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Essays on Issues in Salesforce Management

by

Pradeep Bhardwaj

A thesis submitted in conformity with the requirements

for the degree of Doctor of Philosophy

Faculty of Management

University of Toronto

O Copyright by Pradeep Bhardwaj 1998

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Essays on Issues in Salesforce Management, Ph.D. Degree, 1998

Pradeep Bhardwaj, Faculty of Manzgement, Uni-icrsity of Toronto

Abstract

This dissertution contains three essays that examine diflerent marketing issues arising in the

management of a salesj5orce. The first essay examines the effect of delegating prices to the sales

representatives when firms Zompete in the market. The major result is that even when the firm

and the sales representative have the same information about the market, firms find it optimal to

delegate the pricing decision to the representatives under intense price competition. Price

delegation under intense price competition results in higher prices which helps in softening the

price competition. Also, in the presence of competition a contract based on sales volume will not

achieve the desired result of softening the price competition but a contract based on margins

does achieve this result.

In the second essay we first examine whether price delegation is a strategic substitute or a

strategic complement variable for firms and then analyze its role in entry deterrence and

accommodation. When cross price and cross selling effort impacts are almost equal, price

delegation is a strategic substitute variable. In the remaining region of cross price and cross

selling @art impacts space we fiitd that price delegation is a strategic complement variable.

Thus when competition is in two dimensions the same variable cun be a strategic complement or

a strategic substitute. The results also show that when cross price impact is high the inclrmbent

firm accommodates entry by choosing price delegation. But when cross price impact is not too

strong but still greater than cross selling effort impact the incumbent deters entry by choosing no

price delegation.

The third essay examines the issues that arise when sales representatives are expected to sell

multiple products. We model a situation where there is complementarity in #on in the sense

that selling a focal product gives the sales representative some valuable information about the

client which helps in selling the secondary product. The results show that in this situation the

commission on secondary product is always less than the commission on the focal product. The

optimal effort devoted to selling the focal product increases while the optimal e$ort devoted to

selling the secondary product decreases as the complementarig iiicreases.

Acknowledgements

This dissertation was made possible by the invaluable help, insight and encouragement of

Professors Frank Mathewson, Andy Mitchell, and Ralph Winter and the patience, love and

optimism of my family.

Table of Contents

1. Introduction

2. Delegating Pricing Decisions to the Salesforce

In a Duopoly

3. Entry Accommodation and Entry

Deterrence Strategies

4. Managing Multi Product Salesforce

5. Conclusion

6 . References

List of Tables

Chapter 2: Delegating Pricing Decisions to the Salesforce In a Duopoly

Table 2.1 Some Examples of Price Delegation 57

Table 2.2 Comparison with McGuire and Staelin Research 58

Table 2.3 Explanations from the Model 66

Chapter 3: Entry Accommodation and Entry Deterrence Strategies

Table 3.1 Possible Strategies 96

List of Figures

Chapter 2: Delegating Pricing Decisions to the Salesforce In a Duopoly

Figure 2. I Sequence of Events 59

Figure 2.2 Equilibrium Regions 60

Figure 2.3 Effect of Change in Utility Cost of Uncertainty 6 1

Figure 2.4 Price Under Price Delegation Higher than Price 62

Under No Price Delegation

Figure 2.5 Commission Under Price Delegation Higher than 63

Commission Under No Price Delegation

Figure 2.6 Salary Lower Under Price Delegation 64

Figure 2.7 Effort Under No Price Delegation Higher 65

than Effort Under Price Delegation

Chapter 3: Entry Accommodation and Entry Deterrence Strategies

Figure 3.1 Sequence of Events 90

Figure 3.2 Strategic Substitutes and Strategic Complements 9 1

Figure 3.3 Equilibrium Regions 92

Figure 3.4 Sequential Game 93

Figure 3.5 Equilibrium Regions: Sequential Game 94

Figure 3.6 Delegation Making Incumbent Tough or Soft 95

Figure 3.7 Equilibrium Strategies 97

vii

Chapter 1

Introduction

Introduction

Salesforce performance is affected not only by factors specific to the

saiesperson such as skill and aptitude, b u t also by the reward structure

used by a c?mpany (Churchill, Ford, and Walker 1981). Consequently it is

not surprising that firms spend a significant amount of time and effort

designing reward structures for their salesforce. The rewards can be

outcome-based or behavior-based. In the outcome-based reward system

the final outcomes of the selling process (unit sales, gross margins,

profits, etc.) are monitored and in the behavior-based system the

individual stages i n the process of selling (calls made, number of active

accounts, development and use of technical knowledge, sales

presentations, etc.) are monitored (Weitz 198 1 , Peck 1982, Behrman and

Perreault 1982). Historically, performance appraisal systems for

determining compensation have tended to emphasize outcomes rather than

behavior (Anderson and Oliver, 1987). A major reason being the

availability of simple and seemingly Fair measures of sales volume or

dollars.

By its nature, selling is an independent occupation. Sales reps spend

considerable time on the road which makes supervision difficult and

expensive. The sales personnel can have varying skill levels and hence

their productivities would be different. Also, managers may not exactly

know the skill levels of their sales personnel and the market conditions

and so they tend to give a free hand to their sales people but hold them

responsible for the results ir? their sales territory.

Firms are known to use monetary and non-monetary reward structure for

their sales personnel. For instance, exemplary sales reps make i t to

President's Club (a kind of recognition) and are taken on all-expenses-

paid family cruises with the senior managers of the firm. However,

research has shown that salespeople are much more highly motivated by

monetary rewards (Ford, Walker and Churchill, 1981). Monetary or non-

monetary rewards may be based on individual performance or relative

performance. For example, a sliding commission structure on percentage

of quota achieved is based on individual performance but allocation of

largest pie from a bonus pool to the best sales representative is an

example of relative performance evaluation. This relative compensation

issue has been analyzed in economics as a tournament (Lazear and Rosen

1981, Green and Stokey 1983, and Rosen 1986) for identifying optimal

spread between loser's and winner's prize not only to attract individuals

but to also induce them to put in desired level of effort to win the prize.

Reward mechanisms based on individual performance have been analyzed

within the framework of Principal-Agent (P-Ag) theory or Agency theory.

Agency theory provides a general analysis of the following situation. A

principal (e.g. a firm) employs an agent (e-g. a salesperson) to carry out

some activity (e-g. selling) on her behalf. The agent must choose some

decision variable (e-g. sales effort) which determines an outcome ( e . g

sales volume). The outcome is a function of not only the decision variable

but also a random variab!e with a known distribution, Thus the

iesponsiveness of the outcome to agent's input is stochastic.

Varying assumptions about the amount of information the principal has

about the agent's response function have been made in the literature.

Moral hazard models are games of complete information with uncertainty.

The principal offers a contract, and after the agent accepts, Nature adds

noise to the task being performed. In moral hazard with hidden actions the

agent moves before Nature, and in moral hazard with hidden information

the agent moves after Nature and conveys a "message" to the principal

about Nature's move. Thus if the employer knows the worker's ability but

not his effort level, the problem is moral hazard with hidden actions. If

neither player initially knows the worker's ability, but discovers i t after

the worker has accepted the contract the problem is moral hazard with

hidden information.

In adverse selection models, the principal has incomplete information

about the agent's response function. Nature moves first and picks the type

of the agent, i.e., usually the ability of the agent to perform the task. In

the simplest model the agent accepts or rejects the contract (Akerlof

1970). If the agent can send a signal to the principal before the principal

offers a contract it is a signaling model (Spence 1973) and screening

otherwise.

It has long been recognized that the moral hazard problem may arise when

individuals engage in risk sharing u n r i ~ r conditions such that their

privately taken actions affect the probability distribution of the outcome

(Holmstrom 1979). Harris and Raviv ( i976) in the context of principal-

agent relationship, study monitors which provide information that is

independent of the state of nature and allows the principal to detect a n y

shirking by the agent with positive probability. However, such monitors

are of limited interest since they are equivalent to observing the agent's

action directly. Holmstrom (1979) has shown that any additional

information about the agent's action can be used to improve the welfare of

both the principal and the agent. Optimal compensation contracts i n the

principal-agent situation ensure that the interests of the principal and the

agent are aligned given that the agent is willing to work for the principal.

The agency theory research stream i n salesforce management draws

heavily on the work in economics by Ross (1973), Harris and Raviv

(1979), Shave11 (1979), Holrnstrom (1979), Holmstrom ( 1 982), and

Holmstrom and Milgrom (1987, 1991). These papers focus on the

derivation of an optimal compensation contract in a moral hazard context.

The first article in marketing literature which applied agency theory to

sales force compensation problem (Basu, Lal, Srinivasan and Staelin

1984) is patterned after Holmstrom (1979) but applies the agency-

theoretic framework directly to the salesforce compensation area and

develops many detailed predictions based on the distributional

assumptiorls of sales response function (gamma and binomial) and sales

person's utility function (power, log and constant risk aversion utility

functions). Their model considers one sales person (or a homogeneous

salesforce) selling one product. The only input by the sa!es person is

effort. In a later paper, Lal and Staelin (1986) simultaneously consider

both moral hazard and adverse selection situations and identify conditions

where it is optimal for the firm to not offer multiple contracts even

though this means that some sales regions may not be served. Rao (1990)

has also considered a similar problem under the assumptions of risk

neutral sales reps and deterministic sales response function. His model of

a heterogeneous salesforce, examines conditions where a linear

compensation plan may be used to separate low skill sales reps from high

skill sales reps.

Srinivasan and Raju (1994) extended the BLSS model to show how

optimal compensation changes when the firm constrains compensation to

be in the form of salary and commission paid when sales exceed a

specified quota and the sales territories have unequal potential. The key

result is that all reps have the same salary and commission rate but the

reps i n territories with higher potential have a higher quota to achieve.

Finally, La1 and Srinivasan (1993) have applied Holmstrom and

Milgrom's (1987) model to a selling situation where the effort decision by

the sales reps is of intertemporal nature and the rep can change the effort

decision more frequently than the firm can adjust the compensation plan.

The optimal compensation plan is shown to be linear in total sales over

the accounting period. They also extend the agency theory approach to

compare commission rates across products for a sales rep selling multiple

products that have no demand interdependence. Their results are broadly

consistent with those of BLSS.

All these papers assume that the only decision made by the sales rep is

that of effort level. Firms, however, frequently delegate other

responsibilities to their sales reps like pricing, service level, debt

collection, etc. These reps are expected to perform multiple tasks. Some

of these tasks may not involve putting i n effort (for example, price

setting) while others may require the rep to divide the time between

selling and non selling activities (for example, debt collection). Thus

besides the reward structure, firms also have to decide on the

responsibilities to be delegated to the sales personnel, i-e., besides selling

should the sales representatives have the authority to set prices, change

payment terms, etc. La1 (1986) has addressed the issue of price delegation

in a monopoly situation and concludes that the player wi th better

information should have the pricing decision.

In some situations delegation may act as a signal to potential entrants to a

market. For instance, delegating price responsibilities to the reps may

signal an aggressive style of management to the competitors while

delegating others may signal an accommodating style. Finally, in many

business situations the firm's sales representatives are responsible for

selling multiple products. Selling one product may provide the sales rep

with valuable information that might help in selling anothir product.

My thesis is an anaiysis of three issues that focus on delegation of piicing

decision to company bales force and managing muti-product sales force.

In Chapter 2, I examine the conditions when firms should delegate price

to the sales rep when there is competition in the market. In this model, the

firm and the sale reps have the same information, so unlike the monopoly

results of La1 (1986) the results here do not depend on which player has

better information about the market.

In Chapter 3, I examine how price delegation can be used strategically

when there is threat of competition. The results from these two chapters

provide insights into why, contrary to what one would expect, firms

delegate the pricing decision to their sales reps under intense price

competition and how firms can use this delegation tool to deter or

accommodate entry.

In Chapter 4 I examine a situation where sales representatives are

responsible for selling multiple products. Selling one product, the focal

product, provides valuable information to the rep that may help in selling

a different product. For example, an insurance agent responsible for

selling life insurance and children's eductaion plans.

Chapter 2

In marketing literature, the issue of piice delegation has been analyzed

only i n a monopolistic situation (Lal, 1986). In a deterministic setting,

the sales representative whose commission is based on a percentage of

gross margin can be given control over price and be expected to set

prices which are optimal for the firm and for himself (Weinberg, 1975).

However, in a monopolistic situation where demand is stochastic, price

delegation is more profitable when the sales rep's information about the

selling environment is superior to that of the firm's (Lal, 1986). There is

no apparent reason for the firm to delegate the pricing responsibility

when there are no information asymmetries between the rep and the firm.

An empirical study by Stephenson, Cron and Frazier (1979), however,

finds various market conditions under which price delegation is more

likely to be observed, but they do not provide an explanation of why w e

tend to observe such a phenomenon. One of the conditions identified by

them under which price delegation is more likely to be observed is

intense price competition in the market

The model developed to analyze the price delegation decision involves

two firms selling through their own sales representatives. Specifically,

each firm first simultaneously chooses whether or not to delegate the

pricing decision to the sales reps and offers a contract to its sales rep. The

decision by a firm to delegate or not to delegate pricing authority to the

sales rep is observed by the competing firm-rep pair. However, the actual

contents of the compensation contract are not observable to the competing

firm-rep pair. The quantity sold by each firm depends on the prices and

the selling effort put in by the sales reps of the two f ~ r m s .

The major result is that even when the firm and the sales rep have the

same information about the market, there are market conditions under

which it is optimal for the firm to delegate pricing decision to the sales

reps. This is in contrast to the existing monopoly results where with

symmetric information between the firm and the rep, i t does not matter

who sets the price. The results show that when the price competition is

more intense it is optimal to delegate the pricing decision to the sales rep.

However, when the effort competition is more intense it is beneficial not

to delegate the pricing decision to the rep. Unlike the monopoly case (La1

1986) in the presence of competition a contract based on sales volume

will not achieve the desired result of softening the price competition but a

contract on margin does achieve this result.

Chapter 3

In this chapter, I examine whether price delegation can be used as a

strategic variable to deter or accommodate entry. Unlike Fudenberg and

Tirole (1984), the entrant firm has to decide on entry with price or no

price delegation. Hence, in analyzing the entry accommodation and

deterrence strategies, we need to fix the type of delegation for the entrant.

Previous work (Fudenberg and Tirole 1984, Schrnalensee 1983) has

modeled this strategic decision as a two stage game with the first stage

decision being on the strategic variable and :he second stage competition

being on only one dimension, price or quantity. In our model the second

stage competition is on two dimensions - price and selliag effort.

The results show that price delegation variable can be a strategic

substitute or a strategic complement depending on the intensity of price

and sales effort competition. When cross price and cross selling effort

impacts are almost equal, price delegation is a strategic substitute

variable. In the remaining region of cross price and cross selling effort

space, we find that price delegation is a strategic complement variable.

Thus when competition is i n two dimensions, the same variable can be a

strategic complement or a strategic substitute. The results also show that

when cross-price impact is high, the incumbent firm accommodates entry

by choosing price delegation. But when the cross-price impact is not too

strong, but still greater than the cross-selling effort impact, the incumbent

deters entry by choosing no price delegation.

Chapter 4

In many business situations the firm's sales representatives are

responsible for selling multiple products. There are situations where the

effort devoted to selling one product affects the sales of the other product

by providing valuable information that reduces the amount of effort

required to sell the other product.

When firms have sales reps selling multiple products the issue is not only

whether the reps are putting in the right level of effort, but also how they

are allocating the effort bctween the products. When the sales of the

products are independent, the cornmi;;ion rates are higher for products

with lower product cost, higher sales effort effectiveness and lower

uncertainty (La1 and Srinivasan. 1993).

In this chapter we develop a model for effort complementarity. Analysis

shows that with complementarity in efforts, t h e commission on the

secondary product is always less than the commission on the focal

product. The optimal effort devoted to selling the first product increases

and that to selling second product decreases as the complementarity

increases. Also, the risk premium increases as the uncertainty in the

selling environment increases.

Chapter 2

Delegating Pricing Decisions to the Salesforce in a Duopoly

1. Introduction

Two key activities involved in virtually all selling situations are effort

and pricing. Firms that employ sales personnel generally let them decide

on the effort level required for selling the product either because the firm

is unable to observe the interaction between the sales rep and the client

or it is too expensive to monitor.

In some industries the firms also delegate the pricing decision to their

reps. As shown in Table 1 , in the heavy equipment industry General

Electric and ASEA Brown Boveri delegate pricing decision to the reps, as

do KSB, Inc. and Wallace and Tieman, Inc. in the pumps industry.

However, Allen-Bradely and Cutler-Hammer, i n the switchgear industry

and Siemens and FluroScan in medical imaging do not delegate the

pricing decision. Previous research has demonstrated that under

monopoly conditions it does not matter who sets the price, the firm or the

rep, if both have the same information about the market and commissions

based on sales and gross margins will have the same effect (Lal, 1986).

However, since most markets are competitive, a critical issue is whether

these results will hold i n competitive markets if there is no information

asymmetry? The purpose of this paper is to provide an answer to th is

question. In particular, we examine the impact of competition on the

price delegation decision, and derive the optimal compensation contracts

that should be offered to reps under different levels of delegation.

--- --------------------

Insert Table 2.1 here

Our results indizait: that with competition the type of commikon and

market structure elements affect the incentives to the reps and the market

outcome. If the commissions to the sales reps are based on gross margins,

we find that price competition plays a key role in the delegation decision.

When the cross-price impact is high, delegating the pricing decision is

optimal, while when it is low we find that pricing decisions shouid be

made by the firm, not the sales rep. The reason is that the price set by the

rep is higher than what the firm would set and thus, delegating the

pricing decision helps soften price competition when i t is intense.

However, i f the commissions to the reps are based on sales volume, then

the reps will reduce the price to increase sales, which, in turn, will

increase their wages. This will lead to increased price competition.

In the next section we review related literature from marketing and

economics. We develop our model i n Section 3 and present and discuss

the results of our analysis in Section 4. The final section contains a

summary and concluding remarks.

2. Literature Review

The issue of delegation of selling activity to an agency outside of the

firm has received attention in channels of distribution and salesforce

research on both conceptual and theoretical levels (Anderson 1985, John

and Weitz 1988, Weiss and Anderson 1992). Weiss and Anderson (1992)

have integrated concepts from channel distribution theory and transaction

cost analysis (Wi!liamson 1%5) to examine when should firms use

independent sales agents instead of a direct salesforce. The central result

of Weiss and Anderson (1992) is that managers will avoid converting

from a rep to a direct salesforce when they perceive h igh overall

switching costs. For a firm using direct salesforce (sales reps are

employees of the firm), the issue of price delegation has been analyzed

only under monopoly conditions. Under deterministic conditions, the use

of a commission based on a percentage of the gross margin aligns the

objectives of the firm and the sales representative. Therefore, the pricing

decision can be delegated and the sales representative can be expected to

set prices which are optimal for the firm and for himself (Weinberg,

1975). When the demand is stochastic, price delegation is more profitable

when the sales rep's information about the selling environment is

superior to that of the firm's (Lal, 1986). Consequently, under monopoly

conditions, the firm is indifferent to delegating price when there are no

information asymmetries between the rep and the firm. In addition, with

symmetric information, it does not matter whether the commissions are

on unit sales or on gross margins because the firm can always force the

rep to set the price that it desires (Lal, 1986).

An empirical study by Stephenson, Cron and Frazier (1979) finds various

market conditions under which price delegation is more likely to be

observed, but they do not provide an explanation of why we tend to

observe such a phenomenon. One of the conditions identified by them

under which price delegation is more likely to be observed is intense

price competition in the market

For a monopolistic firm, the firm-rep relationship can bc described as a

standard principal-agent problem where providing insurance to the agent

is in conflict with providing the right incentives. However, when the

profit accruing to the firm-rep pair depends on the decisions that other

rational agents are making, the potential interactions between the

structure of internal incentives within a firm and the market structure

elements external to the firm may affect the incentives. Once we start

thinking of incentives as strategic tools, it is possible that there may be

value to the firm of distorting the rep's incentives away from profit

maximization, i f the reaction of the competing firm is beneficial. Thus

the firm, instead of giving incentives to the rep to maximize profits, may

give incentives to maximize unit sales. For example, i f firms are

competing in price, the firms may pay reps to keep sales low (Fershtman

and Judd, 1987). Due to this distortion, non profit-maximizing firms may

enjoy more profits than the profit-maximizing firms (Fershtman, 1985).

However, under monopoly conditions the firm will motivate agents to

maximize the profits.

In a competitive market, the observability or unobservability of the

contract may affect the credibility of specific future behavior by the

firm. By manipulating the contract to its reps, a firm can affect the

market outcome because the contract with the reps is a credible

commitment to adopting a certain type of behavior (Sklivas, 1987).

Recently, several authors have examined the case of simultaneoiis

contracting by competing firms io settings where the contracts are

observable (Fershtman and Judd, 1987; Rey and Stiglitz, 1988; and

Sklivas, 1987). In a multiperiod financial predation situation, Bolton and

Scharfstein (1990) find that the unobservable contracts are less effective

pecommitments than the observable contracts in deterring predation.

When the agents are risk neutral, Katz (1991) shows that i t is important

that the contracts be observable to the competitors to be of any strategic

value. However, i f the agents are risk averse the contract dealing with

the incentive and risk sharing issues may actually be credibly committing

the agent in the next stage of actions.

In an oligopolistic market with price or quantity competition and

observable contracts, profit-maximizing firms will usually never tell

their risk neutral managers to maximize profits when each firm's

managers are aware of the other managers' incentives. This is because

each manager will react to the incentives given to the competing

managers (Fershtman and Judd, 1987). The nature of the desired

distortion depends on the nature of the oligopolistic competition,

quantity or price competition. In the Cournot-quantity competition the

firms will give incentives for sales, but in a price competition they will

pay the managers to keep sales low. Sales can be kept low by increasing

the prices which encourages competing managers to also increase their

prices. The financial terms of a contract are not disclosed to everyone

and there is always the possibility that cnly certain parts of the contract

are observable. Also, the contracts can be modified through a

renegotiation (Caillaud. Jullien and Picard. 1995).

In our model risk neutral firms compete i n the market through risk averse

sales representatives. The competition i n the market is between different

brands (interbrand competition) unlike in Rey and Tirole (1986) where a

single firm is selling through two different retailers and there is

competition between the retailers selling the same brand (intrabrand

competition). Under these conditions and with demand uncertainty, the

firm would prefer to set the price. However, when the retailers are risk

neutral and the products are non differentiated, the firm would want to

divide up the territorylmarket between the retailers and let them set the

price.

In our model price delegation is essentially an observable w a y to allocate

the decision making power between the rep and the firm without making

public the decisions itself. Thus the firms, when hiring their reps, can

make it explicit that in their organization the rep has a great deal of

responsibility and has to set the price besides choosing the effort level.

When the reps are risk averse the interests of the two parties, the firm

and the rep, are not aligned and so the decision to delegate price or not

can be a credible commitment to a certain type of behavior in product

market competition. An important assumption here is that whether or not

price is delegrtted is observaXc by the competing firm-rep pair before the

rep makes decisions. Thus the rep and the firm can negotiate about the

terms of the contract but not about price delegation decision.

3. Overview of Model

We consider two firms selling a differentiated product through sales reps.

The marginal cost of the product, c, is constant. The demand for each

firm's product (q l and qz) depends on the price (p, and pz) and effort ( e l

and el) put i n by the reps and a common random shock (6). An increase i n

effort b y the competing rep decreases the demand for one's own product.

Since effort is not observable by the firm, it is not contractible. We

consider two kinds of contracts. The first contract, when the firm

delegates pricing decision, consists of a commission rate and a fixed

salary. The second contract, when the firm does not delegate pricing

decision, consists of the price that the rep wi l l charge i n the market i n

addition to a fixed salary and commission rate.

Extensive form of the Game

Although the game is modeled as a simultaneous single shot game i n

which the players choose optimal strategies, there is an implied order of

the play (Figure 2.1 ):

Stage 1: Each firm simultaneously decides on whether or not to delegate

price which is specified in the contract that she will sign with her rep.

This decision (namely whether pricing authority is delegated or not) is

observable to the competing firm-rep pair.

Stage 2 : Reps examine the contract and decide whether to accept or reject

i t .

Stage 3: If the reps accept the contract then each rep chooses price and

effort or only effort to maximize her own expected utility. The common

random shock is realized and the demand for each firm's product is

determined.

....................

Insert Figure 2.1 here

The model is a Principal-Agent set up in a competitive scenario with

standard assumptions about demand, utility and cost of effort functions. 1

Assumption 1: The demand' for firm i's product is given by

where 6 is the common random shock3 and is normally distributed with a

mean zero and variance 6;'. The parameter 8, is the ratio of rate of change

' We consider a standard, differentiated products Bertrand competition. The competition is modeled at the firm level which assumes compIetely flexible supply side. Thus the issues related to market clearing price and industry level supply and demand curves do not exist

% i s is the demand equation of a rescaled model with following constraints - (i) prices are greater than or equal to sum of marginal cost and wages (selling expense), (ii) quantities sold are non-negative given that reps put in no effort. (iii) industry demand does not increase with increase in price of either him's product

of quantity sold with respect to competitor's price to the rate of change of

quantity sold with respect to own price. Similarly, 8, is the ratio of rate of

change of quantity sold with respect to the competing rep's effort to the

rate of change of quantity sold with respect to own rep's effortJ.

Assumpt ion 2: The marginal cost c for both the firms is a constant. The

values of the constant h in the demand function and of marginal cost c are

such that the expected demand is always positive in the relevant range of

price and effort.

Assumpt ion 3: The cost of effort is a convex function given by G(ei) = ei'

. The cost is expressed in dollar equivalent.

The marginal cost of providing a higher effort increases with the level of

effort. The more time the rep spends on selling the less is left for leisure.

Thus the leisure time becomes more valuable on a per unit time basis.

This results in the marginal disutility of effort increasing with effort.

Assumpt ion 4: The firms are assumed to be risk neutral. The agents are

risk averse with a constant absolute risk aversion (CARA) utility function

given by U(x) = 1 - e "" where x is the sales rep's wealth o r earnings and

r is the coefficient of risk aversion.

-- - -

Also, the industry demand does not decrease with increase in effort by the rep of either firm. (Details in Appendix 2.2) ? h e qualitative results do not change with different but uncorrelated random shock for each fm ' s demand as long as expected value of each random shock is zero. Even with corretated random shocks the qualitative results remain same because we do not need to evaluate expected value of total demand and its variance.

Refer Appendix 2.2.

The agents are assumed to have a constant absolute risk aversion, i.e., the

risk preaiurn is uneffected by equal increases in income at any state.

Howard (1971) ohserves that the exponential utility function provides a

gcod approximation for representing preferences of many decision

makers. The assumption is reasonable in contexts where the likely

variation in the compensation to the sales reps is not large relative to the

sum of her wealth and expected total income. Pratt (1964) shows that the

risk premium and the probability premium for the exponential utility

function remain constant as wages vary. With a CARA function the effect

of wealth on risk aversion is not present. This helps by keeping the wealth

effect constant so that the other effects that are of interest can be

identified (Grossman and Hart 1986, Holmstrom and Milgrom 1991).

4.0 Model Development

General wage structures consisting of salary plus commission are

commonly observed in the market (Peck, 1982). Basu, Lal, Srinivasan and

Staelin (1985) analyze how and why different components of this wage

structures vary in a monopoly situation. La1 (1986) has shown that in a

monopoly situation with symmetric information it does not matter whether

the commission to the rep is based on margins or on unit sales. We first

examine this result when there is competition in the market.

Sales Based Commission

The agent is offered a contract of the form W = a + P(qi) where a is the

fixed salary and is the commission on sales. The rep does not make any

pricing decisions. Under this set up the firm will meximize expected

profit. The rap will maxir?.i=e txpected utility given that it is greater than

or equal to h is reservation utility. The optimization problem is given by;

subject to

e, E argmax ~ ( a + f l qi ) Incentive Compatibility Constraint

u(~+A,) 2 r Participation Constraint

Since we are using a CARA function the participation constraint could be

written in terms of certainty equivalent CE. The optimization problem,

assuming reservation utility to be zero, is simplified to

subject to

The first order conditions for the firm's optimization problem, after

substituting for salary a and effort ei, are;

Simplifying the above conditions gives

When the price competition is intense as compared to effort competition

(0, > 0,/(2 + 4ras2)) the reaction to a decrease in price by the rival firm is

to decrease own price. Thus when the price competition is intense and

reps are paid on sales volume, the prices drop which exacerbates the

situation. Even if the reps were to set the prices, because they are paid

commissions on sales volume, the firms could not commit credibly to

setting a higher price. If the effort competition is intense (8, < 0,/(2 +

4ras2)) the reaction to a decrease in price by the rival firm is to increase

own price. The symmetric Nash equilibrium of this game is

Margin Based Commission

We now consider the game subsequent to the announcement by the firm of

its price delegation decision and acceptance by the rep of the contract.

Thus the feasible contract depends only on the announcement. The

equilibrium consists of the contracts offered by the firms and the prices

and effort levels chosen by the representatives. Each firm offers its sales

representative a contract specifying a fixed salary Cti and a commission

rate pi = p i - y i . The variable y i can be interpreted as the firm's

communication to the rep of the cost of production which can be equal to

c or higher. By overweighting the marginal cost of production c the firm

can make the rep less aggressive in a market. This commission structure is

equivalent to commission on gross margin since the wages can be

rewritten as y(p i - c i ) (unit sales) where y = 1-(xi)/( p i - c i ). Since the

agent is making the price decision the firm's decision variable becomes y i

(or xi).

4.1 Reps make Effort and Pricing Decisions (Price Delegation)

Each firm, while deciding on the contract with her rep, considers only the

effect of the contract on her rep's actions, taking the actions of competing

rep as given. The equilibrium contracts, prices and efforts simultaneously

solve the following maximization program for each firm:

Max ~ [ (y , - c )q j (6 ) - a i ] ?', .a, $8 4

The objective function is the firm's profits. Equation (6) is the incentive

compatibility constraint and equation (7) is the individual rationality

constraint for the rep. We can assume the reservation utility of the agent

to be zero. From assumption 1 the firm's profit is normally distributed.

Since the rep's utility function is exponential her expected utility can be

expressed in certainty equivalent terms as;

Thus the agent wil l now choose price and effort levels to maximize her

CE. The incentive compatibil i ty condition can now be replaced by the

first order conditions given by;

(P, - y, )(-1) + E[q , (&I - r(p; - Y , ) 4 = 0 (9 )

Since the salary component ai does not enter the agent ' s first order

conditions, the firm can adjust i t without affecting the agent 's choice of

price and effort level. Thus f rom equation (7) and equation (8) the binding

participation constraint can be written as:

The risk premium that the f i rm needs to give to the rep is the last term on

the left hand s ide of equation (1 1). It increases with the uncertainty (as ')

in demand and the risk aversion ( r ) of the sales rep.

Lemma I : A pair of contracts {yi, ai) and a pair of prices and efforts { p i .

e i ) , where i = 1 ,2 constitute an equilibrium if and only if the following

are satisfied

Proof: (Refer Appendix 2.1 A)

The effect of risk aversion on market competit ion can be seen by

comparing equations (3) and (13) . For a given value of yi a risk averse

agent chooses a price that is lower than what the firm would choose

result ing in a lower risk premium. This does not imply that equilibrium

price is lower, since yi can be different from marginal cost c. In fact , the

condition by equation 1A. 1 (Appendix 2.1A) shows that yi is greater than

c. Rewriting the firm's payoff as:

we can see that the firm's expected payoff i s the expected payoff, if the

firm sel ls directly, less the risk premium that has to be given to the agent.

When yi is set equal to marginal cost c , a small increase in yi from c has

no marginal effect on firm's profits, but has a negative effect on the risk

premium which is a gain for the firm. This private incentive due to the

reduction in the risk premium makes it credible for the f i rm to increase yi

over the marginal cost c. This i s an example of the proposition put forth

by Katz (1991) that unobservable contracts can be manipulated for

strategic purposes when the agents are risk-averse.

Proposition I : In the symmetric Nash equilibrium under price delegation

the prices, effort levels and the commissions rates are given by:

Proof: (Refer Appendix 2.1 B )

The prices increase with an increase in cross price impact and so does yi.

However, the increase in pi is greater than the increase in yi and so the

commission pi to the rep increases as the cross price impact increases.

This gives an incentive to the rep to put in more effort or to keep the

price higher and thereby keep the commission rate higher.

4.2 Reps make only Effort Decision (No Price Delegation)

Now let us consider the case where the firm sets the retail price and the

agent selects the effort level. The agent selects the effort level given the

price and the demand. Each firm will simultaneously solve the following

maximization program:

Max E [ ( ~ , -c)q, -all y, .pi .a, ;ti

Lemma 2: Under no price delegation a pair of contracts {vil ail and a

pair of prices and efforts { p i , eiJl i = 1,2 constitute an equilibrium if and

only if the following are satisfied

Proof: (Refer Appendix 2.1C)

We need to see if yiD, when the rep sets the price and effort level (case l ) ,

is higher than the y i N D when the rep sets only effort level (case 2).

Comparing equation (12) and equation (1C.2, Appendix 2.1C) for a given

commission rate we get:

Similarly comparing equation (13) and equation ( lC.3 , Appendix 1C) we

get:

- P.m = r< EIq, ] ) 0 for a given value of yi . a Pi t

Proposition 2 : The price of the product when the rep makes effort and

pricing decisions is higher than the price when the rep makes only effort

decision.

Thus when the firm is making the pricing decision it would set a higher

value of yi (equation 22) given the agent gets the same commission rate

and would set a lower price for the same level of yi (equation 23). The

indirect effect of price on profit through effort level and its effect on risk

premium cancel each other out in the equilibrium.

Proposition 3 : In the symmetric Nash equilibrium under no price

delegation the prices, effort levels and the commission rates are given by:

and,

where W = 3 - 20, + 0, + 8r0: - 4Bpr4

Proof:

The symmetric Nash equilibrium in prices ( p i ' N D ) is obtained using

equation (1C.3), in effort levels (e imND) using equation (1C.L) and in

margins ( y i * N D ) using first order condition given by equation (1C.2) . The

equilibrium is:

and,

The firm sets higher values of yi with increase in cross effort impact and

so even though the price increases the commission to the reps do not

increase as rr.uch with increase in cross effort impact.

If efforts were contractible, we could consider a delegation scenario in

which only the pricing decisions were left to the reps. Given the

framework being used in this paper the outcome would be the same as the

no price delegation situation because of perfect observability of the price

being charged. The firm could setup a forcing contract giving the rep

wages that would meet the participation constraint in the event that rep

set the price desired by the firm and a large penalty if she did not set the

desired price.

4.3 Firm 1 has Price Delegation and Firm 2 has No Price Delegation

Now we consider a situation where one firm delegates pricing decision

and the other firm does not. The earlier analysis can be used here because

in finding the equilibrium conditions we do not assume any specific

contract offered by the competing firm. Thus in equilibrium the contract

by firm 1 ( y ~ , a ~ ; p ~ , e , D ) must satisfy the conditions given in Lemma I and

the contract by firm 2 ( f , a ; ~ ~ , ~ ; ~ ; e ; ' ~ ) must satisfy the conditions given

in Lemma 2, simultaneously. The results and proof is given in Appendix

2.1D.

Having looked at the equilibrium contracts under various cases we can

comment on the strategic role of price delegation. The firm, while

deciding on the contract, has to consider the effect of her delegation

decision on the price and effort level offered by the competing firm's rep.

Choosing a different delegation decision results in a commitment to a

different behavior in terms of price, effort and commission. This is what

the competing firm will take into account while designing the contract.

4.4 Equilibrium Delegation Decision

Now we need to look at the firm's choice of price delegation. Their

decision would depend on the payoffs resulting from the equilibrium

contract under each type of delegation. This can be represented as a 2 x 2

matrix shown below.

Firm 2

The diagonal entries are the profits to each firm under identical types of

delegation. The off-diagonal entries are the profits under different

Firm 1

D

ND

Price Delegation

(Dl

( nD, nD,

( mND, nzD)

No Price Delegation

(ND)

( m D , bND,

( rIND9 nND)

delegation strategies. Thus nD and lIND are the profits to each firm under

price and no price delegation, respectively. Also, ( nlD, nZND) represents

the profits under mixed equilibrium when Firm 1 decides on price

delegation and Firm 2 on no price delegation. To find the equilibrium we

first need to calculate the profits.

Lemma 3: The profit to a firm that decides to delegate pricing decision,

regardless of what the other firm decides, is given b y

The profit to a firm that decides not to delegate pricing decision,

regardless of what the other firm decides, is given b y

Proof:

Using equation (12) and (13) the profit to the firm that chooses to

delegate pricing decision is:

Similarly, using equation (18) and equation (19) the profit to the firm

Aoosing not to delegate the pricing decision is determined. Thus the

profit l lD would vary under (D, D) and (D, ND) case only through the

component pi - yi. Similarly, ITND would vary under (ND, ND) and (ND,

D) case only through the component pi - yl since r and 06' are exogeneous.

The next step is to compute the commission rate pi (= pi - yi ) by using the

equilibrium outcomes for the case when both firms decide on price

delegation (D, D) and the case when Firm 1 decides on price delegation

and Firm 2 on no price delegation (D, ND). From the equilibrium values

stated in Proposition 1 we can calculate pi - yi for (D, D) case to be

From the equilibrium values in Proposition 4 (Appendix 2.1D) we can

calculate pi - yi for (D, N D ) case to be

From the equilibrium values stated in Proposition 3 we can calculate pi -

yi for (ND, ND) case to be

Similarly, from Proposition 4 the value of pi - yi for (ND, D) case is

To find the equilibrium we need to compare the following payoffs;

where R , ~ , R D, R l ND and R ND are functions of cross price impact, cross

effort impact and the utility cost of uncertainty (Appendix 2. LE).

Therefore, to find the Nash ~ ~ u i l i b r i u r n ' we now have to compare R ~ ~ , R

D, R I ND and R ND.

Firm 2

No Price Delegation

(ND)

Firm 1

h e existence of Nash Equilibrium has been checked in each subgame for the entire range of cross price and cross effort impacts. At the delegation decision stage existence can be proved using best-response correspondence for the two f i i and the Kakutani's fixed-point theorem. At the price and effort subgarne the strategy sets are convex. non-empty, closed and bounded. The utility functions are concave and so have quasi-concave contours.

Price Delegation

(Dl

Thus price delegation is the dominant strategy if R~ > R~~~ and R , ~ >

R ~ ~ . If these two inequalities hold, then firm 1 would prefer to delegate

the pricing decision no matter what firm 2 prefers. Similarly, firm 2

would prefer price delegation regardless of firm 1's choice. If R~ < R~~~

and R~~ < R ~ ~ , no price delegation is the dominant strategy. However, if

R~ < R~~~ and R~~ > R ~ ~ , we have an equilibrium in which one firm

delegates the pricing decision and the other does not, that is, (D, ND) and

(ND, D) are the equilibria.

The analytical solutions for these conditions are, to say the least, difficult

to interpret and so we look at graphical solutions. The only variables in

these conditions are 8,, Br and r ~ ' ~ . We call the term r& the utility cost

of uncertainty. As r approaches zero the rep's risk attitude approaches

risk neutrality and the product r& approaches zero, implying that the rep

and the firm bear no cost due to uncertainty. As r increases the product

r& also increases and so one can say that the cost due to uncertainty

(scaled by the risk attitude of the rep) also increases. To analyze, we fix

the value of r& to one and then look at the contours of R~ - R I ~ ~ , R~~ -

R~~ and R~ - R ~ ~ . These contours are shown in Figure 2.2 as curves TT,

PP and QQ, respectively. In the region marked TD both R~ > R~~~ and

R~~ > R ~ ~ , and in region marked PD both RD < RIND and ~l~ < R ~ ~ .

Insert F i ~ u r e 2.2 here

Thus in region TD price delegation by both the firms is the equilibrium

and in region PD no price delegation by both the firms is the equilibrium.

In the region marked PTTP, R~ z R ~ ~ ~ , R~~ < R~~ and R~ > RND. Thus

there are multiple Nash Equilibria in this region with both firms either

delegating the pricing decision o r both firms not delegating the pricing

decision. Thus given 0, the higher the value of 8, (i-e., greater the price

competition) the more likely is the firm to pick a price delegation

strategy. Similarly, for a given value of 8, the higher the value of €I,, (i.e.,

greater the effort competition) the more likely is the firm to pick the no

price delegation strategy6. These equilibria are stable. In region P I P

(Price Delegation) if both firms were to adopt no price delegation then the

question is would one firm want to deviate and choose price delegation.

The answer is yes since in this region R~~ > R ~ ~ . However, since R~ >

R I N D in this region, the other firm would also want to switch to price

delegation since it would make higher profits. We can apply the same

logic to check the stability of the equilibrium in region TOlT (No Price

Delegation Equilibrium).

Proposition 5: For a f irm wi th a risk averse sa les r e p facing a n uncertain

demand, pr ice de lega t ion i s the equil ibrium when the price compet i t ion is

If 8, and 8, are zero it implies that the demands are independent and so the f w are monopolists. Under these conditions the profit to the monopolist with price delegation are found to be same as the profit from no price delegation. The result is what La1 ( 1986) finds under no information asymmetry condition.

39

more intense and no price delegat ion i s the equil ibrium when effort

compet i t ion is more intense.

The competition in the product market is in two dimensions - price and

effort. The type of delegation that will be preferred in equilibrium is the

one that is more effective in reducing the competit ion in the dimension in

which it is more intense. Under price delegation the rep tends to charge a

higher price than what the firm would charge under no price delegation.

The firm does this by giving the rep a higher commission on gross margin.

Under no price delegation the rep has a lower commission rate which

reduces her incentive to provide higher effort . However, the equilibrium

level of effort could be higher under no price delegation because the rep

can maximize his utility only by selling more which in turn requires more

effort .

As can be seen in Figure 2.2, the effect of price and effort are not

symmetric, the price effect being greater than the effort impact. This is

because Figure 2.2 plots profit functions and price i s a quadratic term in

the profit function. In region TQQT, R~ > R~~ and so both firms should

prefer price delegation. The firms would want to commit to a price

delegation strategy before making the actual choice. However, the

commitment is not credible: each firm would want to unilaterally deviate

to no price delegation s ince the profits a re highest ( in this region) to the

firm that does not delegate the pricing decision when the other firm does.

Hence we have a prisoners' dilemma situation.

..........................

Insert Figure 2.3 here

Figure 2.3 shows the effect of an increase in utility cost of uncertainty

(ras2 = 3) on delegation strategy. The region TD becomes smaller while

the region PD increases, i.e., with increase in risk aversion andlor demand

uncertainty there is a greater possibility of the firm choosing not to

delegate the pricing decision, because it reduces the risk premium to be

given to the rep7.

McGuire and Staelin (1983) look at the issue of decentralization in a

channel relationship with only price competition and risk neutral retailers.

Table 2.2 shows the primary differences in their approach and the

approach taken in this paper. They conclude that for degree of

substitutability

Insert Table 2.2 here

(8) greater than 0.708 the manufacturer delegates the pricing decision. A

similar result would be obtained in our framework if effort levels did not

affect the demand. They also find that prices are highest for a pure

decentralized system for any given value of theta. This is equivalent to

saying that the prices are higher under price delegation. However, in our

' When the reps are risk neual the f m do not have to pay a risk premium to the reps, so there is no inefficiency due to risk sharing. For all values of cross price and cross effort impacts the firms can earn the same profits with price delegation as with no price delegation and vice versa Thus with risk neutral reps one can observe an equilibrium where F i 1 delegates pricing decision and Finn 2 adopts no price delegation strategy. Using a decreasing absolute risk aversion (DARA) utility function would Iead to greater regions of price delegation due to the wealth effect on risk aversion.

model this difference in prices between price delegation and no price

delegation scenarios decreases as effort competition increases.

4.5 Prices under Price Delegation and No Price Delegation Scenarios

How do prices vary with changes in price competition and effort

competition? Assuming that c, the marginal cost of production, is zero

for both firms and h is large enough to guarantee a non-negative demand

we plot the prices under price delegation and no price delegation in Fig

.........................

Insert Figure 2.4 here

Note that for any given level of effort competition, as price competition

increases the price of the product also increases. However, as Fig 2.4

shows, the price under price delegation is always greater than the price

under no price delegation. When the effort competition is intense firms

prefer not to delegate the pricing decision for then the only way for the

reps to earn more is to work more. This ensures that the rep works hard

enough so as not to lose sales to competition. If there were to be an

asymmetric equilibrium, i.e., one firm delegates the pricing decision and

the other does not, the prices would vary in a different way. The firm that

believes that there is greater effort competition would not delegate price

and the firm that believes that there is higher price competition would

delegate pricing decision. The firm that is not delegating price would set

lower price and higher effort level and the firm delegating price would b e

setting a higher price and lower effort level.*

4.6 Commissions and Salaries under Price and No Price Delegation

Again setting c=O, and a high value of h we can plot the variation in

commission rates with changes in price and effort competition. For a n y

given value of effort competition, it is observed that the commission rate

increases as the price competition increases. This is also true under no

price delegation (Figure 2.5).

Insert Figure 2.5 here

We have shown earlier that as effort competition increases the firms move

from price delegation to no price delegation i n order to ensure that the

reps work hard. This is brought about b y decreasing the commission rate

so that the only way to earn more is to increase volume. On the other hand

as price competition increases firms move towards price delegation

hoping to soften price competition. Increased commission rate on gross

margins gives greater incentive to the reps to increase price. This in turn

reduces price competition. The firm, whether adopting price delegation or

no price delegation, has to prcvide the rep with the same minimum utility

to ensure that he works for the firm. The salary component under price

delegation is reduced due to higher prices and commissions on gross

With non linear demand functions it is expected that the optimal prices would be different. Prices would be higher for a concave demand function and lower for a convex demand function. However, it is expected that there still would be regions of price delegation because of the need to soften price competition.

43

margins. This results in higher salaries under no price delegation

scenario.

Insert Figure 2.6 here

The sales effort under price delegation scenario is lower than the effort

under no price delegation scenario. As discussed before, when there is

effort competition the firms want that their reps do not lose sales to

competitors. With no price delegation since the rep cannot influence the

commission rate the only instrument remaining to increase utility is sales

effort which increases the sales volume. Thus under price delegation the

reps set higher prices, put in lower effort, earn higher wages and the firm

too makes higher profits due to softening of price competition.

........................ Insert Figure 2.7 here

5. Conclusions

We have examined salesforce incentives and price delegation using

agency theory with competition. Previous research has examined these

issues under monopoly conditions. Under these conditions, the firm is

indifferent to delegating price when the firm and the rep have same

information about the market. Also, with symmetric information, i t does

not matter whether the commissions are on unit sales or on gross margins

because the firm can always force the sales rep to set the desired price. If

the commissions are on unit sales, they do not achieve the objective of

softening price competition, however, if they are based on gross margins

price delegation will soften price competition when the cross price impact

is high. In addition, we find that even when the firm and the risk-averse

reps have same information about the market, there are conditions under

which firms should delegate the pricing decision.

Under intense price competition, the firms offer contracts with higher

commissions on gross margins which allows the reps to set a higher price.

This helps to soften the price competition. Thus the firm earns more, the

prices are higher, the reps earn more and they put in less effort as

compared to the no price delegation situation.

When the effort competition is intense the firms prefer not to delegate the

pricing decision. The contract under no price delegation is found to be

more effective in ensuring that the reps do not lose sales to competitors.

When price is not delegated the firms give the reps lower commissions on

margins, so the only way to earn more is to sell more which, in turn,

requires a higher effort level. As the utility cost of uncertainty increases,

the region of price delegation shrinks because of the increase in risk

premium to be paid to the sales reps.

Appendix 2.1A

Proof of Lemma I

The firm's maximization problem can be written as:

Since the ICC and the IR for the agent define pi, ei, and Cti a s functions o f

yi w e can use the envelope theorem to write the first order condition for

the commiss ion rate (= pi - y i ) as :

The expected value of demand qi i s ;

The expected value of derivative of qi with respect to yi is;

The derivative is always negative indicating that as you leave less

incentive with the rep (due to increase in yi) the quantity sold also

reduces. Thus the contract {yi , ai} and the prices and efforts {p i , ei} for i

= 1,2 constitute an equilibrium if and only if they satisfy the conditions

given in the Lemma.

Appendix 2.1B

Proof of Proposition 1

The symmetric Nash equilibrium in prices (pi'D )and effort levels (eiaD )

calculated using equations (9) and (10) is:

Now substituting the value of p i * D in equation (12) we get the value for

y i * D as:

Appendix 2.1C

Proof of Lemma 2

Since the utility function o f the agent is assumed to be exponential s/he

maximizes the certainty equivalent:

1 -I 'I

Mar C E = ~ , + ( p i - Y , ) ( ~ - P , +@,p-i+ei -0,e-,) - ef - ( p l - y, ) - r G ti 2

The firm therefore maximizes:

subject to

Using the envelope theorem to obtain the f .0 .c . with respect yi we get:

We substitute in the firm's maximization program the values for ai, ei and

E[qi] which gives :

Using the above function to obtain f .0 .c with respect to pi we get:

7 ( y i -c)(-I 1 2 ) - ( p i - y i ) - ( p i - y i ) ' c i + E [ q i I = C *

Using equation (18) to simplify we get:

2 ( p i - y i ) ( l + 2 r 0 6 ) - E [ q i ] = O *

Appendix 2.1D

Proposition 4: In the Nash equil ibrium when one f i rm de lega tes pricing

dec i s ion and the o ther does not the pr ices , effort l e v e l s and commission

ra tes a r e given by:

Proof of Proposition 4

Assume that Firm 1 follows price delegation and firm 2 follows no price

delegation. For firm 1 , the contract and the rep's price and effort levels

satisfy equations (12) to (15) in Lemma I . For firm 2, the contract and the

rep's price and effort levels satisfy equations (18) to (21) in Lemma 2.

We have from equation ( 13)

where terms with superscript D are for firm 1 (price delegation) and terms

with superscript ND are for firm 2 (no price delegation).

From equations (1 8) and ( 19) we get;

Substituting in 1.Dl from 1.D2 and solving for p i D

Once again from equation ( 13) we get;

Substituting for p i D in equation (19) we have;

Substituting for p i D in equation (12) and collecting terms i n y i D and yjND

we get;

From equation ( 1 8 ) we get;

Equations ( l D . 6 ) and (lD.7) can now be solved simultaneously to get

values for y i D and y j N D -

Appendix 2.1E

Appendix 2.2: Resealed Model

The expected demand for Firm 1 and Firm 2 is

The scale factor S is industry demand when the prices of both products

are zero and so reps do not need to put in any effort. The parameters p, O p

and 8, capture different aspects of product differentiation and market

competition - p is the absolute difference in demand, is the effect of

price competition in the market as reflected by cross price elasticities and

8, is the effect of sales effort competition. The parameter €Ip affects the

substitutability of products in terms of changes in prices and the

parameter 8, affects the substitutability of the products in terms of effort

put in by the sales reps.The marginal cost of production is c and the

variable selling cost (wages to reps) is w. The following additional

constraints are placed on these parameters to ensure the following

conditions - ( 1 ) prices must exceed the sum of marginal costs and wages,

(2) quantities sold must be non-negative given that the reps put in no

effort, (3) industry demand should not increase with increase in price of

either firm's product and should not decrease with increase in effort b y

either firm's sales rep.

B y condition ( I ) we have

Given that the reps d o not put in any effort condition (2 ) g ives

k which implies, f l S --

c + w

The expected industry demand is g iven by

The coeff ic ients o f prices and of efforts must be non-negative to satisfy

condition ( 3 ) . This implies that,

Applying the fo l lowing equalities

(i) h = k - P ( C + W ) t

41 (ii) q , = -- P S

42 - . . -. . .- . - (iii) qr - ( 1 4 s

to rewrite the demand equations we get

which are a function of only the two parameters, ep and 8,.

Chapter 3

ENTRY ACCOMMODATION AND ENTRY DETERRENCE

STRATEGIES

1. Introduction

In the previous chapter we examined how two firms selling differentiated

products delegate the pricing decision to their sales representatives. The

decision to delegate or not was found to depend on the type of

competition in the product market. Even when the firm and the risk-averse

rep have the same information about the market, price delegation is found

to be the equilibrium when the price competition is more intense and no

price delegation is found to be the equilibrium when the effort

competition is more intense. In this chapter we examine the role of price

delegation as a strategic variable to deter entry.

An important issue in industrial organization is how the firms can protect

their market when there is a threat of entry, i.e., the second firm is not in

the market but is thinking of entering the market. Bain (1956) suggests

three kinds of behavior by an incumbent when faced by an entry threat:

( 1 ) blockaded entry - the incumbent behaves as if there is no threat of

entry but the market is not attractive enough for the entrants, (2) deterred

entry - entry cannot be blockaded, that is, the market is attractive enough

for the entrants but the incumbent can alter its behavior to increase the

cost of entry in the hope of deterring entry, and (3) accommodated entry -

the incumbent finds it more profitable to let the entrant enter than to

create costly barriers to entry. Bain (1956) has also examined w h y the

profit rate in certain industries is systematically greater than in other

industries. He concludes that these industries have barriers to entry that

allow the incumbent firms to earn supranormal profits without threat of

entry.

There are a number of business strategies available to a firm, depending

on whether it wants to deter entry, induce exit or accommodate entry. For

example, the firm can invest in capacity (Dixit, 1980) to deter entry or to

send a signal about the market conditions or its marginal cost through the

first period pricing (Milgrom and Roberts, 1982). Work on strategic

investment on cost-reducing machinery (Spence 1979 and Dixit 1979) and

in "learning by doing" (Spence 1931, and Fudenberg and Tirole 1983)

suggests that the strategic incentives always encourage the incumbent

firm to overinvest. Fudenberg and Tirole (1984) show that in some

circumstances overinvestment may be a strategic handicap, because i t may

reduce the incentive to respond aggressively to the competitors. In their

advertising model the incumbent in the first period decides on the amount

to spend on advertising to generate goodwill. After observing the

incumbent's action the entrant decides whether to enter or not. If the

decision is to enter the market the two firms compete on prices in the

second period. The incumbent here will choose to underinvest in

advertising if it chooses to deter entry, because by lowering its stock of

goodwill it establishes a credible threat to c u t prices in the post entry

game. This assumes that lowering of prices by the incumbent will induce

the entrant to also cut prices and thereby reduce the entrant's profits.

Thus the optimal strategy depends on whether the reaction curves of the

two firms are upward or downward sloping. This is equivalent to the

decision variables being strategic complements or strategic substitutes

(Bulow, Geanakoplos and K!emperer 1985).

The key factors i n strategic investment are whether the investment

(example, investment i n advertising) makes the incumbent "tough" or

"soft" i n the post entry game, and how the entrant reacts to tougher play

by the incumbent. This, i n turn, depends on the strategic substitutability

and complementarity. If an increase i n investment reduces the post entry

profits to the second firm, then that investment makes the incumbent

tough. If i t increases the entrant's profits then the investment makes the

incumbent soft.

In our analysis, choosing whether to delegate price or not is equivalent to

investments i n Fudenberg and Tirole (1984) research. Thus i n our

analysis, the incumbent firm needs to decide on the type of delegation -

no price or price delegation. In their research, the second period

competition is in prices i n the advertising game. Thus the second period

competition is on only one dimension - price. In our model the second

period competition is on two dimensions - price and selling effort.

The taxonomy of Fudenberg and Tirole (1984) classifies the market

according to the signs of the incentives for strategic investments. The fat-

cat strategy is an entry accommodation strategy. Overinvestment makes

the incumbent look soft, signaling to the entrant that the incumbent is

committed to taking a less aggressive action in the post entry (pricing)

game. The lean and hungry strategy is an entry deterrence strategy when

the investment makes the incumbent look soft. Here the incumbent

underinvests to look tougher. If the investment makes the incumbent look

tough, then the top dog strategy is to overinvest to look tough and thereby

deter the entrant. The puppy dog strategy is that of underinvestment by

the incumbent. This accommodates entry by turning the incumbent into a

nonaggressive player in the post entry game.

The first objective of this chapter is to examine whether delegation is a

strategic substitute or a strategic complement decision variable for the

firms. With the firms playing a sequential game we examine how they can

use delegation as a strategic variable to deter or accommodate entry.

Thus, we examine the organizational form (with or without price

delegation) as a strategic variable under threat of entry. The second

objective of this chapter is determine what entry deterrence or entry

accommodation strategies the incumbent firm will adopt for different

levels of price and selling effort competition. The credibility of an action

by the incumbent is important i n signaling entry deterrence or entry

accommodation behavior. Lal, Outland and Staelin (1994) find that it is

difficult for firms to alter the contracts that they have entered into with

their sales personnel, once the sales representatives have been employed.

These contracts are fairly long and usually vary in time from four to seven

years. There is also the reputation effect that the firms have to consider.

Breaching the terms of the contract may affect the firm's reputation and

the highly skilled personnel may want to go elsewhere. Thus the type of

organizational form chosen, which i n turn affects the type of contracts

offered, is a credible commitment.

In section 2.0 we first analyze whether price delegation is a strategic

substitute or a strategic complement variable. To do this we look at the

simultaneous game. In section 3.0 we look at the equilibrium strategies

when firms play a sequential game. In section 3.1 and 3.2 we analyze

what the entry deterrence and entry accommodation strategies are for the

incumbent and compare i t with the equilibrium strategies under the

sequential game.

2.0 Strategic Substitutes or Strategic Complements

The firms can use delegation as a strategic variable to affect the decisions

of the competing firms. We still examine two Firms selling a

differentiated product through their respective sales representatives. The

demand for each firm's product ( q l and ql) depends on the prices (p l and

p2) and the efforts (el and e 2 ) put i n by the sales representatives and a

common random shock (6). The game is modeled as a simultaneous single

shot game and the implied order of the game is as shown in Fig 3.1. Since

the effort is not observable by the firm it is not contractible.

----------------------

Insert Figure - 3.1 here

The demand for firm i's product is given by

where 6 is the common random shock and is normally distributed with a

mean zero and variance 4. The parameters 0, and 0, represent the effect

of change in rival firm's price and effort level on the demand for one's

own product. Both, €Ip and 8, are less than one implying that the effect of

a firm's own price and own rep's effort is greater than the effect of its

competitor's price and effort.

The agents are assumed to have a constant absolute r isk aversion, i.e., the

risk premium is unaffected by equal increases in income at any state. The

firms are assumed to be risk-neutral. The cost of effort for the reps is a

convex function.

Each firm, while deciding on the contract with her rep, considers only the

effect of the contract on her rep's actions, taking the actions of competing

rep as given. Under the price delegation scenario the equilibrium

contracts, prices and efforts simultaneously solve the following

maximization program for each firm:

Now let us consider the case where the firm sets the retail price and the

agent selects the effort level, i.e., there is no price delegation. The agent

selects the effort level given the price and the demand. Each firm will

simultaneously solve the following maximization program:

Max E [ ( yl - dq, - 1 rI .pl .a, x,

Following Bulow, Geanakoplos, and Klemperer (1985) we will consider

the actions of two firms to be strategic complements if the change in the

marginal profitability to Firm 1 from being more aggressive when Firm 2

is more aggressive is positive and strategic substitutes if i t is negative.

Thus we analyze whether an increase in the degree of delegation by a

competing firm induces the manager to increase or decrease delegation. In

the present case since delegation is a binary variable, i.e., either there is

price delegation or there is no price delegation, increase in delegation

implies a move from no price delegation to price delegation. A decrease

in delegation implies a change in strategy from price delegation to no

price delegation.

The profits to the firms from adopting price or no-price delegation

strategies are;

( 1 ) Profit to Firm 1 when Firm 1 delegates pricing decision and Firm 2

does not

(2) Profit to each firm when both firms delegate pricing decision

(3) Profit to Firm 1 when Firm 1 does not delegate and Firm 2 delegates

pricing decision

(4) Profit to each firm when both firms do not delegate pricing decision

where,

r = coefficient of risk aversion

4 = variance in the demand

0, =" cross price" impact

8, =" cross selling effort" impact

Thus profits under different levels of delegation can be compared using

the terms R , ~ , ItD, R ND and R ~ ~ ~ . The term 8, measures the impact of

price change by Firm 2 on Firm 1 ' s demand and 8, measures the impact of

change in sales effort by Rep 2 on Firm 1's demand. The change in profit

to Firm 1 from price delegation instead of no price delegation when Firm

2 does not delegate price is givea by;

A , = R , ~ - R ND (17)

Similarly, the change in profit to Firm 1 from price delegation instead of

no price delegation when Firm 2 adopts price delegation is given by

Az = R~ - R, ND ( 1 8 )

By definition if A, > A2? then types of delegation are strategic substitutes,

and if A2 > A , then types of delegation are strategic complements.

Suppose revenues from price delegation as compared to no price

delegation are higher, when the rival firm does not delegate price than if

the rival firm delegates price, then Firm 1's best response to no price

delegation by Firm 2 is to delegate pricing decision. In order to see if

either of these inequalities holds in the entire range of price impact 8, and

sales effort impact El,, we plot the difference ( A l - A2) in the 8, 0, unit

square. Figure 3.2 is a plot of the A , - A2 curve.

......................... Insert Figure 3.2 here

We identify the regions in which delegation is a strategic complement

variable and region in which it is a strategic substitute variable. In the

regions marked A l B and C I D delegation is a strategic complement and in

the region marked ABDC delegation is a strategic substitute variable. In

region CID we have R~~ > RI ND > R~~ > R D. Thus in this region R l - R

> R~~ - R I ND (since the term to the right of the inequality is negative).

Also, in this region RI N D > R I D. This implies that R < R I and R 1 N D >

R ND. Sinct: R N D > R in this region, we have R l N D > R 1 D. Thus the

following inequality holds in the region ABDC;

R I N D > R I D > R N D > R D

Proposition 2.1: For a given value of cross-effort impact delegation as n

strategic variable changes from a strategic complement to a strategic

substitute and back to a strategic compkment as cross-price impact

increases.

With strategic substitutes, Firm 2's optimal response to a more aggressive

play by Firm 1 (i.e., price delegation by Firm 1) is to be less aggressive,

i.e., no price delegation. This is exactly what Firm 2 would do in region

ABDC where delegation is strategic substitutes. In the region ABDC price

and sales effort impacts (0, and 0, respectively) are nearly equal. Low

price implies low sales effort and high price implies high sales effort.

Thus what a firm gains from having a lower price is lost due to the lower

sales effort by the sales rep. If higher sales effort translates in to higher

service levels, the firms would prefer to differentiate by offering either

low price-low service or high price-high service option to customers. This

can be achieved by following a delegation strategy exactly opposite to

that of the rival.

3.0 Entry Deterrence and Entry Accommodation Strategies

In the model in Section 2, the firms are assumed to choose the type of

delegation simultaneously. With this simultaneous choice we find that i n

the region TPPT (Fig 3.3) there are multiple Nash equilibria. In region

PIP price delegation is the pure strategy equilibrium and i n the region

TOlT no price delegation is the pure strategy equilibrium.

........................ Insert Figure 3.3 here

The question that we now address is what happens when one firm gets to

select the type of delegation first and the second firm, after observing

this, selects its type of delegation, i.e., the firms choose their type of

delegation sequentially. Fig 3.4 shows the extensive form of the

sequential game.

----------*-------------

Insert Figure 3.4 here

Firm 1, the incumbent, first decides whether to adopt a price delegation or

a no price delegation strategy. This is observable to Firm 2, the entrant.

Firm 2, after observing the type of delegation adopted by Firm 1, decides

whether to enter the market or not. If it decides not to enter, Firm 1 faces

no competition. However, if Firm 2 decides to enter it makes a choice

between delegation and no delegation of pricing decision to the sales

representative. The choice of type of delegation by Firm 2 is observable

to Firm 1. The game subsequent to this stage is the same as the

simultaneous game of previous section.

For the different combinations of delegation strategies adopted by the two

firms profits are given by equations (13) to (16). To identify the

equilibrium strategies adopted by the two firms we plot (Figure 3.5) the

following contours: (a) R I - R~~ , (b) R - R l N D , (c) R D - R N D , (d) R I

ND D N D - R N D , (e) R l - R , and (f) R I - R l .

Insert Figure 3.5 here

In region PIP, Firm 1 chooses price delegation and so does Firm 2. In

region TPPT, Firm I selects price delegation because profit, when both

firms price delegate, is greater than the profit when both firms do not

delegate pricing decision, i.e., R > R N D . Firm 2 selects price delegation

because the profit to i t would be lower if i t chose no price delegation

instead of price delegation since R > Rl ND in this region. If Firm 1 had

selected no price delegation then Firm 2 would select no price delegation

too since R N D > Rl D. In region TQQT the profit when both firms price

delegate is greater than the profit when both firms adopt no price

delegation (R > R ND) and so both firms should prefer price delegation

but since R l c R~~ both firms choose no price delegation. In region

QORQ delegation is a strategic substitute variable and under a sequential

choice Firm L would prefer to adopt no price delegation with Firm 2

having adopted price delegation. In region RlR once again both the firms

adopt no price delegation. Thus, in a sequential game we observe an

asymmetric equilibrium in the region QORQ because of the delegation

variable being a strategic substitute in this region.

We now look at the entry accommodation and the entry deterrence

strategy when there is competition in the price and the effort dimensions.

We use the following taxonomy of business strategies as proposed by

Fudenberg and Tirole (1984). If an increase in delegation makes Firm 1

tough, then it must increase delegation to deter entry, i.e., use the "top

dog" strategy and reduce delegation to accommodate entry, i.e., follow

"puppy dog" strategy. If an increase in delegation makes Firm 1 soft then

it should reduce delegation to deter entry, i.e., use the "lean and hungry"

strategy or increase delegation to accommodate entry, i.e., adopt "fat cat"

strategy.

The price under price delegation is higher than the price under no price

delegation and so is the level of sales effort. Price and sales effort are

considered strategic complements because with constant marginal cost the

demand becomes more inelastic when Firm 1 raises price or decreases

effort level and so Firm 2 responds by raising price or decreasing its rep's

effort level. However, delegation is a strategic complement variable in

certain regions of 8,-0, square and a strategic substitute in remaining

regions of 0,-8, square. We first consider which strategy Firm 1 can use

to make Firm 2's entry unprofitable.

3.1 Entry Deterrence

Profit to Firm 2 is a function of delegation by Firm 1, price set by Firm 1 ,

own price, effort level of Firm 1's rep and own rep's effort level. Since

we are considering deterrence of Firm 2's entry we take its delegation

level as given, i-e., either no price or price delegation. We then calculate

the change in profit to Firm 2 as a result of increase in delegation by Firm

1 (i.e., change from no price delegation to price delegation). If the change

is negative it implies that increase in delegation is making Firm 2's entry

less attractive and i f it is positive it implies that the increase in

delegation is making it more attractive for Firm 2 to enter.

Case 1: Firm 2 considering no price delegation and Firm 1 moves from no

price to price delegation

The change in profit to Firm 2 as Firm 1 decides to increase delegation is

given by;

A( profit to find) - - - - - - - -

~ ( ~ r o f i t to f im2) A( price of finnl) . - -Rm) + - - - - - x --- +

A(deg ree of delegation) A( price of ftrml) A(deg ree of delegation)

~ ( p d t to firm2) s sales effort of firml) --- - - - - - - - - - - X - - - - -- - - sales effort of finnl) A(deg ree of delegation)

The first term on the right is the direct effect of change in delegation by

Firm 1 on the Firm 2's profits and for region above RR in Fig 3.5 it is

positive. The next two terms on the right are the strategic effects. These

come from the fact that delegation changes Firm 1 ' s ex post behavior on

price as well as on selling effort, thus affecting Firm 2's profits. The total

effect of change in delegation by Firm 1 on Firm 2's profits is the sum of

direct effect and the two strategic effects. A higher price by Firm 1

increases the profit to Firm 2 and so the second term on the RHS is a

product of two positive terms and so is positive too. However, a higher

sales effort by rep of Firm 1 leads to a lower profit for Firm 2 and so the

third term is negative because it is the product of a negative and a

positive term. If the price impact is greater than sales effort impact (8, >

8,) the absolute value of change in profit to Firm 2 with increase in price

of Firm 1 is greater than the change in profit when Firm 1 increases effort

level. Also, selling effort and price are increasing with delegation. The

change in price with respect to increased delegation is greater than the

Pi - Yi change in effort level due to increased delegation (e, = - 3 ). Hence the

second term is greater than third term in equation above. Therefore, the

change in profit to Firm 2 when Firm 1 increases delegation is positive in

the region where 8, > 0,. Thus when price impact is greater than sales

effort impact price delegation makes Firm 1 soft since i t increases the

profit of Firm 2. For 8, < 0, and in region above RR (where R~~~ > ~l~~

and R~ > R ~ ~ ) the sign of the change in profit to Firm 2 when Firm 1

increases delegation is unclear (Fig 3.6). For 8, < 0, and in region below

RR

......................

Insert Figure 3.6 here

(where R~~~ < R ND and R < R, ') sign of change in profit to Firm 2

when Firm 1 increases delegation is negative. Thus when sales effort

impact is greater than price impact price delegation makes Firm 1 tough

because it reduces the profitability of Firm 2.

Case 2: Firm 2 considering price delegation and Firm 1 moves from no

price delegation to price delegation

A( profit - to fim2) - - ( R D - R , D ) + - - . A( profit to fim~) - X - A( price - -- of - firm - - A 1) - - + A(deg ree of delegation) price of firml) A(deg res of delegation)

The first term on the right is the direct effect and for region above RR in

Fig 3.6 it is positive. The second term on the RHS, the strategic effect, is

a product of two positive terms and so is positive too. The third term, also

the strategic effect, is product of a negative and a positive term and so is

negative. However, for 8, > 8, the second term is greater than the third

and so price delegation makes firm 1 soft when price competition is

greater than the sales effort competition. When 0, < 8, and in region

below RR price delegation makes Firm 1 tough since it reduces the profit

of Firm 2. Table 3.1 shows the impact of price delegation by the

incumbent (Firm 1) on the entrant's (Firm 2) profits. Hence to deter entry

under intense price

---------------------

Insert Table 3.1 here

competition Firm 1 should follow the "Lean and Hungry" strategy

(Fudenberg and Tirole, 1984), i.e., no price delegation. If the firm was to

delegate the pricing decision the prices would be higher but by adopting

no price delegation the firm sends a signal to the rival that i t is not

prepared to sacrifice market share and is willing to enter into a price war

to defend its market share. Also, to deter entry under intense effort

competition (in region below RR) the firm should follow the "Top Dog"

strategy, i.e., delegate the pricing decision to the sales rep. Under price

delegation the effort level is higher and so Firm 1 by selecting price

delegation sends a message to Firm 2 that i t would provide incentives to

its rep to pu t in higher and higher sales effort levels to retain its market

share.

Proposition 2.2: Under intense price competition the firm should adopt

the "Lean and Hungry" strategy to deter entry. However, cinder intense

sales effort competition the firm should follow the " T o p Dog" strategy to

deter entry.

3.2 Entry Accommodation

Having considered the entry deterrence strategies we now consider the

entry accommodation strategies. The total change in profit to Firm 1 as a

result of change in delegation b y it is a sum of direct effect and strategic

effect. The direct effect would exist even if Firm 1 ' s delegation was not

observed by Firm 2 before the choice of price and effort levels. Thus this

effect is ignored for the purpose of classification of strategies. The

strategic effect results from the effect of delegation on Firm 2's second

period behavior. The strategic effect is given by,

A( profit to find) A( price of firm2) X - - - . +

A( price of firm2)

By symmetry we

A( profit to fiml)

~ ( ~ r o f i t to firml) sales effort of firm2) -- - -- - - - - - - - - - -.

~(sa les efon of firm2) ~ ( d e l e ~ a t i o n by firml)

have;

&(profit to f i rm4 - - - and, A( price of f i rm4 - ri rice of firml)

Also,

and,

sales effort of firm2) - - &(sales effort of firm2) sales effort of firml) - - X - - - - - . - - - - - - . - - -

~ ( d e l q a t i o n by firml) &(sales effort of -fiml) ~ ( d e l e ~ a t i o n by finnl) '

Thus the strategic effect can be rewritten as;

The first term is a product of three positive terms and so is always

positive. The second term is negative because the first term in i t is

negative. For €Ip > CIS the first term is greater than the second term and so

the change i n profit to Firm 1 as it increases its delegation is positive and

the firm chooses price delegation. For 0, < 0, the second term is greater

and so the profit to Firm 1 decreases as it increases delegation. Thus i n

this region Firm 1 would choose no price delegation.

Hence the firm should follow a "Fat Cat" strategy under intense price

competition and follow a "Puppy Dog" strategy under intense sales effort

competition so as not to trigger an aggressive response by Firm 2. Fig 3.7

shows the different strategies

that firm should follow to deter and to accommodate entry.

Proposition 2.3: To accommodate entry under intense price competi t ion

the firm should follow the "Fat Cat" s trategy. However, under intense

sales effort competition i t should jollow the "Puppy Dog" s trategy.

If the incumbent firm was to make an investment (KI) i n an organizational

form that would commit to increased delegation to the sales representative

then the strategic effect could be rewritten as

~ ( ~ r o f i t - - to fim2) A( price of fim2) A( price of fiml) X ---

x -- - +

A( price by pml) A( price of fiml) 4 4 ~ ( ~ r o f i - to fim2) )( sales effort of firm2) X sales - - . -. . effort . - - - - of - . - -- fiml) .. . - - + sales effort by ~ m l ) sales eflor? of find) 4 K, ) A( profit to fim2) ~ ( d e l e ~ a t i o n by fim2) d sales effort of ~ m l )

In this case the first term is positive, the second term is negative and the

third term is negative too in the region PQR (Fig 3.7) since in this region

delegation is a strategic substitute variable. In rest of the region

delegation is a strategic complement and so the results remain the same.

4. Conclusion

We have shown in this section the strategic role of price delegation. Price

delegation can be a strategic complement or a strategic substitute variable

depending on the price and the sales effort competition. In the region

where the price and the selling effort impacts are almost equal price

delegation is a strategic substitute variable. However, in the remaining 8,

- 0, square price delegation is a strategic complement variable. Thus we

show how when the competition is in two dimensions - price and selling

effort, the same strategic variable can be a strategic substitute or

complement depending on the values taken by these cross impact.

The chapter also addresses the issue of entry deterrence and entry

accommodation when the organizational form is a decision variable and

the competition is in two dimensions. When cross price impact is high the

incumbent firm accommodates entry by choosing price delegation. This

behavior avoids a price war. When the cross price impact is not too strong

but still greater than cross selling effort impact the incumbent deters entry

by choosing no price delegation. However, in part of the region where

delegation is a strategic substitute variable the incumbent accommodates

entry by adopting no price delegation. When cross selling effort impact is

high deterrence is not an equilibrium strategy. The incumbent then

accommodates entry by choosing no price delegation.

Firms simultaneously decide on type of delegation

Reps decide whether to accept or reject contract

Rep selects price and effort or only effort level L

Common random shock realized and demand for each firm

determined

Figure 3.1 : Sequence of Events (Simultaneous Game)

Strategic Complements

Figure 3.2: Strategic Substitutes & Strategic Complements

Figure 3.3: Equilibrium Regions - Simultaneous Game

Firm 1

From here on the game is same as simultaneous move game

Figure 3.4: Sequential Game

Figure 3.5: Equilibrium Regions - Sequential Game

1 0 1

Price Delegation Makes Firm 1 Soft I

0 I 0

No Price Delegation Makes Finn 1 Tough , 0 !

0 0

0

No Price Delegation Makes Firm 1 Soft

Price Delegation Makes Firm 1 Tough

Figure 3.6: Delegation Making Incumbent Tough or Soft

Strategic Complements

Delegation Makes Firm 1

Tough (8, > 8J Soft (0, > 8, )

Table 3.1 : Possible Strategies

Cross Price

Impact

Accommodate entry with Price Delegation (Fat Cat)

Accommodate entry with No Price Delegation (Puppy Dog)

0 Cross Effort Impact 8, 1

Figure 3.7: Equilibrium Strategies

Chapter 4

Managing Multi Product Salesforce

1, Introduction

In most business situations the firm's sales representatives are responsible

for selling multiple products. Agency thecretic models, however, have

looked at either a single product salesforce (Basu, Lal, Srinivasan and

Staelin 1985, Holmstrom 1979, La1 and Staelin 1986) or a salesforce

selling multiple products that have independent demands (La1 and

Srinivasan 1993). In most situations, however, there is dependence

between products. There are situations, for instance, where the effort

devoted to the sale of one product affects the sales of the other product by

providing valuable information that would help in selling the product. For

example, a salesperson responsible for opening new accounts and

approving credit cards. The customer could decide to open an account

with a particular firm, but apply for another firm's credit card. If a

customer for a credit card, who does not have an account with the firm

approaches the rep, the rep wi l l have to spend a substantial amount of

time to check the liquidity of this client. However, if the rep is

approached by a customer who already has an account with this particular

firm, then the rep has a lot of information about the customer's liquidity.

Moreover, with knowledge of the cash flow of the current accounts of

various customers, the rep can approach them for applying for the

company's credit card. Consequently, selling the focal product enhances

the sale of the secondary product by giving the rep some important

information. Similarly, sales reps in the personal insurance industry first

attempt to sell life insurance policies to the clients. In the process of

selling the life insurance, reps get valuable information about the client's

family size, loans, mortgages, etc. This information can then be useful in

selling products like house insurance, children's education plan, etc. Thus

selling the focal product, in this case life insurance, helps in selling the

secondary products like children's education plan. In these examples

although the demands are not related, selling the focal product increases

the productivity of the rep in selling the secondary product. It is through

this effort complementarity that the two products are related.

In this chapter we analyze how the complementarity in effort affects the

effort allocation decision of the sales rep. We also examine the effect of

effort complementarity on the commission and salary structure that the

firm offers the sales rep.

In section 2 we discuss

compensation. In section 3.0 w

efforts and discuss the results.

2. Literature Review

the previous

e develop the m

literature on salesforce

ode1 for complementarity i n

Agency theory models of salesforce compensation examine situations

where a firm sells its product through a single rep and the effort put in by

the rep is unobservable. D u e to this unobservability of the sales rep's

effort, perfect risk sharing between the risk neutral firm and the risk

averse rep is not achieved. If the effort is observable, the firm can use a

forcing contract, i.e., pay the rep a flat salary if he puts in the desired

level of effort and nothing otherwise. This would lead to the first-best

solution. However, with unobservable effort, the firm can achieve the

second-best solution through a compensation structure of salary and

commissions on sales (Basu, Lal, Srinivasan and Staelin t985). In this

second-best case the proportion of salary to total compensation depends

on the uncertainty, the marginal cost of production and the attractiveness

of outside job opportunities (Basu, Lal, Srinivasan and Staelin 1985 and

Rao, 1990).

When selling multiple products the outcomes of the efforts may be related

i n a number of ways. First, the productivity of effort for the second

product may be increased due to some valuable information about the

client obtained by the rep while selling the first product. An example

would be rep selling life insurance and children's education plans.

Second, the demands of the two products may be related because of

demand complementarity or substitutability. For example, a rep selling

computers and peripherals. Third, the errors i n the stochastic demand

functions of the two products may be related. Factors affecting the sales

of one, such as economic conditions, may also affect the sales of other

products handled by the sales rep.

When firms have sales reps selling multiple products, the issue is not only

whether the reps are putting the right level of effort, but also how they are

allocating the effort between the products. La1 and Srinivasan (1993)

show that when the sales of the products are unrelated the commission

rates are higher for products with lower product cost, higher sales effort

effectiveness and lower uncertainty.

In this chapter we address the issue of complementarity in efforts that

arises i n the financial market example discussed earlier. Analysis shows

that with complementarity in efforts the commission on secondary product

is always less than the commission on focal product. The optimal effort

devoted to selling the first product increases and that to selling second

product decreases as the complementarity increases.

3.0 Model for Complementarity in Efforts

We model a single risk-neutral firm selling two products, a focal product

and a secondary product, through a risk-averse sales rep. The firm is

unable to observe the effort put in by the rep but can observe the sales of

both the products. Due to uncertainty i n the selling environment the firm

cannot ascertain the effort level from the sales volumes. The firm offers

the rep a compensation consisting of salary and commissions on sales of

the products. We make the following assumptions:

(i) The salesperson's utility for income S is a concave increasing function

and satisfies the property of constant absolute risk aversion (r), i.e.,

The salesperson's disutility for effort t is a convex increasing function

given by,

V(t) = d tZ where d > 0.

(ii) The cost of production cl and cz is assumed to be constant for both

products.

(iii) The sales-effort response function and the salesperson's utility

functions are known to the salesperson and the sales manager.

(iv) The salesperson sells two products , product # I (focal product) and

product #2 (secondary product). The sales of each product depend on the

effort devoted and a random variable. The uncertainties i n the sales of the

two products are uncorrelated. However, the effort devoted to selling

product # 1 affects the sales of product #2. The sales for both products are

normally and independently distributed.

( v ) The dollar sales for product # I is given by,

where t l is time devoted to selling product 1 and h l , kl > 0.

The dollar sales for product 2 is given by,

The parameter 1, gives the effect of effort devoted to selling product 1 on

the sales of product 2. The errors are assumed to be uncorrelated.

(vi) The salesperson's monetary equivalent for disutility of effort is

determined by the total effort ( t l+tz) devoted to selling, i.e.,

(vii) The firm offers a linear compensation plan to the salesperson which

is given by,

The game is modeled as a single-shot game. However there is a certain

sequence in which the events unfold. At time t = 0 the firm offers the rep

a contract consisting of salary and commissions on the sales of product 1

and product 2. At time t = 1 the rep accepts or rejects the contract. If the

contract is accepted s/he decides on how much effort to put in selling the

two products. At time t = 2 the sales of the two products are observed and

the rep is compensated.

The expected wages to salesperson from selling the products is,

Since effort is costly to the rep the net income to the salesperson is,

The expected utility to salesperson is given by,

The certainty equivalent C by definition must provide the same expected

utility as the net income. Thus,

Using Taylor series expansion we get,

So the salesperson's choice of t l and t z so as to maximize expected utility

is equivalent to maximizing the certainty equivalent C. The salesperson's

maximization problem is,

r M a r C = A+ B,h, + ~ ~ k , t : " + B,h? + ~ , i , t : ' ~ + BZl2t;I2 - d ( t l + t 2 ) - - - (B~'$ + ~ : 6 )

ti .t? 2 r t . t , + t , d T where T is the total time available.

Setting up the Lagrangean for the above problem we get,

- A ( T - t , - t J

First order conditions

i. w.r.t. t ,

ii. w.r.1. t2

From conditions (i) and (ii) we get

From (iii) and (viii) we get,

Proposition 1 . As the degree of complementarity I I (> 0) increases the

optimal effort devoted to selling product I increases and that to selling

product 2 decreases . Also, the optimal level of efforts tl and t2 increase

with the increase in respective marginal productivities k l and 12 .

Proof:

Taking derivative of equations (9) and (10) with respect to 1, we get,

Differentiating equation (9) with respect to lz we get,

a t ; Similarly, it can also be shown that -

d kl > 0 .

Q.E.D.

The ratio of optimal efforts tl and t t is given by the relationship,

The ratio is a quadratic relationship of the form al: +bl, + c where a, b and

c are greater than or equal to zero. As the degree of complementarity

increases the ratio increases at an increasing rate. If there is perfect

complementarity then the optimal value of t l is zero and the ratio tends to

infinity, i.e., the salesperson does not need to put in any effort in selling

product 2. If there is no complementarity then 1, is zero and the ratio i s a

constant value depending on the values of k l and lz, the marginal

productivity of efforts tl and t 2 respectively.

The expected profit to the firm is,

The firm maximizes the expected profits provided that the minimum

expected utility to salesperson in monetary terms is greater than or equal

to the reservation utility m to ensure participation. That is,

Since A does not affect the optimal values of t l and tr but reduces the

firm's expected profits, the firm will choose A so as to satisfy equation

( 1 I ) with equality. Substituting for A from ( 1 1) i n the equation for

expected profits we get,

Proposition 2 ( i ) Commissions on sales: With constant marginal costs

(kl +I,) and d > - - the commission BZ on secondary product is less than the 4

commission B l on focal product.

( i i ) Commissions on margins: With constant marginal costs and

(1- )(k ) + ( l - c N 1 ) d , 1- 1 . . . . -A . the commission B2 on secondary product is less 4

than the commission B , on focal product.

Proof of Proposition 2 ( i )

Let B, = 8 B , . The ratio of efforts from ( ix) and ( x ) i s -; = . The

firm's maximization problem is,

e L Substituting 6 = - in the above equation we get,

k , + 0 1,

Evaluating the first order condition at 8 = 0 ( i - e . , 6 = 0) we get

which implies that 6 and 8 are greater than zero. Thus the commission B 2

is greater than zero. Evaluating the first order condition at 8 = 1 we get

2 'a;' ~ f ( k , +1J3 where X = > 0 and Z = >O. Thus the first derivative

(k1 + I , ) 2 4dk&t:

is negative if d > (k, + 1, 4

Q.E.D.

This implies that 0 < 1 and the commission Br on secondary product is

less than the commission B I on focal product when the marginal cost of

effort is greater than one quarter the sum of productivities of effort t l .

Proof of Proposition 2 ( i i )

If Bl and B3 are commission s on margin en expected a s are,

E [ S ( ~ ~ , . T ~ ) ] = A + B,(l-cl)xl +(B B,)(l-c2)x2, and the net income is

Solving the rep's problem of maximizing the certainty equivalent C

subject to time constraint we get,

The firm wants to maximize expected profits subject to incentive

compatibility constraints. The firm's problem can be written as,

(1-c t )e Substituting 6 = - - - . . - - - - - we can rewrite the firm's problem as,

( l - c l ) k l +(I-cz)O 1,

The first order condition with respect to 6 evaluated at 8 = 0 (6 = 0) and

at 0 = 1 gives,

Thus 6 >O which implies that 8 > 0 and so B2 > 0. Evaluating the first

order condition at 8 = 1 we get,

If d > (1-c*)(k1)+(1-c2)([ , )

then - 4 d S

This implies that 0 < 1 and Br < B I when the cost of effort is greater than

one quarter the sum of productivity of effort tl weighted by the margins of

the products it helps in selling.

So far we have shown that B2 c B I . Now we analyze the optimal

commissions structures. Substituting for t l l " and t2"' from (9) and (10) in

the firm's maximization problem we get,

Max 4 14

First order conditions are,

(i) w.r.t. Bl

(i i) w.r . t . B2

Proposition 3 . As complementarity increases the commission rate B2* on

sales of product 2 decreases. Also, as the variance in sales of product 2

increases the commission rate B2* decreuses and the salary component A

increases.

Proof:

Considering the F.O.C. with respect to B2 as an implicit function

f (4;4 ,$) = 0 we can get the following comparativc statics

where means equal in sign and ' % B, < 0 by S.0.C for maximization.

Blkl + Bzll where Q =

With complementarity in effort 1 p 0 and so are all other parameters by

assumption. Thus the sign within { } bracket is negative. Hence,

d f --rBL<O a ~ s r ? BS.1 Also, -- d r

From equation ( 1 1 ) we get

d A 1 - ( B ; O ~ + B : O , ' ) > O Also, --- d r 2 .. *

The above analysis indicates that as complementarity increases the

commission on sales of product 2 decreases. This is intuitively appealing

since due to complementarity the salesperson has to put in less effort for

selling product 2. Moreover, as variance in sales of product 2 increases it

implies that there is greater uncertainty and hence the salary component

must increase and the commission rate must decrease to compensate for

the increased risk.

Proposition 4 . As variance in sales of product I increases the commission

rate B I * decreases and the salary A increases. The effect of changes in

complementarity on & * depends on the ratio of prices of product I and 2

( the ratio p l / p 2 ) .

Proof:

Considering the first order condition with respect to B I as an implicit

function we get,

df > O as I, increases B; also increases dl1

Thus the effect of complementarity on commission BI depends on the

ratio of prices pl to p2. If p2 is small then the gain to the firm from

compiementarity is low. The firm thus has l imited interest in motivating

the rep to sell more of product 1 and then to take advantage of

complementarity in sell ing more of product 2. However, if p2 is large the

firm wants the rep to sell more of product 1 and reap the benefits of rep's

increased productivity in sell ing product 2. This the f i rm achieves by

giving a higher commission on product 1.

The effect of uncertainty and risk aversion on the optimal values of

efforts can be assessed indirectly. As uncertainty and risk aversion

increase the commission rate B i * falls. The decrease in Bi* affects ti*. All

e lse remaining constant any decrease in B i * results in a decrease i n ti*.

The problem of designing salesforce compensation plans when sell ing

multiple products that have complementarity in effor ts is modeled in this

section. The effects of various parameters on effor t desoted, salary and

commission rates is analyzed and shown in Table 4.1 below.

Table 4.1

Increased Uncertainty

Increased Uncertainty

Increased Risk Aversion ( r )

Increased Effectiveness of Sales Effort ( k l )

Increased Effectiveness of Sales Effort (I:)

Increased Effectiveness of Complementarity

Effort t l * Effort t2* Salary A

F n d s t h e 1 1 ratio p lIp2

The analysis shows that a number of results obtained by BLSS (1985) still

hold. As shown by BLSS (1985) increased uncertainty results in a

decrease in effort levels and an increase in salary. With complementarity

in efforts the commission on secondary product is always less than the

commission on the focal product This is true whether the commissions are

on sales volume or on margins. The effect of complementarity in efforts

on effort rate, salary and commission is an addition to the existing results

in the literature. The effect of complementarity on commission B I depends

on the ratio of prices pi to pr. If pz is large the firm wants the rep to sell

more of product 1 and reap the benefits of rep's increased productivity in

selling product 2. This the firm achieves by giving a higher commission

on product I .

4.0 Conclusions

In this chapter we have examined the role of complementarity in efforts

when the sales rep sells multiple products. The analysis shows tha t with

complementarity in efforts the commission on secondary product is

always less than the commission on the focal product. The optimal effort

devoted to selling the focal product increases with an increase i n

complementarity. The effect of complementarity on the commission rate

for the focal product depends on the prices for the two products. This is

equivalent to the ratio of margins on the two products if the marginal

costs are assumed to be zero.

The analysis also shows that a number of results obtained by Basu, Lal,

Srinivasan and Staelin (1985) still hold when there is complementarity in

efforts. For example, the salary component increases with increase i n

uncertainty. Consequently, the optimal efforts devoted to selling both the

products decrease. Also. increase in risk aversion results in higher risk

premiums and lower selling efforts.

Chapter 5

Conclusion

Conclusion

The purpose of this dissertation is to study three issues i n salesforce

management related to the delegation of pricing responsibilities to the

sales personnel and the selling of multiple products by the salesforce. The

objectives of Chapters 2 and 3 are to contribute to the literature on

contracting under conditions of competition in two dimensions, price and

selling effort, and the strategic use of the price delegation variable to

deter entry. The objective of Chapter 4 is to study contracts and effort

allocation strategies when the sales reps sell multiple products.

In this section I will provide a brief summary of the findings for each

chapter and then discuss possible extensions and new questions raised by

the findings. I will also discuss testable hypothesis that emerge from the

dissertation.

Chapter 2: Delegating Pricing Decisions to the Salesforce in o Duopolv

The main objective of this chapter is to study the effects of competition

on the price delegation decision. In addressing this theoretical issue the

research also explains the puzzling pattern of why firms i n some

industries delegate the pricing decision to their reps while firms in other

industries do not. The results differ from those of La1 (1986) who shows

that under monopoly conditions, if there is symmetric information, then it

is optimal for either the firm or the rep to set the price, i.e., delegation of

pricing decision is irrelevant. However, it is shown in this chapter that

when there is intense price competition, firms are better off delegating the

pricing decision to the reps. The prices under price delegation are higher

than the prices snder no price delegation which causes a softening of

price competition that is mutually beneficial. It is also shown that only a

specific type of contract - a contract based on margins can achieve the

desired result of reducing price competition.

Future Research

There are a number of additional issues concerning price delegation which

should be examined. First, competing firms may have different cost

structure or sell products of differing qualities. Under these conditions,

the cross price and cross effort impacts may be firm specific. This can be

incorporated into the model by using firm specific €Ip and 8, parameters.

This modification would allow the price delegation decision to be

examined under price-tier theory (Blattberg and Wisniewski 1989).

Second, i n many selling situations, the firm and sales rep have

asymmetric information about t h e market. Under these conditions. the

firm may be willing to pay to collect this information from the

representatives. The question is what type of contract would be required

under these conditions. Finally, this dissertation has examined two forms

of compensation packages - vo lume based and margin based commissions.

An interesting extension would be to endogenize the contract type. La1

and Staelin (1986) have analyzed the compensation plans under

asymmetric information and salesforce heterogeneity in a standard agency

theory model with no competition. Their results give conditions under

which one would observe a menu of contracts being offered by the firm.

The question is whether firms, when competing in two dimensions i n an

asymmetric environment, would also offer a menu of contracts.

Empirically testing the results of this chapter is a challenging task.

Knowledge of the price delegation strategies of firms within an industry

would be required. Moreover, these firms should also have the same

perceptions of cross price and cross selling effort impacts. If historical

data is available on firms that changed price delegation strategies, then

the model predicts that price and commission structures should also

change. It w i l l be important, however, to control for other latent variables

which may affect prices and commissions.

Chapter 3: Entry Accommodation and Entry Deterrence Strategies

This chapter has two objectives. First, i t addresses the question of

whether price delegation is a strategic substitute or a strategic

complement. Bulow, Geanakoplos, and Klemperer (1985) show that price

is a strategic complement and the quantity decision is a strategic

substitute. In this chapter we show that price delegation can be either a

strategic substitute or a strategic complement depending on the cross

price and cross selling effort impacts. The second objective of this

chapter is to explain how an incumbent firm can use price delegation

strategically to accommodate or deter entry of a possible entrant firm. It

is shown that when cross price impact is high, the incumbent firm

accommodates entry by choosing price delegation. However, when cross

price impact is low but still greater than cross selling effort impact the

incumbent deters entry by choosing no price delegation.

Future Research

One important extension would be to assess the changes in entry

deterrence and entry accommodation strategies under conditions of

asymmetric information between the firm and the sales rep. With

asymmetric information, the contract to the sales rep would reveal the

value of the additional information that the rep may have. The

observability of this contract could be a signal for the incumbent's

strategy. The entry deterrence and entry accommodation strategies would

also vary if the firms were to offer products of differing qualities.

Empirically testing the results for entry deterrence and entry

accommodation is an ambitious task. What needs to be found is a situation

where there is an incumbent and a potential entrant. Alternatively, pre

merger and post merger situations could be examined. If the firms merged

because they were not profitable due to intense price competition, then

they should be found to delegate pricing prior to merger. Once again. it

will be important to control for other variables which may affect the

merger decision.

Chapter 4: Managing Multi Product Salesforce

The objective of this chapter is to model a multiproduct selling situation.

The model addresses the issue of complementarity in efforts that may

arise in an insurance or banking market. The demands in this model are

assumed to be uncorrelated, but there is an information advantage. The

analysis shows that with complementarity i n efforts, the commission on

the secondary product is Aways less than the commission on the focal

product. The optimal effort devoted to selling the focal product increases

while the effort devoted to selling the secondary product decreases as the

complementarity increases. The effect of effort complementarity on the

commission on the focal product depends on the ratio of prices of the two

products. The commission on the focal product increases w i t h effort

complementarity only if the price of the secondary product is high enough

to be profitable.

Future Research

There are a number of interesting extensions to the model which was

presented. First, an interesting extension of the model with effort

complementarity would be to examine what occurs with a two-sided

complementarity in effort rather than a one-sided complementarity and

how the contracts to the sales reps vary under this situation.

Second, the model assumes no demand interdependence. An interesting

extension would be to model a situation where the demands of the two

products are correlated and the products can be substitutes or

complements. This would help in identifying how contracts change with

demand interdependence.

Third, the model does not examine the decision of whether to have a

single pruduct or a multiple product sales force. The model can be

extended to include a stage i n the game where the firm first needs to

decide on type of salesforce - a single product or a multiple product

salesforce. This would help in identifying conditions i n which one selling

structure would be preferred over the other.

Finally, the issue of price delegation i n a multiple product salesforce

could be analyzed to understand conditions under which firms would

delegate the pricing decision of all the products.

Empirically, the results on salary and commission structures with effort

complementarity could be tested by surveying a cross-section of firms

from different industries. Measures of salary, commissions on different

products and complementarity i n effort could be obtained through a

questionnaire administered to the management and sales personnel of

these firms.

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