Tension at the Marketing – Sales Interface:
Why Do Sales People Spend So Much Time Lobbying for Low Prices?
June 2012
Duncan Simester and Juanjuan Zhang
MIT Sloan School of Management
Tension at the Marketing – Sales Interface:
Why Do Sales People Spend So Much Time Lobbying for Low Prices?
In many companies there is persistent tension between the sales force and the managers responsible for
pricing decisions. The sales force regularly proposes lowering prices, while the pricing managers focus
on maintaining profit margins. We show that the sales force’s lobbying activities serve an important
role – they help the firm elicit truthful reporting of demand information. As a result, it may be profitable
for the firm to require lobbying (and make the requirement onerous), even though lobbying is a nonproductive activity that creates an additional administrative burden and imposes a deadweight loss.
Key words: lobbying, influence activities, sales force management, pricing, incentives, information
elicitation, marketing-sales interface.
1. Introduction
Product managers frequently complain that their sales force is too focused on closing deals
rather than increasing profits. The sales force lobbies for lower prices, while managers are
concerned about maintaining margins. We offer an explanation for why lobbying for lower
prices is an equilibrium outcome.
The explanation recognizes that the sales force often has private information about the
strength of demand. However, if the firm lowers prices when the sales force reports demand is
low this may create an incentive for the sales force to understate demand, as it takes less effort
to convince customers to buy when prices are low. As a result, the firm must pay the sales
force information rents to admit when demand is high. Lobbying is a mechanism that the firm
uses to help mitigate these rents. We model the requirement to lobby for low prices as a
requirement to present evidence that demand is really low. If it is easier for the sales force to
produce evidence that demand is low when it truly is low, then making this evidence a
condition of approving a discount can be profitable for the firm. This is true even if the
lobbying costs incurred to produce this evidence represent a deadweight loss. Intuitively,
lobbying allows the firm to use the private information of the sales force in the low demand
condition to reduce the information rents it has to pay when demand is high.
We motivate our investigation using examples acquired through a series of interviews with
product managers and sales managers. 1 The examples illustrate the different ways that sales
people engage in lobbying for low prices, and the mechanisms that firms use to manage this
process. We heard many examples of sales people spending as much time negotiating
internally as they spend interacting with external customers. Much of this time is spent
collecting evidence to justify requests to lower prices. This includes collecting information
1
As additional background research for this study we investigated the prevalence of the phenomenon by surveying
managers attending executive education classes. In particular, we asked whether there was often concern at their
firms that “sales people want to charge prices that are too low.” Almost three quarters of the respondents
indicated that they agreed with this statement. A more detailed description of these results is provided in the
Appendix.
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about competitors’ prices, or reviewing historical sales data to highlight examples in which
lower prices led to additional sales.
Notably, firms do not simply banish lobbying as doing so may mean forgoing access to the sales
force’s private information about demand. In almost every interview product managers
acknowledged that their sales force is in a better position to evaluate customers’ willingness to
pay. However, they also recognized the need to manage this lobbying activity. Many firms
report that they do compensate their sales force at least partially on the basis of prices. It is
also common for firms to shift the power to make pricing decisions away from the sales force,
and pass it to a committee or manager who must approve any discount. Most firms allow
“exceptions,” in which the sales force can lobby for price discounts. However, the firm imposes
requirements on the sales force when using this exception process. We will illustrate why
simply paying the sales force based on prices may not fully resolve the incentive problem, and
will show how imposing evidentiary requirements can contribute to higher profits.
Previous studies have recognized the tension between the sales force and marketing. For
example, Kotler, Rackham and Krishnaswamy (2006) vividly describe this tension: “In many
companies, sales forces and marketers feud like Capulets and Montagues. Salespeople accuse
marketers of being out of touch with what customers really want or setting prices too high.
Marketers insist that salespeople focus too myopically on individual customers and short-term
sales at the expense of longer-term profits.” Homburg and Jensen (2007) find that this tension
can hinder cooperation and hurt market performances. Ernst, Hoyer, and Rübsaamen (2010)
also call for better cross-functional cooperation among sales, marketing, and R&D in product
development. Our paper takes an agency theory approach to understanding the tension at the
marketing-sales interface, and describes ways that companies can manage this tension.
Sales force management is an important topic in marketing. Previous studies have investigated
various facets of this problem, including the optimal design of sales force compensation (Basu
et al. 1985; Lal and Staelin 1986; Rao 1990; Coughlan and Narasimhan 1992; Raju and
Srinivasan 1996), the role of sales assistance in product evaluations (Wernerfelt 1994; Kalra,
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Shi, and Srinivasan 2003), firms’ choice between surveillance and commissions (Anderson
1985), firms’ assignment of different selling skills to different products (Godes 2003), and the
design of sales contests (Kalra and Shi 2001; Lim, Ahearne, and Ham 2009; Lim 2010). 2
In particular, there is a body of research that investigates whether firms should delegate pricing
authority to the sales force. Weinberg (1975) shows that when sales outcomes are
deterministic a firm can delegate pricing and ensure efficient prices using margin-based
commissions. Lal (1986) finds that delegation can be profit-enhancing if the sales force has
better information about the selling environment. Revisiting this conclusion, Joseph (2001)
shows that delegation is inefficient if salespeople rely on price discounts to grow sales rather
than exert effort to pursue high-valuation customers. Mishra and Prasad (2004) further
demonstrate that centralized pricing is profit-maximizing if contracting occurs after the
salesperson receives his private information. Extending the investigation to competitive
settings, Bhardwaj (2001) finds that delegation can soften price competition, and Mishra and
Prasad (2004) prove that there always exists an equilibrium in which all firms choose
centralized pricing. In a recent working paper, Lim and Ham (2012) find that delegation
benefits the firm because of positive reciprocity of the salespeople.
We contribute to the sales force management literature by explicitly studying lobbying – a
widely observed yet under-investigated phenomenon. Our benchmark contract implements
price delegation, which outperforms centralized pricing by exploiting the sales rep’s private
information about demand, but is nevertheless inefficient because the firm must pay an
information rent. We identify conditions in which the firm can reduce this information rent by
requiring that the sales force lobby in order to obtain discounts, even when the costs
associated with lobbying represent a deadweight loss.
The paper is also closely related to the economics literature on “influence activities.” In many
organizations significant effort is exerted on influencing organizational decisions, such as capital
2
See Mantrala et al. (2010) for a recent survey of the literature on sales force modeling, and Misra and Nair (2011)
for a structural model of sales force compensation dynamics.
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allocation among competing projects. The literature has largely focused on the inefficiencies
caused by influence activities. For example, Milgrom (1988) studies how employees waste time
trying to influence managers, and how organization redesign mitigates this inefficiency. Meyer,
Milgrom and Roberts (1992) argue that the prospect of layoffs creates influence costs as
threatened managers strive to defend their jobs. Scharfstein and Stein (2000) find that division
managers’ rent-seeking influence activities distort the internal capital markets as the CEO, an
agent to outside investors herself, responds by granting the division managers favorable capital
allocations. Wulf (2009) shows that division managers’ influence activities (in the form of
information distortion) jeopardizes investment efficiency because headquarters reacts by
putting too little weight on the division managers’ valuable yet distortable private information.
One notable exception to this influence activities literature is Laux (2008), who argues that
influence activities can benefit the firm’s capital budgeting process – the act of lobbying reveals
to the firm which projects are worth defending. Similar to Laux (2008), we find that companies
can improve profits by allowing the sales force to lobby for lower prices, which explains why
lobbying is so common despite its seemingly wasteful nature. The difference is that, in our
paper, the screening effect of lobbying relies on lobbying costs increasing with the strength of
demand. In Laux (2008), the screening effect comes from the fact that good projects offer
higher returns to justify the cost of lobbying.
The paper proceeds in Section 2 with examples that help to illustrate the context and motivate
the modeling assumptions. We then introduce the baseline model, which provides the
framework that we build on in subsequent sections. In Section 3 we show that allowing
lobbying can mitigate this conflict and improve expected profits beyond paying based on prices
alone. A key element of the explanation is that lobbying costs are higher when demand is high.
In Section 4 we explain why this is likely to be true. In particular, we show how the search for
evidence can lead to this outcome, and show how the firm can design the lobbying mechanism
to improve its effectiveness. The paper concludes in Section 5.
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2. Initial Model
To motivate our model, we begin with two examples that arose during background interviews
for this research.
A US military contractor sells through a closed bid system with one primary competitor. The
sales people commonly spend more time negotiating internal price reductions than they do
interacting with the customers. For large discounts the price has to enter an exception process,
which is intentionally difficult to navigate. Success depends upon the sales force presenting
sufficient “evidence” to justify the discount. In addition to informal information about the
competitor’s prices, the sales force develops forecasts using past examples to substantiate
claims that the current transaction will lead to future transactions with either this client or
another client. To discourage overuse of the exception process the firm ensures that the
process is onerous, so that the sales force has to invest effort to navigate it. This is intended to
ensure that “sales people only ask for lower prices when they need it to close the deal, rather
than just when it would be easier to close the deal.”
Our second example is from the telecommunications industry, where the success of Apple’s
iPhone had convinced this firm’s product managers that it was possible to design a product that
would “shift the demand curve.” In contrast, the sales force was skeptical that any of the firm’s
products would shift the demand curve, and focused instead on “where to locate on the
demand curve.” The sales force spent approximately 75% of their time lobbying internally for
lower prices. To support their lobbying they present data on competitors’ prices, and use
historical sales data to illustrate the relationship between sales and price (the demand curve).
These examples share several common features that form the basis of our analytical model.
First, the sales force has asymmetric information about demand. Second, lowering prices
makes it easier for the sales force to close transactions. The resulting potential for moral
hazard leads to an atmosphere of distrust when the sales force requests a discount. Third, the
sales force can exert effort on lobbying internally, and in equilibrium many sales people spend
considerable time on this activity. Finally, the firm can influence these lobbying activities by
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changing the sales force commissions, establishing an exception process to approve discounts,
and requiring evidence before approving discounts.
We next present a baseline model, which we will use in Section 3 to explain why firms adopt
these mechanisms.
Model Setup
We consider a firm that hires a sales rep to sell its product to a customer. The customer’s
willingness-to-pay has three possible outcomes: VH > VL > 0. The sales rep can choose to incur a
selling effort denoted as s. We assume that there is an upper limit to how much work a sales
rep can perform, and normalize this effort constraint to 1 such that s ≤ 1.
The customer’s willingness-to-pay depends on this selling effort and the customer’s intrinsic
state of demand. There are two demand states, high and low, where demand is high with
probability u � (0, 1), and low with probability 1 – u. If demand is high and the sales rep makes
selling effort s, the customer will pay VH with probability s and pay VL with probability 1 – s. If
demand is low, the firm cannot achieve VH. Instead, given selling effort s, the customer will pay
VL with probability s and pay 0 with probability 1 – s. We summarize these outcomes below:
Table 1: Probability of Customer Willingness-to-Pay
High Demand
Low Demand
VH
VL
s
1–s
s
0
1–s
The ordering VH > VL > 0 ensures that both high demand and diligent selling contribute to higher
willingness-to-pay.
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Selling effort is costly to the sales rep. Let the marginal cost of selling effort be eH when
demand is high and eL when demand is low. We allow eH and eL to be different from each other
without imposing a rank order between them.
To focus on the mechanism of interest, we assume that demand shocks are i.i.d. across time
and so the firm does not learn demand over time. Demand shocks are also i.i.d. across
customers and only one sales rep can work with each customer, so that there is no competition
between sales people.
Both the firm and the sales rep are risk-neutral. We normalize the sales rep’s outside options
to zero. The sales rep holds limited liability to the firm, and is guaranteed to receive
nonnegative wages. The limited liability assumption is common in the literature (e.g., Bester
and Krähmer 2008; Bergmann and Friedl 2008; Shin 2008; and Simester and Zhang 2010). It
rules out the possibility that the firm sells its business to the sales rep. This assumption is also
plausible because employees generally retain the right to leave the firm ex post at any time.3 In
particular, if the sales rep can leave the firm before paying any punishment, the firm must
design its incentive scheme as if the sales rep were protected with nonnegative wages. We will
nevertheless relax the limited liability assumption later. 4 Finally, we normalize the firm’s
marginal cost of producing the good to zero.
First Best
Suppose the firm and the sales rep are integrated and they observe the demand state before
they choose whether to incur selling effort. The marginal return of selling effort is VH – VL if
demand is high, and VL if demand is low. The optimal selling effort is thus in boundary solutions
3
For this reason, the limited liability assumption has sometimes been justified by laws prohibiting indentured
servitude. It also appears to be consistent with what we observe in practice. More recently, the threat of
employees leaving has hindered the finance industry in its efforts to introduce negative wages to manage risk
taking.
4
Notice that the joint assumptions that the sales rep has limited liability and the sales rep’s outside option is equal
to zero cannot be interpreted as a mere re-scaling of the parameters. This is an additional reason for exploring the
impact of relaxing the limited liability assumption.
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– the joint entity should either exert full effort or no effort. We focus on the case in which
selling effort is worthwhile in both demand states: 5
(1) VH – VL > eH
(2) VL > eL
It follows that the integrated entity will charge an efficient price of VH and exert full effort sH* =
1 when demand is high; it will charge an efficient price of VL and also exert full effort sL* = 1 if
demand is low. The first-best expected profit is
EΠ* = u(VH – eH)+ (1 – u)(VL – eL)
Basing Compensation on Prices
If the firm and the sales rep are not integrated, the firm must design an incentive scheme to
influence the sales rep’s decisions. Specifically, the firm does not observe the sales rep’s selling
effort. Neither does the firm observe the demand state because the sales rep has more
localized information about customer valuation. This combination of adverse selection and
moral hazard provides the sales rep with an opportunity to understate demand, which in turn
leads to distrust when the sales rep requests a discount.
To motivate effort, the firm needs a performance-based compensation scheme; it must pay the
sales rep a positive wage if he is able to sell. If the sales rep fails to sell, the firm should
optimally pay a wage of zero given the limited liability assumptions. In addition, charging a low
price makes selling easier. Therefore, the firm may further condition its compensation on the
price being charged. However, we will show that this “price-based compensation” is
insufficient to restore the first-best profit. We consider a game with the following sequence of
moves.
5
In subsequent analysis, we make analogous assumptions to Conditions (1) and (2) to ensure that the firm wants
to induce selling effort in equilibrium.
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Timing
1. The firm and the sales rep share the common prior belief that demand is high with
probability u and low with probability 1 – u.
2. The firm offers a compensation scheme. If the sales rep rejects the offer, the game
ends. If the sales rep accepts the offer, the game proceeds.
3. The sales rep privately observes the realized demand state.
4. The sales rep reports to the firm whether demand is high or low.
5. The firm sets the price.
6. The sales rep chooses his level of selling effort.
7. The customer decides whether to buy and this decision is commonly observed. The firm
receives its profit and the sales rep receives his compensation.
Optimal Contract without Lobbying
The firm must decide whether to base its pricing decision on the sales rep’s report of demand.
If the firm decides to ignore the sales rep’s report it has three options: 6
1. Always charge a price VH and offer a wage W = eH. The customer will buy only if demand
is high and if the sales rep has made full selling effort. If demand is high, the sales rep is
just willing to exert full selling effort. (In practice, the firm can offer a wage
infinitesimally larger than eH to make sure that the sales rep strictly prefers to work.) If
demand is low, the sales rep will shirk, knowing it is impossible to earn the wage
anyway. The firm makes an expected profit of EΠ1 = u(VH – eH).
2. Always charge a price VL and offer a wage W = eL. If demand is low, the wage is just
sufficient to motivate full selling effort. If demand is high, the sales rep can sell at price
VL at no effort. The firm earns an expected profit of EΠ2 = VL – eL.
6
Notice that the only price levels that we need to consider are VH and VL.
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3. Always charge a price VL and offer a wage W = 0. The sales rep will shirk in both
demand states. The customer will buy only if demand is high. The firm earns an
expected profit of EΠ3 = uVL.
Not surprisingly, expected profits in all three options are lower than the first-best expected
profit because the firm ignores demand information when setting prices. Alternatively, the firm
could use price-based compensation and set prices following the sale rep’s demand report,
which leads to the fourth option:
4. Charge VH and offer WH if the sales rep claims that demand is high; charge VL and offer
WL if the sales rep claims that demand is low. 7 For the sales rep in the low demand
state to be willing to work and honestly report the demand condition, it suffices to offer
WL = eL. However, for the sales rep to work and truthfully report high demand, the firm
must offer WH = eH + eL, otherwise the sales rep will understate demand, sell at price VL
and receive the wage WL without making any selling effort. Using “P” to denote “pricebased compensation,” we write the firm’s expected profit as
EΠP = u(VH – eH – eL)+ (1 – u)(VL – eL)
It can be easily shown that EΠ1 > EΠ3 and EΠP > EΠ2 by Condition (1). We will focus on the more
interesting case in which EΠP > EΠ1 such that the firm prefers price-based compensation to
mandating a high price VH. This comparison holds when the following condition is satisfied:
(3) (1 – u)VL > eL
This is an important condition. In the remaining sections of the paper we will treat the
expected profit under price-based compensation as the benchmark profit, against which we will
compare the profitability of lobbying. To ensure that this is a valid benchmark, we will assume
7
The firm could also charge VH and offer WH if demand is claimed to be low, and charge VL and offer WL if demand
is claimed to be high. However, the sales rep will then claim that demand is high when it is low, and vice versa.
The firm achieves the same outcomes as in Option 4.
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that Condition (3) holds for the remainder of the paper (and will refer back to this condition in
future sections).
We conclude this section with four observations. First, in this initial version of the model the
effort choices are all determined by the boundary conditions. Therefore, the sales rep
effectively chooses between full effort and no effort and the equilibrium sales outcomes are
deterministic (conditional on both the selling effort and the demand state). This might suggest
that the probabilistic outcomes depicted in Table 1 are redundant. However, in later versions
of the model we recognize that lobbying effort may conflict with selling effort. This results in
scenarios where the effort focused on selling activities is partial, and so the sales outcomes are
no longer deterministic.
Second, the term “price-based compensation” highlights that the wage scheme offered to the
sales rep depends upon the price rather than just the unit volume. Notice that in our model
where unit sales are either zero or one (and where the marginal cost of production is zero),
price-based compensation is equivalent to both revenue-based and margin-based
compensation. However, we recognize that in a more general model it may be possible to
achieve the same level of revenue with different unit sales, and the role of marginal costs may
be nontrivial. It is in these settings that the distinction between prices, revenue and margins
becomes more meaningful. Understanding this distinction is important as some firms persist in
compensating their sales forces based upon revenue alone, even though this appears to be suboptimal. Explaining the persistence of this behavior, however, is outside the scope of our
paper.
Third, in our model the price-based compensation scheme is equivalent to delegating pricing
authority to the sales rep. Because the firm adopts whatever price the sales rep recommends,
we obtain the same outcome if the decision-rights are transferred to the sales rep. Of course,
because compensation depends upon the price that the customer pays, the sales rep has an
incentive to charge the correct price. Meanwhile, Option 1 is equivalent to centralized pricing.
By mandating a high price, the firm fails to exploit the sales rep’s private demand information.
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Finally, it is important to recognize that price-based compensation cannot on its own restore
the first-best profit. Although the firm is able to condition prices on demand information, to
elicit demand information it pays the sales rep in the high demand state an information rent of
WL = eL. This helps explain why companies often find price-based compensation inadequate.
From the observation in the previous paragraph we know that delegating the pricing decision to
the sales rep also cannot achieve the first-best profits in this setting. We note that this is a
standard result in the agency literature (Laffont and Martimort 2002). Indeed, up until this
point, we have presented a standard agency model describing the distortions that result from
the presence of moral hazard and adverse selection. In the next section, we depart from this
standard model by introducing lobbying as a screening mechanism. In particular, we
investigate if the firm can do better than price-based compensation by allowing the sales rep to
lobby for lower prices.
3. Lobbying
We introduce our study of lobbying in this section by exogenously fixing the costs that the sales
rep incurs when engaging in lobbying. We modify the timing of the game as follows.
Timing
1. The firm and the sales rep share the common prior belief that demand is high with
probability u and low with probability 1 – u.
2. The firm offers a compensation scheme. If the sales rep rejects the offer, the game
ends. If the sales rep accepts the offer, the game proceeds.
3. The sales rep privately observes the realized demand state.
4. The sales rep decides whether to lobby for a lower price. When lobbying the sales rep
incurs cost cH if demand is high and cL if demand is low.
5. Observing whether the sales rep lobbies, the firm sets the price.
6. The sales rep chooses his level of selling effort.
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7. The customer decides whether to buy and this decision is commonly observed. The firm
receives its profit and the sales rep receives his compensation.
This modification to the initial model represents a first step, intended to illustrate why lobbying
can be profit-enhancing. As we shall see, a key element of the explanation is that the costs of
lobbying are different in the two demand states. In this first step we treat these costs (cH and
cL) as exogenous. However, an important contribution of the paper is explaining why this is
likely to be true. This second step is the focus of the next section, where we model the microactivities that contribute to these costs.
We also note that we begin this first step by assuming that lobbying and selling are not
conflicting activities, so that lobbying does not limit how much time is available for selling. We
will later consider a scenario in which lobbying reduces the time available for selling activities.
When Can Lobbying Increase Profits?
We begin with some preliminary observations. The firm will want to induce selling effort in
both demand states. If the firm does not induce selling effort when demand is high, the
customer’s willingness-to-pay can only be VL or 0, and the firm might as well mandate a
constant price of VL. If the firm does induce selling effort when demand is high but does not
when demand is low, willingness-to-pay will be VH if demand is high and 0 otherwise. The firm
should then mandate a constant price of VH. Both outcomes defeat the purpose of enforcing a
lobbying mechanism.
Moreover, the firm will respond to lobbying by cutting prices, otherwise the sales rep will not
engage in (costly) lobbying in either demand condition. 8 Meanwhile, to elicit truthful reporting
of demand information, the firm will want the sales rep to lobby for a low price only when
8
Recall that we began by recognizing that the firm could use price-based compensation to dissuade the sales force
from lobbying for low prices. Simply ignoring the lobbying activities is another response that the firm could use to
dissuade lobbying. In this latter case the best the firm could do is mandate a high price VH (Option 1). However,
this option is dominated by price-based compensation given Condition (3).
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demand is low. Suppose the firm offers a wage WH if the sales rep fulfills a sale without
lobbying, and a wage WL if he sells after lobbying. We derive the optimal wage offers below.
First consider the case of low demand. If the sales rep does not lobby, the price will be VH
which makes it impossible to sell regardless of selling effort. The sales rep will thus shirk and
earn a surplus of zero. If the sales rep lobbies, the price will be VL. With selling effort s, he
earns a surplus of (WL – eL)s – cL. To motivate selling effort, the firm must offer a wage WL of at
least eL. It follows that the highest surplus the sales rep could earn by lobbying is WL – eL – cL.
Therefore, the optimal wage to induce the sales rep to lobby and make selling effort is
WL = eL + cL
Next we consider the case of high demand. By lobbying, the sales rep can sell without effort
and thus earns a surplus of WL – cH. Without lobbying, the sales rep earns a surplus of (WH –
eH)s if he incurs selling effort s. To motive selling effort the firm must offer WH ≥ eH. The sale
rep’s highest-possible surplus is thus WH – eH if he does not lobby. To induce the sales rep to
work and not to lobby when demand is high, the firm must thus offer a wage of
WH = eH + max(0, eL + cL – cH)
It follows that by enforcing a lobbying process (denoted as “L”) the firm earns an expected
profit of
EΠL = u[VH – eH – max(0, eL + cL – cH)] + (1 – u)(VL – eL – cL)
We are interested in whether the lobbying mechanism can improve the firm’s expected profit
beyond price-based compensation. Both mechanisms lead to the same efficient pricing
decisions, but differ in payroll costs. With the lobbying mechanism the firm essentially
subsidizes the sales rep’s lobbying cost cL when demand is low, but pays the sales rep a rent of
max(0, eL + cL – cH) rather than eL when demand is high. This amounts to a saving of min(eL, cH –
cL) in information rent. Hence, lobbying improves expected profits iff
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(4) u min(eL, cH – cL) > (1 – u) cL
Intuitively, by allowing lobbying the firm harnesses the sales rep’s private information in the
low demand condition to avoiding paying information rents in the high demand condition. This
benefit is greater when demand is more likely to be high (larger u), and when the information
rent is higher under price-based compensation (larger eL). In addition, Condition (4) is more
likely to hold with larger values of cH and smaller values of cL. The more costly lobbying is for
the high-demand sales rep, the smaller the information rent the firm has to pay to prevent him
from lobbying. The more costly lobbying is for the low-demand sales rep, the lower the firm’s
expected profit because it is the firm that eventually bears the lobbying cost.
For Condition (4) to hold, we need cH > cL. We formally state this result with the following
proposition.
Proposition 1: The lobbying mechanism improves the firm’s expected profit beyond
price-based compensation only if lobbying is more costly to the sales rep when demand
is high than when demand is low.
Proof: By construction.
If lobbying is just as easy (or easier) in the high demand condition as in the low demand
condition then it no longer provides an effective screening mechanism. The sales rep in the
high demand condition can always mimic the actions in the low demand condition. In Section 4
we will explicitly address why there may be differences in the cost of lobbying in low and high
demand conditions. In particular, we will model the lobbying process as a requirement to
present evidence that demand truly is low. By recognizing that the firm can choose what
constitutes “evidence” and how much evidence is required, we will see that the firm can design
the lobbying process to help ensure that cH > cL. However, before turning to these issues, we
first discuss two extensions to this baseline model that explore the robustness of the results to
different modeling assumptions.
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When Lobbying Constrains Selling Activities
The time and energy a sales rep spends on lobbying might limit how much effort he can put into
selling. 9 We can investigate this possibility by assuming that the sales rep’s total selling and
lobbying efforts cannot exceed 1.10 We derive the firm’s optimal contract and expected profit
in the Technical Appendix.
We find that the lobbying mechanism can still improve the firm’s expected profit beyond pricebased compensation, although the profit is lower than if lobbying does not constrain selling.
This occurs for the following reasons. To elicit truthful demand information the firm will induce
lobbying only when demand is low. However, lobbying now prevents the low-demand sales rep
from exerting full selling effort. Without full selling effort, a sale is not guaranteed even though
the firm agrees to reduce the price (Table 1). This reduces firm profits in two ways.
First, the firm now faces the possibility of losing a low-demand customer even if it charges the
low price VL. This directly reduces the firm’s expected profits in the low demand state. Second,
the low-demand sales rep also faces the possibility of not earning a wage after lobbying. To
induce lobbying, the firm must offer a higher wage WL. However, a higher WL also increases a
high-demand sales rep’s information rent, which means the firm must raise the wage WH to
induce truthful reporting of high demand. This indirectly reduces firm profit in the high
demand state. We formalize these results with Proposition 2.
Proposition 2: If a sales rep’s lobbying activities constrain his selling effort, the lobbying
mechanism achieves lower expected profit than if lobbying does not constrain selling.
However, the lobbying mechanism can still improve the firm’s expected profit beyond
price-based compensation.
Proof: See the Technical Appendix.
9
We thank the review team for suggesting this possibility.
This assumption requires a normalized expression of lobbying costs such that cH and cL are less than or equal to
1.
10
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Limited Liability
We have assumed that the sales rep is guaranteed a minimum wage of zero. We extend the
analysis by allowing the firm to punish the sales rep up to the amount of F ≥ 0. In addition,
once the sales rep has accepted the contract, he is “locked in” with the firm over the contract
duration. We continue to assume that the sales rep enjoys an outside opportunity of zero. As a
result, the firm must ensure that the sales rep earns a nonnegative net surplus ex ante.
We present the analysis in the Technical Appendix. As we would expect, if F > 0 so that the firm
can punish the sales rep with a negative wage then the firm earns higher expected profits. In
equilibrium, the firm always punishes the sales rep if he fails to sell. This allows the firm to
induce selling effort with smaller wages in both demand states. Moreover, cutting the wage in
the low demand state (WL) makes it less attractive for a high-demand sales rep to deviate,
which helps the firm reduce its information rent.
We also ask how the extent of limited liability (the value of F) affects the firm’s choice between
price-based compensation and lobbying. If cH ≤ cL, the firm should always choose price-based
compensation regardless of the extent of limited liability, which is consistent with Proposition
1. If cH > cL, we derive a cutoff value FL = u max(0, eL + cL – cH). If the magnitude of punishment
cannot exceed FL, then the firm should use lobbying rather than price-based compensation iff
Condition (4) holds. This is because punishments have the same rent-reduction effect on these
two mechanisms. We conclude that our results do not require that wages are nonnegative;
they only require a limit on how large any punishment can be.
Finally, when the firm is allowed to charge a sufficiently severe punishment, it will be able to
reduce the sales rep’s ex ante surplus to zero. Using price-based compensation, the firm will
restore the first-best expected profit because, in expectation, it only pays the sales rep for his
selling effort. Using the lobbying system, however, the firm cannot achieve the first-best
expected profit because it must also cover the sales rep’s lobbying cost. Therefore, the firm
should choose price-based compensation when severe punishments are allowed.
17 | P a g e
Summary
In this section we have shown that the firm can use lobbying to reduce the information rent it
pays to the sales rep when demand is high. Lobbying may be profitable, even though it is an
unproductive activity that leads to additional bureaucracy. This is true even if lobbying
activities limit how much effort the sales rep can apply to selling, and if the firm is allowed to
moderately punish the sales rep for not making a sale.
The profitability of lobbying depends upon the cost of lobbying in the high and low demand
conditions (the values of cH and cL). In the next section we investigate these costs by modeling
the activities that contribute to them. The findings illustrate how the firm can design the
process to improve the efficiency of lobbying.
4. Requiring Evidence that Demand is Low
A frequent observation from our interviews is that firms require the sales rep to “acquire
convincing evidence of low demand” in order to lobby for a lower price. In the
telecommunications and military contractor examples, the sales force searches through
historical transactions to find evidence that past discounts contributed to additional sales.
In modeling terms, we can think of this information acquisition process as the sales rep
searching for “signals” to support claims that demand is low (and justify the recommendation
to lower prices). The sales rep incurs effort to draw signals of demand without knowing
whether any individual signal will indicate that demand is high or low. He can continue to
search for evidence of low demand by making additional draws.
The firm can decide whether to require evidence of low demand before agreeing to lower
prices. We interpret this as a decision about whether to require lobbying. We will show that it
may be profitable to require lobbying, even where the cost of lobbying represents a
deadweight loss. The firm may also vary how much evidence is required before it will lower
prices, and in some situations it may also be able to influence the cost of searching for that
18 | P a g e
evidence. We investigate how the firm will make these decisions, and how the outcome will be
influenced by the accuracy of the demand signals.
We begin by considering whether the firm will require a signal that demand is low. Assume
that each demand signal drawn by a sales rep could indicate whether demand is high or low
and that the signals are i.i.d. conditional on the true state of demand. In particular, the signal
generating process is characterized by the following conditional probabilities:
Pr(high signal | high demand) = Pr(low signal | low demand) = r
where ½ < r < 1. Demand signals are noisy yet diagnostic of demand.11
The sales rep incurs a search cost c for each draw of a demand signal. This could represent the
cost of researching historical transactions or documenting the intensity of competition in the
marketplace. The number of draws needed until the encounter of a low signal follows the
negative binomial distribution. If demand is high, the expected total number of draws is
NH = 1/(1–r).
If demand is low, the expected total number of draws is
NL = 1/r.
Naturally, in expectation fewer draws are needed if demand is low. In addition, the more
precise the demand signals are (the closer r approaches 1), the fewer draws are needed if
demand is low, and the more draws are needed if demand is high. That is, more precise
demand signals polarize the lobbying costs between the two demand states.
We now rewrite the firm’s contract offer as a function of c and r. To induce the low-demand
sales rep to lobby and to make selling efforts, the firm must offer a wage of
11
This assumption is consistent with the premise of demand measurement, that market data are noisy yet
reflective of the true state of demand.
19 | P a g e
WL = eL + c NL = eL + c/r
For notational simplicity, we define g(r) = (2r–1)/[r(1–r)]. It is easy to verify that g(r) > 0 and
g(r)’ > 0 over (1/2, 1). To induce the high-demand sales rep to not lobby and to make selling
efforts, the firm must offer a wage of
WH = eH + max[0, eL + c(NL – NH)] = eH + max[0, eL – g(r)c]
It follows that by requiring evidence of low demand (denoted as “E”) the firm earns an
expected profit of
EΠE = EΠ* – u max[0, eL – g(r)c] – (1 – u) c/r
EΠE increases with r, the accuracy of the signals. When the signals are more precise, lobbying is
less costly for the low-demand sales rep and more costly for the high-demand sales rep, which
makes the lobbying process more effective at eliciting truthful demand information.
Notice that the firm can choose what represents “evidence” that demand is low. This provides
an important opportunity to improve the efficiency of the lobbying mechanism. When
choosing what represents evidence, the firm should choose signals that are easy to obtain
when demand is low, but hard to obtain when demand is high. For example, a manager at an
African beverage manufacturer described how his sales force gathers evidence of competitors’
“dealer communications,” revealing the competitors’ prices. Should the firm accept evidence
that a competitor is charging lower prices as evidence of the need to lower the price to all
dealers? The answer depends upon how easy it is to find this evidence. If the competitor
charges the same price to all dealers, then evidence that this price is low may indeed represent
sufficient evidence to lower the price. However, if the competitor charges different prices to
different dealers, so that it is always possible to find examples of some dealers who are getting
20 | P a g e
lower prices from the competitor, then the firm should generally not accept this as evidence to
lower prices to other dealers. 12
Interestingly, the firm’s expected profit can increase with the search cost c (see the Technical
Appendix for proof). This result reflects a trade-off between two forces. On the negative side,
a higher search cost increases the lobbying cost when demand is low, which the firm has to
subsidize. On the positive side, it discourages lobbying when demand is high, which reduces
the information rent. Higher accuracy of demand signals (r) diminishes the negative side and
amplifies the positive side because finding an accurate, negative signal is disproportionately
hard if demand is high. Therefore, if evidence is sufficiently accurate, higher search costs can
increase the effectiveness of the lobbying system.
The above result leads to the following question – what should the optimal search cost be if the
firm is able to influence it? In the context of our examples, the African beverage company
could provide infrastructural support for its sales reps to visit distributors and dealers, and the
military contractor could make historical transaction data more accessible to its sales force. In
the Technical Appendix we derive a positive optimal search cost c*=eL/g(r). This result echoes
observations that companies often allow lobbying but make the lobbying process “somewhat
difficult” for the sales people. If lobbying is too frustrating, sales people who truly face low
demand cannot easily communicate this information; if lobbying is reduced to a rubber stamp,
sales people in favorable markets will argue for a low price as well.
In some situations, it may be difficult for the firm to directly control the sales rep’s search cost.
For these firms an alternative is to vary the amount of evidence required before agreeing to
12
Recall also the example of the military contractor whose sales force used an example of a past transaction
leading to additional sales as evidence that lowering the price to a new customer was justified. If the original
customer had the same characteristics as the new customer, then the firm might decide this represents sufficient
evidence. However, if the original and new customers do not have the same characteristics (so that the past
example could be used for any future example) then the firm may decide not to accept this as sufficient evidence
to justify a discount. Other examples include a sales rep’s claims that a customer is also requesting prices from
competitors. The firm should only lower the price if these claims can be substantiated by evidence (such as
customer’s printed price comparisons from the Internet).
21 | P a g e
lower prices. In terms of our model, the firm can decide how many signals of low demand are
required before it is willing to approve a discount. We analyze this decision next.
Suppose the firm requires the sales rep to provide n signals of low demand. If demand is high,
the expected total number of draws the sales rep needs to meet this requirement is
NH = n/(1–r).
If demand is low, the expected total number of draws needed is
NL = n/r.
Notice that the difference between NH and NL equals n g(r), which increases with n. This result
drives the firm’s trade-off in deciding how much evidence to require before approving a
discount. A higher bar (larger n) raises the lobbying costs in both demand states, which in turn
increases the firm’s payroll costs. However, a higher bar also increases the discriminatory
power of the lobbying system because it is disproportionately difficult to collect many low
signals when demand is actually high. To manage this trade-off the firm will want to choose an
“intermediate” value of n. We obtain the following result.
Proposition 3: If evidence is sufficiently accurate (r > 1/(1+u)), the firm should require
evidence of low demand before approving price cuts rather than use price-based
compensation. The optimal number of low demand signals increases with the effort
cost in the low demand condition (eL) and decreases with both the cost of search (c) and
the accuracy of evidence (r).
Proof: See the Technical Appendix.
22 | P a g e
The optimal amount of evidence is given by n* = eL/[g(r)c]. 13 The comparative statics on this
expression have intuitive interpretations. First, recall that eL is the sales rep’s information rent
in the high demand state under price-based compensation. The larger this rent, the more the
firm wants to extract it with an onerous evidence requirement. Second, the sales rep’s search
cost c has a similar effect on profit as the required number of low signals; both make the
lobbying system more costly yet more discerning as a screening mechanism. 14 Therefore, when
acquiring evidence is costly, the firm will reduce the evidentiary requirement (requiring fewer
low signals). Finally, the more precise demand signals are, the more difficult it is to gather low
signals when demand is actually high. As a result, fewer low signals are needed to prevent the
sales rep from understating demand.
Notice that the sales rep’s search cost is effectively a deadweight loss in this system, yet the
firm is willing to introduce this loss in order to reclaim the rent it would otherwise pay when
demand is high. When n = n*, the firm’s expected profit is
EΠE = EΠ* – (1 – u)cn*/r
This optimal lobbying mechanism introduces a deadweight loss of (1 – u)cn*/r, which equals
the subsidy the firm pays the low-demand sales rep to cover his lobbying cost. This result
reflects the different implications of the costly lobbying process. From the social efficiency
perspective, lobbying is wasteful. However, from the firm’s perspective, the costly nature of
lobbying helps it better regulate the incentives of the sales force.
When Searching for Evidence Constrains Selling Activities
In this section, we revisit the possibility that searching for evidence of low demand may limit
how much effort a sales rep can apply to selling. How should the firm adjust its evidentiary
13
To facilitate exposition, we ignore the discrete nature of n. The solution to the discrete case follows the same
logic.
14
Mathematically, the total cost of search is scaled by both the cost of each draw (c), and the number of signals of
low demand that are required (n), so that the firm can change either of these design variables to achieve an
equivalent outcome.
23 | P a g e
requirement for lobbying? One might expect the firm to lower its requirement because search
is especially wasteful when it conflicts with selling (Section 3). However, we find that the
opposite may be true. We collect the full analysis in the Technical Appendix, and present an
example in Figure 1. The upper curve plots the firm’s expected profit as a function of its
evidentiary bar when lobbying does not constrain selling, where n* denotes the optimal
number of low signals required. The lower curve corresponds to the case in which search does
constrain selling. The expected profit is lower in this case (Proposition 2). However, the
optimal number of low signals required, as denoted by ñ, is higher.
Figure 1: The Firm May Raise Its Evidentiary Requirement If Search Constrains Selling
Notes: This figure sets VH=1, VL=0.8, eH=0.1, eL=0.1, c=0.006, u=0.6, and r=0.7.
The reason for this counterintuitive result is that a higher evidentiary bar makes it
disproportionately harder for the sales rep to lobby if demand is high. When lobbying prevents
the sales rep from exerting full selling effort, the firm must offer the low-demand sales rep a
higher wage WL to compensate him for the risk of not earning this wage. A higher WL makes it
more attractive for the high-demand sales rep to understate demand. The firm can counter this
tendency by raising the evidentiary requirement, although doing so increases the low-demand
sales rep’s burden of search as well. There exist parameter values such that the former effect
dominates. We state this result with the proposition below.
24 | P a g e
Proposition 4: The firm may require more evidence of low demand when the search for
evidence constrains selling effort than when it does not.
Proof: See the Technical Appendix.
This result provides further insight into why sales people spend so much time lobbying. The
socially efficient amount of lobbying should be zero. However, in equilibrium a firm may
enforce lobbying to elicit demand information from its sales rep. The surprising insight of
Proposition 4 is that the equilibrium amount of lobbying might further increase if lobbying is
more wasteful – when lobbying erodes selling, the lobbying mechanism becomes less effective
as a screening device, and so the firm may want to raise the evidentiary bar to restore its
discriminatory power.
Why the Firm Does Not Acquire Evidence on Its Own
Since there exist signals of demand in the market, a natural question is why the firm does not
acquire these signals on its own. To answer this question, notice that it is not the evidence per
se that provides demand information. It is the sales rep’s decision of whether to collect the
evidence that reveals his private information about demand. In other words, evidence does not
create any new information in the system, but its costly generating process serves as a
screening device that helps the firm extract information from the sales rep. 15
In addition, it might be more costly for the firm to gather evidence on its own. The reason is
that the sales rep knows when to search given his private demand information. For instance,
suppose demand signals are highly accurate (r� 1). It might appear that the firm should
conduct search on its own because search is highly informative. Indeed, one signal draw will
resolve most of the demand uncertainty and leaves the firm an expected profit that approaches
15
Similar results can be found in the economics literature on mechanism design with costly evidence. See Glazer
and Rubinstein (2006), Bull and Watson (2007), Deneckere and Severionov (2008), Kartik (2009), and Kartik and
Tercieux (2012) for some of the most recent publications in this area.
25 | P a g e
EΠ* – c
However, the firm can do better by requiring the sales rep to provide evidence of low demand –
one low signal would suffice. The low-demand sales rep will generally find the evidence with
one draw, whereas the high-demand sales rep will have to admit high demand, knowing the
evidence is almost impossible to find. The firm earns an expected profit that approaches
EΠ* – (1 – u)c
Notice that the expected profit is higher when the sales rep is responsible for providing the
evidence. In general, because the sales rep knows to only look for evidence if demand is low, it
may be more efficient to have the sales rep responsible for providing evidence.
Competition for the Sales Rep’s Services
In this model we have restricted attention to a single firm. However, in some markets there are
multiple competing firms, which raises the issue of competition for the sales rep’s services. If
the sales rep’s switching costs are sufficiently low and the sales person acquired the private
information before contracting, then this could result in the firms competing on how much
surplus the sales rep receives. One way that the firms might compete is by offering the sales
rep more of the information rents in the high-demand state. If the payoffs in the high-demand
state are more attractive, then the sales rep has less incentive to deviate, which will lower the
level of evidence that the firm will require before agreeing to a discount. However, if there are
multiple potential agents to hire and they agree on the contract before getting their private
information we effectively return to the game that we model.
Summary
In Section 3 we treated the costs of lobbying as exogenous. In this section we have explicitly
modeled the process that contributes to these costs. The analysis allowed us to investigate
how the firm designs the lobbying process to improve its efficiency. We have shown that the
26 | P a g e
firm will define what constitutes “evidence” of low demand by choosing signals that are easy to
obtain when demand is truly low, but difficult to obtain if demand is high.
The firm can also control how much evidence is required before it will agree to a discount. As
long as the evidence is sufficiently accurate, the firm may require substantial evidence before
agreeing to a discount. The firm may also make the search for evidence more cumbersome,
even though increasing this administrative burden contributes an additional deadweight loss.
These findings hold even when the search for evidence limits selling activities, in which case the
firm may actually further increase the amount of evidence required.
5. Conclusions
In many companies there is a persistent tension between the sales force and the managers
responsible for making pricing decisions. The sales force regularly proposes lowering prices,
while the managers focus on maintaining profit margins. We begin this paper by confirming
that compensating the sales force based on prices can help to increase firm profits. However,
because the sales force always has the option of claiming that demand is low, the firm can only
induce truthful reporting of demand (and hence efficient pricing) if it pays the sales force
information rents in the high demand state. The focus of the paper is on exploring what
internal mechanisms the firm can use to reduce these rents.
The key finding in the paper is that lobbying is a mechanism that serves this role. By requiring
that the sales force go through a costly process of lobbying before agreeing to lower prices, the
firm uses lobbying as a screening mechanism. As long as it is less costly to lobby when demand
is low, then lobbying allows the firm to use the private information of the sales force in the lowdemand condition to reduce the rents that it pays in high demand conditions. We show that
the firm will require that the sales force lobby for low prices even if lobbying costs represent a
deadweight loss.
27 | P a g e
We model the requirement to lobby for low prices as a requirement to present evidence that
demand is really low. The profitability of this mechanism depends upon how easily the sales
force can acquire this evidence in the different demand states. If the evidence is a lot easier to
produce in the low demand state than in the high demand state, then lobbying is a more
efficient screening mechanism. The firm will find it profitable to implement a positive search
cost and set a substantial evidentiary threshold before approving any discounts.
Throughout the paper we assume that the sales rep knows the state of demand. The search for
evidence is socially wasteful as it does not bring any new information into the system. Future
research might consider markets in which the sales rep’s prior information about demand is
imperfect, but he can update his information by collecting demand signals. This possibility may
yield interesting effects. On the one hand, the sales rep’s private information is of worse
quality, which reduces the firm’s incentive to elicit this information through a costly evidentiary
process. On the other hand, the sales rep now has the private incentive to acquire more
information to improve his decisions, which means the firm might not need to fully cover his
search cost. It would be interesting to fully investigate these effects in future research.
28 | P a g e
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Appendix
Survey Findings
A sample of 99 managers attending “Strategic Marketing” Executive Education programs at a
major university were asked whether they agreed with the following statement about their
organizations:
“Managers are often concerned that sales people want to charge prices that are too low.”
Responses were recorded using a 7-point Likert scale, anchored by “strongly agree” and
“strongly disagree”. The responses are summarized in the figure below.
30%
26%
23%
25%
23%
20%
15%
8%
10%
5%
5%
9%
5%
0%
Strongly Disagree
32 | P a g e
Strongly Agree
Tension at the Marketing – Sales Interface:
Why Do Sales People Spend So Much Time Lobbying for Low Prices?
Technical Appendix
June 2012
Duncan Simester and Juanjuan Zhang
MIT Sloan School of Management
33 | P a g e
Lobbying that Constrains Selling (Baseline Model)
In this section we examine the case in which selling and lobbying are competing activities.
Again, in equilibrium the firm will want the sales rep to lobby if and only if demand is low; it will
charge a price of VL if the sales rep lobbies, and VH otherwise.
When demand is low, the sales rep earns a surplus of zero if he does not lobby. He earns a
surplus of (WL – eL)s – cL if he lobbies and exerts selling effort s, which cannot exceed 1 – cL. For
this sales rep to be willing to exert selling effort, the firm must ensure that WL ≥ eL. The sales
rep will in turn put in the maximum available selling effort of s = 1 – cL, and will earn a surplus
of (WL – eL)(1 – cL) – cL. Therefore, to induce the sales rep in the low demand state to lobby and
exert selling effort, the firm needs to offer a wage equal to
WL = eL + cL/(1 – cL)
When demand is high, by lobbying, the sales rep can sell without effort and thus earns a surplus
of WL – cH. By not lobbying, the sales rep earns a surplus of (WH – eH)s if he exerts selling effort
s. To induce selling effort, the firm must offer WH ≥ eH. The sales rep’s highest-possible surplus
from not lobbying is thus WH – eH, whereby he maximizes his selling effort as s = 1. Therefore,
to induce the sales rep to work and not to lobby when demand is high, the firm must offer
WH = eH + max[0, eL + cL/(1 – cL) – cH]
By enforcing a lobbying process when lobbying constrains selling (denoted as “LC”), the firm
earns an expected profit of
EΠLC = u{VH – eH – max[0, eL + cL/(1 – cL) – cH]}+ (1 – u)[(1 – cL)(VL – eL) – cL]
We are again interested in whether the lobbying mechanism can improve the firm’s expected
profit beyond price-based compensation. We see that EΠLC > EΠP iff
(A1)
u min[eL, cH – cL/(1 – cL)] > (1 – u) cL (VL – eL + 1)
The above condition is more likely to hold for larger values of u, eL, and cH, and smaller values of
VL and cL. As in the case where lobbying does not constrain selling, the benefit of the lobbying
mechanism over price-based compensation is that it leverages the high-demand sales rep’s
lobbying cost cH to reduce his information rent eL; the downside is that the firm must subsidize
the low-demand sales rep’s lobbying cost cL. In addition, the low-demand sales rep’s lobbying
activity now limits his selling effort. Without full selling effort, sale is not guaranteed even
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though the firm agrees to cut prices. The possibility of losing the business of a low-demand
customer is higher if lobbying requires more effort in the low demand state (greater cL).
Meanwhile, losing a sale is more costly if VL is higher.
The lobbying mechanism achieves lower expected profit when lobbying constrains selling than
when it does not. Indeed, Condition (A1) is more stringent than Condition (4). Nevertheless, it
is easy to verify that there exist parameter values for Condition (A1) to hold. These results
establish Proposition 2.
Limited Liability
Recall that when the firm mandates a high price VH (Option 1), it does not overcompensate the
sales rep for his selling effort. It is when the firm wants to elicit truthful reporting of demand
(through price-based compensation or lobbying) that it pays the sales rep an information rent.
Ex post, the sales rep enjoys a positive surplus when demand is high and zero surplus when
demand is low. Ex ante, the sales rep earns a positive surplus as a result.
If negative wages are allowed, the firm will be able to improve profit by reducing the sales rep’s
ex ante surplus. The idea is to make the sales rep earn a negative surplus when demand is low,
which helps to reduce his information rent when demand is high. The optimal contract
depends on whether the firm uses price-based compensation or the lobbying system. We
analyze these two cases in order.16
Price-Based Compensation
When using price-based compensation, the firm should offer to pay the sales rep WH if he sells
at the high price, WL if he sells at the low price, and WF if he fails to sell. The firm could further
condition the value of WF on the price being charged. However, since the sales rep can always
charge either price and shirk, it is the higher of the WF wages that regulates his work incentives,
which reduces WF to a single instrument.
Suppose demand is low. By charging a high price, sale is impossible, and the sales rep will shirk
selling effort to earn WF. By charging a low price, the sales rep earns an expected surplus of
sWL + (1 – s)WF – seL with selling effort s. To induce selling effort, the firm should offer
16
If F ≥ EΠ*, the firm can also sell its entire business to the sales rep at the price of EΠ*. The firm earns the firstbest expected profit, and the sales rep earns a surplus of zero. We will show that, when F ≥ ueL, the firm can also
restore the first-best expected profit using price-based compensation.
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WL = eL + WF
It follows that the sales rep will exert full selling effort and earn WF. In practice, the firm could
make WL infinitesimally higher than eL + WF to ensure that the sales rep strictly prefers to
charge a low price.
Now suppose demand is high. By charging a high price, the sales rep earns an expected surplus
of sWH + (1 – s)WF – seH with selling effort s. To induce selling effort, the firm should offer WH ≥
eH + WF. By charging a low price, the sales rep can sell without effort, in which case he earns WL
= eL + WF. Therefore, to induce the sales rep to work and charge a high price, the firm must
offer
WH = eH + eL + WF
Since the sales rep is induced to charge the efficient prices and exert full selling effort, the
firm’s optimization problem becomes
min u WH + (1 – u) WL
s.t.
u (WH – eH) + (1 – u) (WL – eL) ≥ 0
(ex ante participation constraint)
WH, WL , WF ≥ – F
(limited liability constraint)
where WH and WL are derived above. Without the limited liability constraint, the firm’s
optimization problem yields WF = –ueL. This result establishes the following cutoff value for F:
FM = ueL
If F ≥ FM, the limited liability constraint holds with slack. The firm sets WF = –FM, which reduces
the sales rep’s ex ante surplus to zero, and restores the first-best expected profit EΠ*.
If F < FM, the limited liability constraint is binding. The firm sets WF = –F and earns an expected
profit of EΠ* – (FM – F), which is below the first-best expected profit, but is increasing with F.
Lobbying
We now analyze how the extent of limited liability affects the lobbying mechanism. Recall that
the firm will want to induce selling effort, and will induce lobbying if and only if demand is low.
It pays the sales rep WH if he sells without lobbying, WL if he sells after lobbying, and WF if he
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fails to sell. As in the case of price-based compensation, it can be shown that further
conditioning WF on whether the sales rep lobbies does not improve firm profit. We derive the
optimal wage offers below.
Suppose demand is low. By not lobbying, sale is impossible, and the sales rep will shirk selling
effort to earn WF. By lobbying, the sales rep earns an expected surplus of sWL + (1 – s)WF – seL
– cL with selling effort s. To induce selling effort, the firm should offer WL ≥ eL + WF. It follows
that the sales rep will exert full selling effort and earn WL – eL – cL. To induce lobbying and
selling effort, the firm must thus offer
WL = eL + WF + cL
Now suppose demand is high. By not lobbying, the sales rep earns an expected surplus of sWH
+ (1 – s)WF – seH with selling effort s. To induce selling effort, the firm should offer WH ≥ eH +
WF. By lobbying, the sales rep can effortlessly sell and earn WL – cH = eL + WF + cL – cH.
Therefore, to induce the sales rep to not lobby and to exert selling effort, the firm must offer
WH = eH + WF + max(0, eL + cL – cH)
Since the sales rep is induced to make the efficient lobbying decisions and exert full selling
effort, the firm’s optimization problem becomes
min u WH + (1 – u) WL
s.t.
u (WH – eH) + (1 – u) (WL – eL – cL) ≥ 0
(ex ante participation constraint)
WH, WL , WF ≥ – F
(limited liability constraint)
where WH and WL are derived above. Without the limited liability constraint, the firm’s
optimization problem yields WF = –u max(0, eL + cL – cH). This result establishes the following
cutoff value for F:
FL = u max(0, eL + cL – cH)
If F ≥ FL, the limited liability constraint holds with slack. The firm sets WF = –FL to reduce the
sales rep’s ex ante surplus to zero and to achieve an expected profit of EΠ* – (1 – u)cL. Notice
that the firm cannot restore the first-best expected profit because it must subsidize the sales
rep’s lobbying cost in the low demand state.
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If F < FL, the limited liability constraint is binding. The firm sets WF = –F and earns an expected
profit of EΠ* – (1 – u)cL – (FL – F), which is increasing with F.
Price-Based Compensation versus Lobbying
Finally, we compare how the extent of limited liability affects the firm’s choice between pricebased compensation and lobbying. First notice that FM > FL iff cH > cL. Intuitively, if lobbying is
more costly when demand is high, the firm relies less on severe punishments to extract the
sales rep’s information rent. If cH > cL, we consider the following three scenarios.
If F ≤ FL, we have EΠP = EΠ* – (FM – F) and EΠL = EΠ* – (1 – u)cL – (FL – F). It follows that EΠL >
EΠP iff FM – FL > (1 – u)cL, which is equivalent to Condition (4).
If FL < F < FM, we have EΠP = EΠ* – (FM – F) and EΠL = EΠ* – (1 – u)cL. It follows that EΠL > EΠP iff
FM – F > (1 – u)cL, which is harder to satisfy as F increases, is more stringent than Condition (4),
and will not hold if F is close enough to FM.
If F ≥ FM, we have EΠP = EΠ*, which is always greater than EΠL = EΠ* – (1 – u)cL.
Finally, if cH ≤ cL, then FM ≤ FL. It can be similarly shown that EΠP is always greater than EΠL.
Requiring Evidence that Demand is Low
Result 1: If the firm requires the sales rep to provide evidence of low demand before lowering
prices, then as long as evidence is sufficiently accurate (r > 1/(1+u)) the firm’s expected profit
can increase with the cost of search.
Proof of Result 1: First define c* = eL/g(r). If c ≥ c*, then EΠE = EΠ* – (1–u)c/r, so that d EΠE/ d c
< 0. If c < c*, then EΠE = EΠ* – u [eL – c g(r)] – (1–u)c/r, so that d EΠE/ d c = [r(1+u)–1]/[r(1–r)],
which is positive if r>1/(1+u) and negative otherwise. Therefore, if r < 1/(1+u), then EΠE
decreases with c; if r > 1/(1+u), then EΠE increases with c over [0, c*] and decreases with c over
(c*, ∞).
Result 2: If evidence is sufficiently accurate (r > 1/(1+u)) then the firm should require evidence
of low demand before lowering prices rather than use price-based compensation otherwise. If
the firm has control over the sales rep’s search cost, it should impose a positive search cost of
c* = eL/g(r).
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Proof Result 2: Since EΠE decreases with c over (c*, ∞) for all values of r, the optimal c must fall
within [0, c*]. Given Condition (4), the firm prefers lobbying over price-based compensation iff
u eL min(1, c/c*) > (1–u) c/r
Since c ≤ c* in equilibrium, Condition (4) becomes
u eL/c* > (1–u)/r
Rearranging terms, the above condition is equivalent to
r > 1/(1+u)
However, from the proof of Result 1 we know that EΠE increases with c over [0, c*] when r >
1/(1+u). Therefore, the optimal c equals c*.
Proof of Proposition 3: The firm’s expected profit from using the lobbying mechanism is:
EΠE = EΠ* – u max[0, eL –g(r)cn] – (1–u) cn/r
Solving eL = g(r)cn we obtain
n = n* = eL/[g(r)c]
If n ≥ n*, then EΠE = EΠ* – (1–u)cn/r, which decreases with n. Therefore, the optimal n must
fall within [0, n*].
If n ≤ n*, then EΠE = EΠ* – u [eL – c n g(r)] – (1–u) c n/r, so that
d EΠE/ d n = u c g(r) – (1–u)c/r
which is positive iff r > 1/(1+u).
Given Condition (4), the firm will prefer lobbying over price-based compensation iff
u eL min(1, n/n*) > (1–u) cn/r
Since n ≤ n* in equilibrium, Condition (4) becomes
u eL/n* > (1–u)c/r
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Rearranging terms, the firm will choose lobbying over price-based compensation iff:
r > 1/(1+u)
But d EΠE/ d n > 0 over [0, n*] iff r > 1/(1+u). Therefore, the optimal choice of n equals n* when
the firm adopts the lobbying mechanism.
When Searching for Evidence Constrains Selling Activities
When the firm requires the sales rep to provide n signals of low demand, the costs of lobbying
are cL = cn/r and cH = cn/(1–r). Following early analysis of the Technical Appendix, the firm’s
optimal wage offers are
WL = eL + cn/(r–cn)
WH = eH + max[0, eL + cn/(r–cn) – cn/(1–r)]
We denote as ñ the n that solves 0 = eL + cn/(r–cn) – cn/(1–r). That is, by requiring ñ low signals
before cutting prices, the firm is just able to reduce the high-demand sales rep’s information
rent to zero.
If n ≥ ñ, then EΠEC = u(VH – eH) + (1–u)[(1– cn/r)(VL – eL) – cn/r], where “EC” denotes requiring
evidence when search constrains selling. EΠEC decreases with n. Therefore, the optimal n must
fall within [0, ñ]. It follows that WH = eH + eL + cn/(r–cn) – cn/(1–r). The firm’s expected profit is
EΠEC = u[VH – eH – eL – cn/(r–cn) + cn/(1–r)]+ (1–u)[(1–cn/r)(VL – eL) – cn/r]
It can be shown that d2 EΠEC / d n2 < 0, so that EΠEC is concave in n over [0, ñ].
Next, we compare ñ with n*, where n* is the optimal number of low signals required when
lobbying does not constrain selling. From the proof of Proposition 3, we know that n* solves 0
= eL + cn/r – cn/(1–r). The right-hand side of the equation decreases with n and is negative
when n= ñ. Therefore, n* < ñ.
Finally, it can be shown that there exist parameter values such that: (1) the derivative d EΠEC / d
n > 0 when n = n*; (2) cL = cn*/r < 1 and cH = cn*/(1–r) < 1, which satisfies the normalization
assumption about cL and cH; (3) EΠEC > EΠP such that the firm prefers lobbying over price-based
compensation. One example suffices to prove this result. Figure 1 presents one such example.
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