S-shaped Incentive Schemes and Pay Caps

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. Keyword: agency theory; pay fairness; sales force compensation; pay caps