju

University of Pennsylvania - Marketing Department

Mengze Shi

University of Toronto - Rotman School of Management

Date Written: March 30, 2011

Abstract

S-shaped incentive schemes and pay caps are fairly common in practice. This paper demonstrates the optimality of s-shaped incentive schemes and pay caps by incorporating salespeople’s aversion to pay inequity into the standard agency model. Our analysis shows that salespeople’s desire for pay fairness increases the convexity of the optimal incentive scheme at small sales but increases the concavity at large sales. Consequently, the optimal compensation plan is s-shaped. With aversion to pay inequity, the optimal incentive scheme always contains an upper bound for total payment. For practical implementation, we propose a capped quota plan to approximate the optimal s-shaped scheme. Our numerical analysis indicates that the capped quota plan has an average non-optimality of less than 2% in parametric spaces studied. The numerical analysis also explores the sources of non-optimality and the relationship between market characteristics and the optimal size of pay caps.

Keywords: agency theory; pay fairness; sales force compensation; pay caps

Suggested Citation

Cui, Tony Haitao and Raju, Jagmohan S. and Shi, Mengze, S-Shaped Incentive Schemes and Pay Caps (March 30, 2011). Available at SSRN: https://ssrn.com/abstract=1799294 or http://dx.doi.org/10.2139/ssrn.1799294

Tony Haitao Cui (Contact Author)

University of Minnesota - Twin Cities ( email )

321 19th Ave S
Suite 3-150
Minneapolis, MN 55455
United States

Jagmohan S. Raju

University of Pennsylvania - Marketing Department ( email )

700 Jon M. Huntsman Hall
3730 Walnut Street
Philadelphia, PA 19104-6340
United States
215-898-1114 (Phone)
215-898-2534 (Fax)

Mengze Shi

University of Toronto - Rotman School of Management ( email )

105 St. George Street
Toronto, Ontario M5S 3E6 M5S1S4
Canada

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