21.17 Principal-agent Models and Salesforce Compensation
21.17.1 Gerstner and Hess (1987)
21.17.2 Basu et al. (1985)
21.17.3 Raju and Srinivasan (1996)
Compare to (Basu et al. 1985), basic quota plan is superior in terms of implementation
Different from (Basu et al. 1985), basic quota plan has
- Shape-induced nonoptimality: not a general curvilinear form
- Heterogeneity-induced nonoptimality: common rate across salesforce
However, only 1% of cases in simulation shows up with nonoptimality. Hence, minimal loss in optimality
Basic quota plan is a also robust against changes in
salesperson switching territory
territorial changes (e.g., business condition)
Heterogeneity stems from
Salesperson: effectiveness, risk level, disutility for effort, and alternative opportunity
Territory: Sales potential and volatility
Adjusting quotas can accommodate the heterogeneity
To assess nonoptimality, following Basu and Kalyanaram (1990)
Moral hazard: cannot assess salesperson’s true effort.
Assumptions:
The salesperson reacts to the compensation scheme by deciding on an effort level that maximizes his overall utility, i.e., the expected utility from the (stochastic) compensation minus the effort distuility.
Firm wants to maximize its profit
compensation is greater than saleperson’s alternative.
Dollar sales \(x_i \sim Gamma\) (because sales are non-negative and standard deviation getting proportionately larger as the mean increases) with density \(f_i(x_i|t_i)\)
Expected sales per period
\[ E[x_i |t_i] = h_i + k_i t_i , (h_i > 0, k_i >0) \]
where
- \(h_i\) = base sales level
- \(k_i\) = effectiveness of effort
and \(1/\sqrt{c}\) = uncertainty in sales (coefficient of variation) = standard deviation / mean where \(c \to \infty\) means perfect certainty
salesperson’s overall utility
\[ U_i[s_i(x_i)] - V_i(t_i) = \frac{1}{\delta_i}[s_i (x_i)]^{\delta_i} - d_i t_i^{\gamma_i} \] where
- \(0 < \delta_i <1\) (greater \(\delta\) means less risk-averse salesperson)
- \(\gamma_i >1\) (greater \(\gamma\) means more effort)
- \(V_i(t_i) = d_i t_i^{\gamma_i}\) is the increasing disutility function (convex)
21.17.4 Lal and Staelin (1986)
A menu of compensation plans (salesperson can select, which depends on their own perspective)
Proposes conditions when it’s optimal to offer a menu
Under (Basu et al. 1985), they assume
Salespeople have identical risk characteristics
identical reservation utility
identical information about the environment
When this paper relaxes these assumptions, menu of contract makes sense
If you cannot distinguish (or have a selection mechanisms) between high performer and low performer, a menu is recommended. but if you can, you only need 1 contract like (Basu et al. 1985)