Sales Force Contracting Under Endogenous Risk

Transcription

1 Sales Force Contracting Under Endogenous Risk David Godes November 2003 I am grateful to George Baker, Bob Gibbons, Dina Mayzlin, Duncan Simester and Birger Wernerfelt for many helpful comments on earlier versions of this paper. The paper has also benefited from comments at the MIT Marketing Seminar and the Marketing Science Conference. David Godes is an Assistant Professor of Business Administration at Harvard Business School, Morgan 165, Soldiers Field, Boston MA (dgodes@hbs.edu)

2 Sales Force Contracting Under Endogenous Risk Abstract Salespeople choose actions by trading off cost, return and risk. The literature does not consider the impact of risk on action choice. This tradeoff has important implications for the firm. First, the firm may provide no insurance in the salary. Since the agent s action choice will determine her risk, the salary cannot compensate her for it. Second, the firm may not be able to design an incentive scheme to implement particularly risky actions. Finally, a multi-product firm may not be able to design a scheme in which the agent splits her effort across two products that are technological substitutes. One solution is a sales force structured by product. Complements may be more costly to sell through a product structure. Thus, substitutes (complements) should be sold through a product (territory) structure. Keywords: Sales Force Management, Incentives, Compensation, Agency Theory JEL Classifications: J33, M30, M50, M52, M54

3 Scene from My Little Chickadee in which a group of men are playing cards: Cousin Zeb: (Walking by, surprised) Uh, is this a game of chance? Cuthbert J. Twillie: Not the way I play it, no. 1 Introduction Liketherestofus, salespeoplecareabout infact, they dislike risk. Rational salespeople make decisions every day that trade off the cost, the expected return and the risk associated with various actions. These decisions might relate to how hard they should work, which accounts to call on or what the focus of a particular sales call should be. Cost, return and risk each factor to different degrees into each of these decisions. Working harder for example, putting in extra effort to anticipate and formulate strategies against every possible objection both increases the return the salesperson might expect from a sales presentation and reduces the risk of a potentially fatal objection. Calling on new prospects, on the other hand, may be a riskier proposition than calling on one s list of current customers: who knows what their needs are? will we be able to meet them? Finally, focusing one s efforts on a sales call towards building a long-term relationship in lieu of pursuing current sales also may be viewed as risky in the sense that one s key contact may move elsewhere or the firm s needs may change. It seems a safer prospect to meet the needs they may have now and worry about tomorrow when it comes. Thus, salespeople not only dislike risk but it is also quite common for them to take actions to decrease it, to the extent such actions are available to them. That is, theirriskisoften endogenous as shown by these examples. Moreover, the risk-reducing actions may sometimes be consistent with the firm s desire to maximize long-term profits, as is probably true in the case of a salesperson working harder to overcome all potential objections. On the other hand, this is not always true. Calling on current, known customers and bypassing the riskier prospects reduces risk but may not increase the expected return. Most models of sales force contracting assume that salespeople will avoid effort if not properly compensated. The same is not, however, true of risk. We argue that the relationship between risk and return in particular, the extent to which the actions that decrease the former increase or decrease the latter is of critical importance to the firm in its design of compensation schemes. We present clear analytical evidence that explicit consideration of this phenomenon may lead to very different normative implications for sales force contracting. As well, we believe that our results may in some cases match significantly better the sales force compensation schemes and job designs we observe in practice. The paper proceeds as follows. After a review of the related literature in Section 2, Section 3 presents a model in which the salesperson s effort choice drives the binary outcome probability 1

4 of a single-product sales process. More effort means that she ll sell the product successfully with a higher probability. In Section 3.1, we make the standard assumption that the firm would like the agent to put forth the highest possible effort level. Since we assume that the probability of a sale is always greater than 1 2, higher outcome probabilities also decrease her risk. a case in which risk reduction and return maximization are in harmony. Thus, this is We show that, in this case, the firm may provide no insurance in the salary component of the compensation scheme. Since risk is endogenous, the salesperson may opt to implement an effort level that corresponds to low (in fact, zero) risk. Thus, insurance cannot be provided in the salary, as is typically the case. Moreover, this implies that the proportion of a salesperson s compensation that is payable in the form of incentive (as opposed to salary) may, thus, be higher the more risk-averse she is. The intuition for this result is straightforward. The more risk-averse she is, the more insurance she requires, in the sense that the firm needs to pay her enough to ensure that she reaches her reservation utility. However, this insurance cannot come in the form of salary. We argue that this result may partially explain some of the null results found on risk and risk aversion in empirical analyses of sales force compensation. Finally, we show that, in some cases, the firm may actually prefer to have a sales technology in which the agent might face more risk. The key to this result is that this risk must be endogenous and its reduction requires the agent to take actions desirable to the firm. In Section 3.2, we look at a case in which the salesperson may have responsibilities besides just selling. Thus, the firm wants to implement an interior effort level which is not too high and not too low. To effect this, the firm may optimally dampen the incentive scheme in order to ensure that the salesperson is willing to do her other work (paperwork, service, etc.). In this case, then, the agent s desire for risk reduction runs counter to the firm s goals. In this model, we show that the firm may not be able to design any incentive scheme to implement this interior effort level when the salesperson is risk-averse enough. Alternatively, a salesperson with a given level of risk aversion may not be willing to implement particularly risky alternatives. Finally, in Section 4, we extend our analysis of this interior efforttoaspecific concrete problem: sales force structure for a multi-product firm. In particular, we investigate the firm s desire to provide enough sales effort on each product. We begin by looking at a sales force structured along territory lines in which each salesperson is asked to split her effort across products. This requires her to bear more risk on both products as compared with a case in which she puts all of her effort behind one of the products. Similar to the single-product case, this model yields the insight that the firm may not be able to achieve this effort split at all. This problem is particularly acute for products that are substitutes where effort placed on one product decreases the probability that the other is sold. We then investigate a potential solution to this problem: a sales force structured along product lines. Besides guaranteeing that some effort will always be placed on 2

5 both products, the product structure may also do so at lower cost than the territory structure when the products are substitutes. On the other hand, we show that complements may be more costly to sell through a product structure than a territory structure. Thus, we argue, substitutes should be ceteris paribus sold more often through a product structure while the opposite should be true of complements. The paper concludes in Section 5 with a discussion and directions for future research. 2 Related Literature The idea that the risk faced by an agent is partially under her control has been in the background since the earliest analyses of the principal-agent problem. In the economics literature, both Mirrlees (1974) and Holmstrom (1979) present models with general distributions that are conditional on the agent s effort choice and therefore allow for the possibility that risk is endogenous. However, neither specifically addresses this issue or its possible impact on their results. For example, Holmstrom s seminal paper (as well as most of the work that has built on it) focused on a comparison of distributions for which higher effort implied first-order stochastic dominance. 1 This approach, in effect, focused on the mean-increasing impact of effort rather than the risk-increasing or - decreasing impact of effort. Nor have the theoretical analyses of sales compensation schemes in the marketing literature directly considered this phenomenon. As Holmstrom did, Basu et al. (1985) and Lal and Staelin (1986) both consider cases in which the impact of effort on the noise term results in first-order stochastic dominance while Rao (1990) considers a risk-neutral agent. Similarly, the standard approach for applied analyses of sales force compensation is to utilize a separable exogenous error term that is normally distributed. This specification, when combined with an exponential utility function and a linear technology, offers an extremely convenient and tractable certainty equivalent. Examples of this approach in the marketing literature include Lal and Srinivasan (1993); Hauser et al. (1994). The exogeneity of the variance in this formulation, along with the assumption of a linear contract (generally by invoking Holmstrom and Milgrom (1987)) implies that the agent faces exogenous risk. In summary, then, much of the previous work in this area has tended to assume away the possibility of endogenous risk and those papers that didn t do so nevertheless didn t explicitly consider the impact that endogenous risk might have on incentives and/or job design. One paper that does consider the link between an agent s actions and the risk she faces is the empirical study by Chevalier and Ellison (1997). They show that equity mutual fund managers adjust the riskiness of their portfolio in response to the incentives inherent in the relationship between assets and returns. Besides providing interesting insights into 1 That is, they assume that effort level e implements an outcome distribution f (x e) Moreover, for e 0 >e, f (x e 0 ) dominates f (x e 0 ) in a first-order stochastic sense. (and, therefore, equivalently risky) distribution. This is tantamount to a mean-shift of the identically-shaped 3

6 the decision-making process of this important financial institution, this paper also demonstrates the importance of considering explicitly the fact that risk may, in fact, be under the agent s control and that this may have important implications for effort selection and the payoffs of the game s other players. 3 A Simple Model of Endogenous Risk The basis for our model is the standard problem in sales force motivation and compensation: a salesperson for whom effort is costly and unobservable. In order to induce the desired level of effort, the firm must design a compensation scheme based on the only observable outcome: sales. The only significant change we make to this general set-up is that we allow her effort to impact not only the sales volume she produces but also the risk she faces. That is, unlike the standard model, the risk faced by the salesperson here is partially endogenous. In order to investigate the impact of endogenous risk on her decisions and therefore on the firm s compensation scheme we first need to specify risk as a function of her effort level. We choose the simplest possible specification in which the salesperson puts forth effort that results in a binary outcome which we ll refer to as a sale or no sale. She chooses between three levels of effort e {0, 1, 2} whichcorrespondto three probabilities of a sale p e such that: p 0 = 0 (1) p (2) p 2 > p 1 (3) So, if she puts forth no effort, she never makes a sale while higher effort increases the probability of a sale. Moreover, we assume that the selling technology is everywhere concave in effort, implying that p The monetary equivalent of the disutility C (e) associated with effort is linear: 3 C (e) =c e. The agent has exponential utility over monetary rewards x: U (x) =1 Exp[ rx] (4) where r is the coefficient of absolute risk aversion (Pratt, 1965). Finally, she is assumed to have outside options which will yield her expected utility U. The firm s profit function is denoted Π (e) to which we give more structure below. Given the discrete outcome, the optimal contract is necessarily a linear one with salary α paid regardless 2 The assumption that p 1 1 is sufficient to ensure concavity for all p 2 2 and is therefore stronger than we need for any specific p 2. 3 This is not an important assumption, it simply allows for ease of exposition. Note also that, given concave utility, the salesperson s utility is, of course, convex in the cost of effort. 4

7 of the outcome and commission β paid only if there is an observed sale. Thus, the firm chooses α and β to solve the following problem: Max α,β Π (e) βp e α (5) s.t. E [U e ] U (6) e arg max e {0,1,2} E [U e] (7) The first constraint, (6), is the individual rationality constraint, ensuring that the salesperson accepts the contract to work for the firm. The second constraint, (7), ensures that the salesperson s effort selection is an optimal response to the offered contract. We investigate the optimal compensation scheme under two different contexts. The first is a case in which the firm wants the agent to work as hard as possible. The second, which we believe to be very common in practice but less commonly studied, is one in which the firm wants to implement an intermediate outcome. In the former, the firm s goals and the agent s desire for risk reduction are both satisfied by the same effort choices. Thus, there is no conflict. However, we show that the endogeneity of the risk has interesting implications for the optimal scheme. In the latter context, however, there is a potential for conflict. As a result, in some cases, the firm may not be able to implement the desired outcome. 3.1 Case i: Firm Prefers Highest Effort Levels The traditional approach to the agency problem is to assume that the agent has a single task to perform and that the firm prefers that she works as hard as possible (Holmstrom, 1979; Basu et al., 1985; Rao, 1990; Lal and Srinivasan, 1993; Raju and Srinivasan, 1996). In our setting here, then, we might assume that our salesperson has a single product to sell to a single customer and that, further she has no additional responsibilities to draw on her time or effort. Moreover, we assume that there is no downside to her putting all of her effort into selling to a customer. So, for example, we assume that the customer doesn t mind if the salesperson calls her constantly. In Section 3.2, we investigate a context in which such maximal effort devoted to only selling activities is not necessarily preferred. In order to focus our attention on the optimal scheme given the firm s objectives, we assume that the firm s profit function takes the following form: Π (0) = Π (1) = 0 (8) Π (2) = p 2 (1 β) α So, conditional on getting the desired level of work from the salesperson (i.e., e =2), the firm s profit is equal to the sales less compensation costs. This is clearly a non-standard specification 5

8 of firm profits and bears discussion. Our objective is to investigate the impact of endogenous risk on the firm s compensation schemes. In particular, we re interested in how endogenous risk impacts the firm s ability to design a scheme to implement the outcome it desires (in expectation). This is necessarily a function of what it is that the firm would like to implement. We would expect that the results would be a function of the match between the firm s objectives, on one hand, and the salesperson s desire for risk reduction, on the other. Thus, to highlight the impact of these objectives, we have chosen to impose these objectives exogenously. Clearly, the results will be conditional on the actual firm objective. Finally, it is essential to note that this approach is hardly without precedent. Most notably, for very similar reasons, Holmstrom and Milgrom (1991) exogenously impose a benefit function in which the firm earns zero profit unless the agent allocates effort to both products. This is equivalent to the approach we take here. Transforming (6) to solve for α explicitly as a function of the other parameters we get: α U + C (e )+ 1 r Ln [{p e E +(1 p e )}] (9) where E Exp[ rβ]. Since (5) is strictly decreasing in α, Equation (9) will naturally hold with equality and (6) will bind in equilibrium. Thus, in the standard fashion, we can substitute (9) as an equality into (5) to yield Π (2) = p 2 (1 β) 2c 1 r Ln [p 2E +(1 p 2 )] U. Differentiating this with respect to β yields Π (2) E = p 2 1 < 0 (10) p 2 E +1 p 2 Thus, the objective function is decreasing in β. Conditional on the high effort level being implemented, then, we can transform the problem into a simpler form: Min β (11) s.t. β 1 Exp[ 2rc] (1 r Ln p2 ) (12) p 2 β 1 Exp[ rc](1 r Ln p1 ) (1 p 2 ) (13) p 2 p 1 Exp[ rc] Thus, the firm simply wants to minimize the commission it has to pay to the salesperson in order to get her to put forth high effort. The following Lemma tells us which constraint will bind in equilibrium and, thus, what drives β. Lemma 1 In the program (11), for any p 2 there exists a p 1 (p 2,r,c) such that: (a) For all p 1 < p 1 ( ), (12) binds in equilibrium. (b) For all p 1 p 1 ( ), (13) binds in equilibrium. All proofs are contained in the Appendix. more likely to deviate to e =1than to e =0. So, if p 1 is high relative to p 2, the salesperson is When p 1 is low, the salesperson is more likely to 6

9 deviate to e =0. The important thing to note is that e =1is the highest risk outcome for the agent while e =0is the lowest. Thus, her decision to select e =2over the next best alternative must account for not only the relative expected returns associated with these choices but also their relative riskiness. The following surprising result reflects this. Proposition 1 When p 1 < p 1, α = U In this region of the parameter space, the agent receives no risk premium in her salary. That is, she is not compensated for any of the risk she is forced to bear in equilibrium. Note that this is true for arbitrarily high levels of risk aversion as long as IC0 binds. Note also that p 1 p 2 2 as r 0. Thus, when risk aversion becomes negligible, this result does not hold. This result seems surprising and contradictory of the bulk of agency theory literature (Holmstrom, 1979; Holmstrom and Milgrom, 1991) and sales compensation literature (Basu et al., 1985; Lal and Srinivasan, 1993) which highlight the trade-off between insurance and incentives. There is absolutely no insurance provided in this salary. The salary only compensates her for her outside options. The intuition offered for the extant results is that the salesperson must be compensated for the risk she will bear. Since, in these models, risk is exogenous, the salesperson and the firm know ex ante what the agent s level of risk will be and thus the salary can compensate her for it. It is, of course, preferable that the firm compensate her for this risk in a deterministic fashion since, by assumption, she is risk averse and the firm is risk neutral. However, this form of salary as insurance is not possible when (a) risk is endogenous and (b) the agent is a credible threat to select a low risk effort option. This is because the level (and, in fact, existence) of the risk that the agent will bear is only determined in equilibrium. Therefore, incentive compatibility requires that the insurance be provided in the form of (stochastic) bonuses and not (deterministic) salary. The salary is useless as an insurance tool. This highlights an inherent problem of contracting under endogenous risk: to ensure that the agent is willing to accept the risk the firm wishes her to accept, it needs to compensate her for this risk. However, this compensation must, by its nature, be stochastic (i.e., she only gets the bonus if she makes the sale, which is probabilistic). The more risk-averse she is, then, the higher this insurance must be. This result might explain why, in some industries, we sometimes observe schemes in which salespeople s compensation package is comprised of an extremely high proportion of commission. For example, in radio broadcasting it is typically the case that salespeople are paid 100% commission even though the standard theory would never predict this to be true. In absence of some sorting mechanism in which agents with lower risk aversion self-select into these industries, it is not entirely clear why some industries would be characterized by such high-powered incentives. Proposition 1 suggests that it may be at least partially due to the fact that risk is endogenous. Proposition 1 suggests, then, that we ll observe lower salaries and, therefore, proportionally 7

10 more commission than the current theory might predict when the agent has effort options that might yield her lower risk. Since this is driven by the agent s risk aversion, it s important, then, to ask what impact risk aversion will have on the compensation scheme. Below, we present several results on the impact of risk and risk aversion on the optimal contract and firm profit. The following result addresses this question and, again, shows that the simple consideration of endogenous risk yields results that may be quite different from those based on strictly exogenous risk. Proposition 2 When p 1 < p 1, β is increasing in r. When p 1 > p 1, β decreasing in r. values of p 1, β is decreasing in p 2. For all We find that when p 1 is high, we get the standard result that the firm s optimal compensation plan will be of lower power the higher is the agent s risk aversion. However, when p 1 is low then the optimal commission is actually increasing in risk aversion. The key factor here is what the salesperson s credible threat is. When p 1 is high, she s most likely to deviate to e =1so IC1 binds. In this case, the agent has shown a willingness to accept some risk. Moreover, since p 1 is high, that risk relative to the risk she bears for e =2 is not too high. Finally, the baseline risk that associated with p 1 isreflected in the salary. However, when p 1 is low, the opposite is true. In this case, the salesperson is most likely to deviate to e =0which brings her no risk. 4 Thus, the firmmustpayherfortherisksheisbeingaskedtobear. AsshowninProposition 1, this compensation cannot come in the form of a salary but must come in the bonus. Thus, her bonus must be higher and higher the more risk averse she is. This highlights the fact that β has to play two roles when risk is endogenous. It must compensate the agent for her effort and for the risk she will bear in the firm s desired outcome. The riskier the outcome that is, the lower p 2 the more risky the equilibrium outcome and therefore the higher β has to be in order to compensate her for this risk. Combining the results in Propositions 1 and 2 yields the following Corollary: Corollary 1 For all parameter values, the proportion of the salesperson s compensation that is α made up of salary is decreasing in the riskiness of the equilibrium outcome: α+p > 0 2 β Put differently, the riskier the equilibrium outcome, the more of the agent s expected compensation that will come in the form of commission. This is in direct contrast to the existing literature 4 Whilethisisofcourseastylizedmodel,onecancertainly see parallels to real-world decisions. In this case, we might think about the salesperson as not being willing to go out and get new business, which requires a great deal of effort, and is instead comfortable working with the same clients she has known for years. In this case, the firm needs to really increase the incentive power to get her to go out there and find new custoemrs. Moreover, the extent to which her incentive must be increased is increasing in her risk aversion since it is this risk for which she ll be compensated. p 2 8

11 (see for example the comparative statics results in Table 1 in Lal and Srinivasan (1993)). The intuition is analogous to above: as the desired (high effort) outcome becomes riskier (i.e., as p 2 decreases), the firm needs to compensate her for this risk in the form of a higher risk premium. However, as described above, at least part of this risk premium must be paid in the form of a bonus, not salary. Thus, the commission increases and salary decreases. This is, of course, a stylized model and, to the extent that exogenous risk is substantial one would expect a downward force on commissions (compared with salary) as risk increases. The fact that there exists this offsetting interplay between exogenous as endogenous risk may in part explain the lack of clear empirical support for the theoretical prescriptions. For example, John and Weitz (1989) study the relative proportion of salary and incentives in a transactions-cost approach. One of their independent variables environmental uncertainty is a useful proxy for risk in agency theoretic terms. 5 Yet, their model yields no significant results for this construct and thus no support for the hypothesis. Similarly, Cravens et al. (1993) model two dependent variables the percentage of compensation paid in the form of salary and the extent to which the firm monitors salespeople as a function of several independent variables. While they do not model risk directly, they do model risk aversion. They find no support for the hypothesis that the salary percentage is positively related to risk aversion. 6 We argue that a more complete analysis of not only the level of risk but the nature of the risk is necessary. By incorporating the agent s risk reduction strategies explicitly and, thereby, separating the impact of exogenous and endogenous risk one may find more empirical support for these hypotheses. One aspect of this result that is somewhat unappealing is the fact that, as p 2 decreases, the marginal impact of effort also decreases, thus it isn t necessarily surprising that β would increase in this case. However, the following result shows that a similar result holds for risk aversion r when p 1 is low though not when p 1 is high. Proposition 3 When p 1 < p 1, r α α+p < 0. Whenp 2 β 1 > p 1, r α α+p 2 β > 0. So, when p 1 < p 1, the more risk averse the agent is, the less of her expected compensation is payable in the form of salary. Again, the intuition is perfectly straightforward. In equilibrium, she is asked to bear more risk. The fact that she is more risk averse means that she needs to be compensated for that risk, but that compensation must come in the form of bonuses. Thus, she gets more incentive compensation. It is not difficult to make the intuitive leap from the foregoing analysis to a perspective that the firm might, in fact, prefer endogenous risk in some cases. Since the agent doesn t like risk, she ll 5 Indeed, the three items in the scale comprising this construct support this interpretation: (1) Industry volume: stable vs unstable; (2) Sales forecasts: accurate vs inaccurate; (3) Unpredictable vs. predictable. 6 They do, however, find support at the p =.05 level for a positive relationship between risk aversion and monitoring. 9

12 take actions to decrease it. Moreover, as we ve shown, to the extent that these actions might be counter to the firm s desires (for example, choosing e =0), the compensation scheme must reflect this motivation. The manager must consider not only the agent s preference for low effort but also her preference for low risk. To the extent that the firm s desired outcome is aligned with the agent s preference for lower risk, the firm may benefit from this motivation. The final Proposition of this Section addresses this. Proposition 4 When p 1 > p 1, Π p 1 < 0. When p 1 < p 1, firm profits aren t a function of p 1. In this context, the firm prefers lower p 1. Put differently, the firm actually prefers that the technology be riskier in the sense that intermediate effort levels yield the agent strictly higher risk the lower is p 1. This runs counter to the typical belief that risk is always bad for a compensation scheme. Proposition 4 says that, if it could, the firm would make the agent face more risk when she chooses e =1. The key here is that such a case would be tantamount to adding endogenous risk which the agent can decrease by choosing e =2. 7 In this sense, then, it appears that risk may actually be an incentive in that its reduction is a second motivation for the agent to put forth high effort (in addition to higher return). This result is interesting because it is not what one obtains from a model of risk neutrality. 8 So, while we suggest no contradiction to the belief that random exogenous noise is bad for a compensation scheme, we believe that this result may offer an explanation for some firms decisions to increase risk in an endogenous way. 9 For example, many firms run contests and lotteries based on sales results. A typical example might be one in which each salesperson gets to place a certain number of balls in an urn for every sale she makes. Thus, depending on the parameters of the contest, the higher her effort level, the more she may be able to decrease the risk associated with the lottery It is important to note that in this result, the ex post risk faced by the agent conditional on her equilibrium choice is unchanged. However, the risk associated with the off-pathactionmaybeincreasedbythefirm and this may lead to higher firm profits. 8 IC1 in a model of risk neutrality is p 1 β p 1 = p 2 β p 2 c so that β =1 c p 2 p 1. Also, α is set such that α + βp 2 2c =0or α =2c βp 2 =2c 1 c Π p 2 p 1 p 2. Thus, p 1 = α p 1 + p 2 p 1, but since α =2c βp 2 α p 1 = p 2 p 1 so Π p 1 =0. 9 Baron and Besanko (1987) derive a similar result in a very different model. They investigate the interaction among risk sharing, adverse selection and moral hazard. One of their findings is that, in certain regions of the parameter space, the firm prefers that the risk averse agent (the supplier in their model) bears some risk even though there is no uncertainty in either their cost or their output technology. The intuition behind their result is that this risk sharing is required in order to deal with adverse selection; it reduces the information costs associated with true cost revelation. 10 As in Godes (2003a), it is straightforward to show that this prescription that the firm may prefer to add (endogenous) risk in some cases holds in a more-general model as well. In fact, it is shown in this model that the 10

13 3.2 Case ii: Intermediate Effort Levels The results in Section 3.1 are driven by the fact that the agent wants to reduce her risk. Her choice of high effort is attractive to her for two reasons: it reduces her risk and it increases her expected compensation. Moreover, it s attractive to the firm because her risk-reducing actions are consistent with the firm s goal of implementing high effort. While the assumption that the firm would like to implement the highest possible effort level is a common one, it may not always be true in practice. On one hand, the highest effort might represent too hard of a sell for some customers. It might be the case, for example, that the firm would like the agent to attempt to inform and persuade the customer regarding the merits of the product, but only up to a certain point. Selling beyond this point might have negative repercussions for the firm and perhaps, though not always, for the salesperson. More generally, in reality, the responsibilities of a salesperson are varied and multidimensional. In addition to selling, most salespeople are responsible for prospecting, providing after-sales service, delivering products, filling out paperwork, helping other salespeople, expediting orders and interacting with other functional areas of the firm. In fact, these responsibilities may comprise a significant portion of the sales job. In fact, according to a recent survey, salespeople spend more than half of their time on non-selling activities. According to the salespeople, they spent 26.4 hours a week on such tasks. According to their managers, the number was 23.5 hours. 11 With respect to many of these responsibilities, the agent s efforts are unobservable and/or nonverifiable. As discussed extensively by Holmstrom and Milgrom (1991), when this is the case, the firm may need to temper the power of its incentive schemes in order to ensure that not too much of the observable effort is put forth at the expense of the unobservable efforts. For example, we mightassumethatsellingeffort is observed with less noise than servicing effort. Thus, there might be too much selling effort produced and too little servicing effort produced since the salesperson would rather put forth more effort on the less-noisily observed output 12. Some empirical support for this implication can be found in Cravens et al. (1993). They find that lower-powered incentives (in their model, a higher percentage of fixed salary) are associated with high levels of a specific non-selling activity: providing information. 13 Thus, we are interested here in a case in which the firm wants to implement high, but not too high, levels of effort. This context is of particular interest in the case of endogenous risk to the extent that moderate effort may expose the agent to higher risk than would be true if she worked as hard as possible. While the (risk neutral) firm may prefer that she implement firm may design a scheme containing endogenous risk that forces the agent to bear strictly higher ex post risk than would be the case with purely exogenous risk. 11 Source: Salespeople Spend Half of Their Time not Selling, American Salesman, March 1, One remedy that suggested in Holmstrom and Milgrom (1991) is to design jobs in such a way that observable and unobservable tasks are not joined in the same agent. 13 The items in this scale include measures related to the accuracy, timeliness and completeness of paperwork. 11

14 a success probability of.5, the agent would rather work harder ceteris paribus and implement a higher-probability (and therefore less risky) outcome. We begin the analysis of interior effort levels in this Subsection with a simple single-task model. This allows us to develop the basic intuition that it is expensive, difficult and, in some cases, impossible for the firm to implement high-risk interior effort levels. In the following Section, we further develop this idea in a more concrete but more complicated context: multi-product sales forces. Analogous to (8), we capture the firm s preference for interior effort in the following profit function: Π (0) = Π (2) = 0 (14) Π (1) = p 1 (1 β) α We again substitute (6) back into (5). Moreover, we can transform the incentive compatibility constraints to yield an equivalent problem as follows: s.t. Min β β (15) β 1 Exp[ rc] (1 r Ln p1 ) p 1 β 1 Exp[ rc](1 r Ln p1 ) (1 p 2 ) p 2 p 1 Exp[ rc] (16) (17) In (15), the firm minimizes the commission rate necessary to ensure that the salesperson puts forth an interior level of effort. Equation (16) ensures that she prefers to put forth e =1to e =0 while (17) ensures that she won t choose e =2. Since (10) holds with p 1 in place of p 2,profit is again decreasing in β. So,itmustbetruethatIC0 0 always binds and, following the intuition from Section 3.1, it is necessarily the case that α =0. However, as we know from Section 3.1, and Lemma1specifically, the β associated with IC0 0 may or may not be lower than that associated with IC1 0. The following Proposition addresses this issue: Proposition 5 When p 1 > p 1, IC0 0 binds and defines β. implement e =1. Further, p 1 1 as r. When p 1 < p 1, no contract exists to This is shown in Figure 1. The intuition is analogous to that developed above. When the salesperson is asked to implement an outcome that is risky for her, and when options exist that are less risky for her (i.e., when the risk is endogenous), the firm has a problem. It would like to pay her high-powered incentives to bear this risk. However, the agent has two low-risk options in the form of e =0and e =2. As the power of the incentives grows, the latter becomes doubly attractive in that it presents her with high return and low risk. When p 1 gets low enough relative 12

15 β IC1 In case i, the optimal contract is the upper enevlope of these two constraints. IC0 In case ii, the feasible region is all bonuses above IC0 and below IC1. So for high enough p 1, it exists. For low p 1, it does not. p 1 Figure 1: Implementabilty of Risky Effort Levels to p 2, there exists no contract to implement e =1. This problem is particularly salient as the agent becomes very risk averse. This points out the fact that the accuracy of the incentive scheme the ability of the firm to implement whatever effort level it chooses is lowered the more risk averse the agent. It is important to contrast this result with the traditional contracting model in which the agent s risk is exogenous. In that model, the firm can hypothetically implement any outcome it desires, though it will become unprofitable to implement certain outcomes due to risk aversion. Proposition 5 is different in that it says that regardless of the benefit associated with the desired outcome which can be arbitrarily large the firm can simply not create a scheme to implement it. It is not surprising that it would be costly for the firm to implement risky outcomes when the agent is very risk averse. However, this result has nothing to do with the cost of implementation. It is surprising in that it states that the feasible region of contracts vanishes. This idea, which we extend below, is an essential one for the practice of sales force management. There are some contexts in which precise management of the salesperson s effort level is simply not possible. This, of course, raises the question as to what the firmcandointhiscase. Oneoption is monitoring. The firm can increase the resources devoted to observation of sales effort in the form of managers or other oversight mechanisms. Another possible solution would be to design the sales task such that the selling responsibilities and non-selling responsibilities are assigned to different people. This is effectively the solution proposed by Holmstrom and Milgrom (1991). This would allow the firm to increase the power of the incentives on the selling activities. This result suggests that the firm may find it costly to implement outcomes in which the agent 13

16 is asked to work not too hard. As noted, this is of practical interest in the sense that the sales task involves significant non-selling tasks. However, the applicability of this idea is far more general. In the next Section, we extend it to the very common context in which the firm has multiple products. To the extent that the firm assigns responsibility for more than one product to asinglesalesperson,itisnecessarilythecasethatitmustcraftacompensationschemetoensure that each product receives enough effort. That is, the salesperson must split her time across products. Following the intuition developed here, we show in Section 4 that it may be very costly for the firm to do so. Thus, it may find it more profitable to organize the sales force in such a way that this is not a problem. 4 Sales Force Structure for Multi-Product Firms According to Shapiro (1979), At the very core of most organization decisions is the question of how many sales forces the company should have and how they should be focused. 14 The standard choices in this problem are a product structure in which each sales force sells a subset of the firm s products and a geographic, or territory structure in which each salesperson sells allofthefirm s products to an assigned subset of customers. There are, of course, an infinite set of variations and hybrids in between. On one hand, it is clearly less costly to combine sales forces in a product approach. For example, the fixed cost associated with a sales call travel, research, relationship-building must be borne by each sales force. As well, general sales training must be borne for each salesperson. As a result, many firms opt to consolidate their selling activities into fewer sales forces. For example, after acquiring Amana in 2001, Maytag integrated the two brands sales forces into a single sales force in order to maximize synergies. 15 However, this decision is not an easy one. On one hand, some products may require unique skills that are non-transferable across products (Churchill et al., 1985). As well, there may be a risk of organizational strain when heterogeneous groups are combined into one (Walton, 1985). Thus, it s not surprising that we see many firms making the opposite decision. As reported in Rangaswamy et al. (1990), the pharmaceutical manufacturer Glaxo established a separate sales force to sell its products other than Zantac. These authors also report that Pitney Bowes, the dominant manufacturer of postage meters, established a separate sales force to focus on copiers, allowing the rest of the salespeople to focus on the sale of meters. Similarly, in 2002, Oracle, best known for its database software, established a separate sales force for its applications business, which had been performing dismally. Two aspects of these anecdotes are interesting. First, they each seem to be motivated by the desire to implement more effort on some subset of products. 14 This quote is reported in Rangaswamy et al. (1990) 15 Source: Joe Jancsurak, Maytag revs up innovation, execution engines, Appliance Manufacturer, August 1,

17 So, for example, the managers at Glaxo felt that the other products were not getting sufficient exposure. Their expressed goal was to redirect sales effort away from the block-buster product Zantac. Moreover, according to Oracle CEO Larry Ellison, his salespeople were not as focused as they should have been. 16 Second, it is fascinating to note that these firms chose an organizational response to this problem establishing a new sales force structure rather than an incentive-based one. Presumably, the former is more costly and thus we might infer that these managers felt that incentives alone may not always be enough to effect the desired allocation of effort across products. In keeping with the theme of this paper, we explain this phenomenon by analyzing the role of endogenous risk and risk aversion in the salesperson s effort choice. We show below that, when salespeople are sufficiently risk averse, the firm may not be able to design an incentive scheme to get them to allocate effort across products. From Section 3.2, it is clear both (a) why this may hold and (b) why such a result could never hold in a model of exogenous risk. To the latter point, exogenous risk is, by definition, determined ex ante so risk plays no role in the effort decision and thus all effort levels are necessarily implementable. Previous research in multi-product contexts has focused largely on what the incentive scheme should look like. These models have typically assumed either that risk is exogenous or non-existent (Srinivasan, 1981; Easton, 1976). However, as shown in Section 3, neither of these are benign assumptions. Applying the insights particularly that it s hard to implement risky outcomes we show below that, at a minimum, the firm needs to consider the role of risk and risk aversion. Moreover, in some extreme cases, we find that the sales structure decision may be driven by the agent s desire to decrease risk. An important moderating factor that we consider in our analysis is the relationship between the selling effort allocated to product A, on one hand, and product B, on the other. If a salesperson attempts to sell A, does this help or hurt her ability to sell B? In this sense, our analysis revisits an issue first addressed by Holmstrom and Milgrom (1991): optimal design of multi-task jobs. One implication of their model is that firms should optimally assign responsibility for complementary tasks to separate agents while tasks that are substitutes should be assigned to the same agent. One might, then, attempt to apply this intuition to the sales context. Is it necessarily the case that substitutes should be more commonly sold through consolidated sales forces while complements should have their own dedicated sales forces? Casual observation would suggest that, in fact, the opposite case is at least equally likely. Multi-point car dealers are probably good examples of substitutes: most consumers on a given shopping trip are only going to buy one. However, they often have separate sales forces (indeed, separate showrooms) for new vs. used cars and for cars made by different manufacturers. On the other hand, one might make the argument that insurance agents carry products that are at least mildly complementary: auto, home, life. 16 Source: Elise Ackerman, Oracle s Quarterly Profit Exceeds Forecasts. San Jose Mercury News, December 19,

18 It is very common for most agents to offer at least one line in two or three of these categories. There are at least two explanations for the fact that the results in Holmstrom and Milgrom (1991) don t seem to carry over to the sales context. First, one has to be careful with semantics. Their definition of the inter-product relationship may not quite mesh with the manager s interpretation of it. They consider products to be complements (substitutes) if the noise terms in the linear sales equations for the two products are positively (negatively) correlated. 17 However, if the economy heads into recession, we would expect that car sales overall would decline. Thus, in this sense, cars might be stochastic complements though the owner of the dealership would likely think of them as substitutes. We argue that a more useful approach to defining the inter-product relationship is to take a technological perspective. In this interpretation of complementarity, products are complements (substitutes) when the demand for product A is higher (lower) when selling effort is placed on product B. This approach has also been used by other researchers (Gilbert and Riordan, 1995; Bakos and Brynjolfsson, 1999) in analyzing multi-product contexts. To analyze this problem, we begin with the same model as that presented in Section 3 extended to include two products. To make the analysis straightforward, we continue with the assumption that agent s problem is one of allocating two blocks of time between two products i {a, b} and, possibly, leisure. The outcome of the selling effort is again a discrete one: either her efforts yield a sale of one of the products, both of the products or neither. Thus, she chooses e a and e b,theeffort levels on products a and b respectively which yield sale probabilities for product i denoted p ei,e i where the first subscript captures the effortplacedonproducti and the second captures the effort placed on product i (the other product). The products are assumed to be symmetric. To be precise, it is assumed that: e i {0, 1, 2} (18) e a + e b 2 (19) The monetary equivalent of the disutility experienced by the salesperson is again assumed to be linear 18 in the total amount of effort put forth: C (e a,e b ) (e a + e b ) c (20) where c is the per unit cost of effort. We assume c to be relatively small. As noted above, of course, there may also be other fixed costs associated with servicing, and selling to, a customer. These might include travel costs, costs of researching the client and its employees, or costs of 17 Specifically, if the sales equation for product i a, b is X i = e i + ε i then the products are complements if COV (ε a,ε b ) > 0 and substitutes if COV (ε a,ε b ) < 0. This definition of complementarity instochastictermshas also been used by Sarvary and Parker (1997). 18 This is not a restrictive assumption but makes some of the conditions to follow more tractable. The substantive insights from each of the results to follow go through in a model witn convex costs. 16

19 simply managing the relationship. The key is that these are borne for every salesperson-customer pair. We do not model the impact of these costs directly since the core intuitive results do not require them. However, it is clear that when these costs are non-trivial, then the firm will ceteris paribus prefer a single sales force, a territory structure. It is assumed that a product that receives no selling effort is never sold successfully and that the probability of a sale is increasing in the effort put behind it: p 2 >p 1 >p 0 =0 (21) The response functions are assumed to be concave in effort. A sufficient condition for ensuring this generally is that p ij 1 i, j > 0 (22) 2 We further assume that p which is a sufficient condition for the concavity of the constrained profit function. Effort placed on product a may impact the sale of product b and vice versa. The (symmetric) relationship between the products is captured in the parameter p 11. Specifically, we define products as either complements or substitutes according to the following: Complements p ei,e 0 >p j e i,e 00 j Substitutes p ei,e 0 <p j e i,e 00 j (23) (24) where e 0 j >e00 j and e i > 0. So, complementary products are those for which effort placed on one product increases the probability that the other is sold. Effort placed on a substitute product decreases the other s sale probability. We assume that there is no analogous inter-customer relationship. Effort placed selling one customer has no impact on other customers. 19 Besides choosing the contract parameters, the firm also decides on the structure of its sales force. Specifically, it can structure the sales force along product lines or along territory lines. In the former case, a salesperson is responsible for selling her product to each of two customers. In the territory structure, each salesperson sells both products to a single customer. These choices are shown in Figure 2. We now analyze these two choices in turn. In each case, we analyze a context inwhichriskaversionisrelativelylowsoacontractalwaysexiststoimplementtheoutcomethe firm seeks. Then, we investigate extreme cases in which such a contract does not exist. 19 This is, of course, a somewhat unrealistic assumption. For example, start-ups typically scout for the important reference accounts which will make future sales easier. Moreover, consumer products marketers typically like to launch new products by focusing on the opinion leaders since they ll create buzz about the product. To justify this asumption, we argue that (a) the inter-product effectsarelikelytobemorepronouncedand(b)insteadystate, for more mature products, these inter-customer effects are likely to be negligible. 17

20 Territory Structure Product Structure Salesperson A Customer 1 Salesperson A Salesperson B Customer 2 Salesperson B Product a Product b Figure 2: Product Structure vs. Territory Structure 4.1 Territory Structure Analogous to the single product case, given the discrete setting, the only possible contract in this context is one which pays β a if only product a is sold, β b if only product b is sold and β ab if both products a and b are sold. In addition, the firm pays salary αregardless of the sales outcome. The salesperson s expected utility in the territory structure is thus: E [U e a,e b ] = 1 exp [ r (α C ( ))] { p a (1 p b ) E a +p b (1 p a ) E b + p a p b E ab (25) +(1 p a )(1 p b )} whereweabusenotationsomewhatbyreferringtop a as the probability that she sells product a dropping the explicit reference to e a and e b for notational clarity. Further, the E s are defined analogously to Section 3: E i Exp[ rβ i ] and E ab Exp[ rβ ab ]. Following Holmstrom and Milgrom (1991), we model a context in which the firm wants effort placed on both products. These authors defined a benefit function B (t 1,t 2 ) where t 1 and t 2 are the efforts that the agent places on tasks 1 and 2, respectively. They assume that B(0,t 2 )=0 t 2. This specification can be justified on several grounds. The firm might have a purely strategic reason for wanting to sell multiple products. For example, Schmalensee (1978) suggests that the firm may deter entrants by offering multiple products. Or, one product may be a newer product that is expected to generate sales only after a certain period of time on the market. If we assume that the firm s horizon is longer than the salesperson s, then the firm has a preference for sales effort on both products that won t translate into current sales. Similarly, the firm may want to learn 18