The Journal of Socio-Economics 38 (2009) 641–647

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The Journal of Socio-Economics

journa l homepage: www.e lsev ier .com/ locate /soceco

Tipping as risk sharing

Steven J. Holland ∗

Luther College, 700 College Drive, Decorah, IA, USA

a r t i c l e i n f o

Article history:Received 15 August 2008Received in revised form 12 January 2009Accepted 7 February 2009

JEL classification:D81L84

Keywords:

a b s t r a c t

Tipping is often dismissed as an exception to the assumption of rational economic agents. This paperdescribes situations where tipping is, in fact, an effective mechanism for risk sharing and welfare improve-ment. When risk-averse customers purchase a service with uncertain quality, tipping can reduce thecustomer’s exposure to risk by making part of the price of the service discretionary. These findings helpexplain why we tend to tip restaurant workers but not retail workers and why some high-risk serviceproviders, such as lawyers and automobile mechanics, are not typically tipped.

© 2009 Elsevier Inc. All rights reserved.

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. Introduction

Tipping is often described as an odd practice that challenges thessumption of rational economic agents (Frank, 1987; Landsburg,993; Bodvarsson and Gibson, 1997). Tipping requires customers toreely leave money for total strangers in the absence of any require-

ent to do so. What is more, these customers cannot expect anmmediate quid pro quo because the tip is not left until after the ser-ice has been provided. It is difficult to understand why customerso not simply enjoy the service, pay the agreed price, and then

eave with their pocketbooks a bit heavier. In most service indus-ries this is exactly what happens, but in some sectors, especiallyhe restaurant industry, tipping is significant. Tipping in restaurantss estimated to exceed $40 billion per year and makes up over halff many restaurant workers’ incomes (Azar and Yossi, 2008).

In this paper, I examine whether tipping can be explained asrational act of utility maximizing people. Efforts to understandhat could possibly drive a rational customer to leave a tip have

enerated some interesting and imaginative theories.1 Many eco-omic models of tipping focus on the principal–agent relationshipetween tipped employees and their employers (Azar, 2004a). The

dea is that employers want their employees to work hard to pro-

∗ Tel.: +1 563 387 1130.E-mail address: hollst03@luther.edu.

1 For a good overview of theories from many different disciplines, see Lynn (2006).zar (2007a) discusses several types of tipping and many of the theories used toxplain them.

053-5357/$ – see front matter © 2009 Elsevier Inc. All rights reserved.oi:10.1016/j.socec.2009.02.001

vide high quality service but find it difficult to observe employeeeffort. Customers, on the other hand, are in a good position toobserve employee effort because they are ones receiving the ser-vice. Tipping for service quality, it is suggested, creates incentivesfor employees to give a high effort, reduces the employer’s need tomonitor, reduces transaction costs, and increases efficiency (Lynnet al., 1993). Azar (2005a) has developed a formal model that helpsidentify the conditions where tipping improves service quality andincreases social welfare.

While the principal–agent theory explains many aspects oftipping it also has several weaknesses. First, empirical research sug-gests that service quality has a small impact on the size of the tip(Lynn and McCall, 2000), suggesting there are additional factorsthat may be more important. In addition, most of the instanceswhere employer monitoring of service quality is most problem-atic (e.g., out of the office sales, legal services, teaching) have notresulted in widespread tipping. Finally, and perhaps most trou-bling, the principal–agent approach does not adequately explainwhy customers would voluntarily assume the employer’s monitor-ing responsibilities—bringing us back to the claim that tipping isirrational.

Others have explored whether tipping is a mechanism for ratio-nal customers to induce better future service (Ben-Zion and Karni,1977; Azar, 2007b; Azar and Yossi, 2008). By tipping, customers

build a reputation for rewarding good service and rational serversrespond by providing better service in the future (Azar, 2007b).The on-going relationship between customer and server takes ona self-enforcing tit-for-tat reciprocity. The obvious problem withthis theory is that it requires a repeated interaction between the

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42 S.J. Holland / The Journal of So

ustomer and the server. In reality, most of us do not expect toncounter our server again but leave a tip anyway. It is not surpris-ng then that empirical studies have found only a weak relationshipetween tipping and the frequency of patronage (Azar and Yossi,008; Lynn and McCall, 2000).

Social norms have also been employed to explain customer par-icipation in tipping (Azar, 2005a; Conlin et al., 2003). There are

any theories for why social norms exist, but once they are in placet is believed that people conform to them in order to avoid the neg-tive feelings or social stigma associated with violating the norm.hile there is empirical support for treating tipping as a social

orm, most studies treat the existence of the norm as exogenous.s a result, social norm analysis has thus far only helped explainhy tipping persists but not why it started in the first place. Thisas led some to argue that social norms alone cannot explain thexistence of tipping (Azar, 2004b; Bodvarsson and Gibson, 1997).

It has been observed that social norms and informal institutions,f which tipping is one, usually arise on the edge of markets tomprove market outcomes or address market failures (Arrow, 1971;ixit, 2004). The current theories of tipping are all based on the

dea that markets cannot induce the optimal level of server per-ormance due to moral hazard or information asymmetries. Thisaper diverges from the current line of thinking by viewing thearket “failure” not as a problem of monitoring or incentives but

s an inefficient distribution of risk. Lynn et al. (1993) first mentionhe relationship between uncertainty and tipping, and Lynn (2006)otes a correlation between tip rates and the desire to avoid uncer-ainty. Estreicher and Nash (2004) ask why employees would beilling to accept an inherently riskier tip-based compensation, but

elieve the answer lies in tax incentives. This paper aims to makeisk central to the analysis and to show that risk may, in fact, be anmportant factor driving the institution of tipping.

To focus on the role of risk in tipping, this paper assumesutcomes (i.e., the quality of meals) are independent of server per-ormance. This assumption is not intended to imply that serverffort does not affect the quality of service—it is obvious that it doesn most cases. Instead, the assumption is merely intended to high-ight that tipping can exist in the absence of a concrete relationshipetween server effort and the quality of outcomes. This is a signif-

cant point because there is some empirical evidence of a positivend significant correlation between tip size and food quality (Azar,007c). However, the principal–agent and future service theoriesredict the tip should depend entirely on the server’s performancend be unrelated to factors such as food quality that are beyondhe server’s control. Evidence that tips vary with food quality sug-ests that social norms or other factors such as risk are important.his paper, then, supplements rather than contradicts the existingiterature on tipping.

The main finding of this paper is that tipping is a rational wayor customers and servers to share risk more efficiently. Using theestaurant industry as an example, I show that tipping reduces theisk faced by a risk-averse customer (“diner”) by lowering the wageaid to the server (“waiter”), reducing the mandatory part of theeal price, and giving the diner more discretion over the total cost

f the meal. As a result, when the meal is unusually bad the dineran choose to withhold a tip and reduce the loss of utility that wouldtherwise occur.

The level of tipping is constrained by the waiter’s aversion to anncertain level of compensation. As more of the waiter’s compen-ation becomes tip-based the variance of his compensation grows.risk-averse waiter will not give up one dollar in wages in exchange

or a one-dollar increase in the expected tip. Wages will conse-uently fall at a slower rate than any increase in the expected tip,hich increases the diner’s expected total expenditure on the meal.

ipping, then, looks like insurance where the diner pays the waitero assume some of the risk of a bad meal.

onomics 38 (2009) 641–647

2. The model

This paper initially supposes a world where restaurants exist buttipping does not. The question is whether a diner could propose aplan to tip the waiter under certain conditions such that (1) thediner is better off after the plan is implemented, (2) the restaurantand its employed waiter are no worse off as a result of the plan,and (3) the plan is self-enforcing. I will proceed by first defining theobjectives of all the interested parties and then show that tippingcan improve everyone’s well-being. I will then argue that the result-ing “tipping scheme” is stable over time. Finally, I will use some ofthe insights gained from the model to help explain some previouslypuzzling behavior.

2.1. The diner’s objective

When a rational, risk-averse diner sits down to a meal at a restau-rant she is concerned about two things. First, she cares about theexpected net benefit she receives, which is the difference betweenthe expected value of the dining experience and the amount sheknows she has to pay for it. A diner will want to maximize thisdifference. She will also be concerned about the risk she faces.Since the value of the meal is uncertain and cannot be observeduntil after she commits to paying for it, she will want to minimizethe variance of the difference between the meal’s quality and itsprice.

In order to focus on tipping as a way to share risk rather than away to induce greater waiter effort, it is assumed that the qualityof the meal is independent of the effort put forth by the waiter. Wemight suppose that waiter effort is constant and the quality of themeal is determined by other factors such as the ingredients used,the effort of the kitchen staff and the like. The quality or value ofthe meal, which represents the amount the diner would be willingto pay for it, is denoted as V, a random variable that takes on thevalue high (H) with probability p, medium (M) with probability q,and low (L) with probability r, such that H ≥ M ≥ L and p + q + r = 1.

When the diner orders a meal she commits to paying the priceon the menu. It is assumed the restaurant operates in a perfectlycompetitive market so the price of the meal equals its marginalcost. Denote the waiter’s wage as W and assume the cost of the food,the wages of the managers and the restaurant’s operating expensesthat go into producing the meal are equal to a constant, C. Therefore,the total price of the meal is equal to the waiter’s wage per mealplus the cost of other expenses (W + C). Without tipping, the diner’sexpected net benefit of the meal is E (V − W − C).

Now suppose the diner proposes a plan to tip the waiter. Atip is modeled as a complete contract between the diner and thewaiter. A complete contract is perfectly specified, meaning therewill be a tip corresponding to every possible value of V. The con-tract in this model is much like a contract of adhesion where thediner chooses the terms of the contract and the waiter accepts orrejects the contract without negotiation. The waiter will accept thecontract so long as the combination of the expected tip and hiswage makes it worth the waiter’s while to remain employed at therestaurant.

Since the meal value in this model is assumed to take on one ofthree states there are only three possible tips that need to be deter-mined. The terms of the contract, or the proposed tipping scheme,are then defined as:

t ={

tH if V = Ht if V = M

}

M

tL if V = L

The total expenditure by the diner if the tipping scheme is acceptedis (W + C + t) and the net benefit to the diner from eating out is theexpected utility of (V − W − C − t). For the purpose of generality and

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S.J. Holland / The Journal of So

implicity the tip is treated as additive. Later in the paper I williscuss how the practice of tipping as a percent of the bill relates tohis model.

A natural tool to model the diner’s utility is the mean-variancetility model. In this model it is assumed the agent’s preferences cane defined by the mean and variance of the possible outcomes.2

n the diner’s case, her preferences can be fully defined by theean payoff, E (V − W − C − t), and the variance of that payoff, Var

V − W − C − t). Under a mean-variance model, her expected utilitys then:

UD(V − W − C − t) = E(V − W − C − t) − ˛

2Var(V − W − C − t)

(1)

here ˛ > 0 is the diner’s Arrow–Pratt index of absolute risk aver-ion. Larger values of ˛ reflect more risk aversion.

The optimal tipping scheme is the one that maximizes theiner’s expected utility. However, in this model the waiter’s wagesre endogenous so the optimal tip will hinge on how wages respondo tipping. That is the question I take up next.

.2. How do wages respond to tipping?

I will show that increased tipping can effectively reduce theisk of a bad meal, but this reduction of risk comes at a cost.igher tips obviously increase the overall cost of a meal. Fortu-ately for the diner, increased tipping is very likely to reduceaiter wages and temper the cost of achieving more certain out-

omes.Assume the waiter is also a risk-averse, utility maximizing agent

ho faces a choice. Rather than a choice over the size of the tip,owever, the waiter must choose whether to accept the contractffered by the diner and continue working at the restaurant or toake a job where the compensation does not contain an uncertainip component. Here, I make the very important assumption thathe labor market is competitive and has very low barriers to entrynd exit.3 This implies the restaurant must pay a wage sufficiento keep its employees but need not pay any more than that. Asresult, the utility the waiter gains from working at the restau-

ant must equal the utility of taking a comparable non-tipped joblsewhere.

Assume the waiter’s preferences can also be completely definedy his expected compensation, E (W + t), and the variance of thatompensation, Var (W + t). In a mean-variance model, his expectedtility is then:

UW (W + t) = E(W + t) − ˇ

2Var(W + t)

here ˇ > 0 is the waiter’s Arrow–Pratt index of absolute risk aver-ion.

In this model, the waiter’s expected utility is defined by thexpected compensation and the variance of that compensation for

single meal. Of course, a waiter serves many customers and while

he variance across customers may be large, the overall volatilityn compensation throughout the day is likely to be much less asarge tips and small tips “cancel” each other out.4 While the model

2 The mean-variance model is most appropriate when the outcome is normallyistributed (Epps, 1981). Although outcomes are not normally distributed in thisase, it has been shown that the mean-variance utility model gives a close approx-mation of the optimal choice under an expected utility model even in the absencef normally distributed outcomes. Under these circumstances, the mean-varianceodel’s expository convenience justifies any minor imprecision.3 It is reasonable to expect that the waiter could, if he wished, take another job

s a retail sales clerk, a parking lot attendant, or any other relatively unskilled jobhere barriers to mobility are low.4 I thank an anonymous referee for pointing this out.

onomics 38 (2009) 641–647 643

does not specifically account for differences across customers, theeffect of lower variance through aggregation of customers can beeasily captured by reducing ˇ, the waiter’s coefficient of absoluterisk aversion.

Suppose the salary from the next best, non-tipping job is S. Thenthe expected utility of working at the restaurant must equal theutility of working elsewhere, or:

EUW (W + t) = E(W + t) − ˇ

2Var(W + t) = S

or

W = S − E(t) + ˇ

2Var(t) (2)

From Eq. (2) we see that as the expected tip rises the wage paid tothe waiter will fall. Eq. (2) also tells us that a greater variance inthe tip schedule will have the opposite effect. As a result, increasedtipping is likely to reduce wages but, if the variance also increases,the added risk assumed by the waiter will cause wages to fall at aslower rate than the increase in the mean tip.

So while higher tipping reduces the diner’s risk, it also increasesher total expenditure (W + C + t). The marginal increase in (W + C + t)that comes with higher tipping can be thought of as the diner’s“price” of more certainty.

2.3. The optimal tipping scheme

The diner will choose a tipping scheme to maximize herexpected utility (Eq. (1)) knowing that her choice will alter thewaiter’s wage (Eq. (2)) and, consequently, the price of the meal.This leads to the constrained optimization problem:

maxt

EUD = E(V − W − C − t) − ˛

2Var(V − W − C − t)

s.t.W = S − E(t) + ˇ

2Var(t)

Substituting the constraint into the objective function and sim-plifying results in the optimization problem:

maxt

EUD = E(V) − S − ˇ

2Var(t) − C − ˛

2Var(V − W − t) (3)

where the result, t∗ = (t∗H, t∗

M, t∗L ), is the optimal tipping scheme.

Expanding the final term of (3) and further simplifying yields theoptimization problem,

maxt

EUD = E(V) − S − C − (˛ + ˇ)2

Var(t) − ˛

2Var(V) + ˛ Cov(V, t)

and the first order condition,

−(

˛ + ˇ

2

)∂ Var(t)

∂t+ ˛

∂ Cov(V, t)∂t

≤ 0, but = 0 if t > 0.

The variance of t is:

= E[t2] − [E(t)]2 = pt2H + qt2

M + rt2L − (ptH + qtM + rtL)2

and the covariance between V and t is:

= E(V · t) − E(V) · E(t) = pHtH + qMtM + rLtL − �V (ptH + qtM + rtL).

where �V = E (V). The complete set of first order conditions is then:

∂EUD

∂tH= ˛p(H − �V ) − (˛ + ˇ)p(tH − �t) ≤ 0, but = 0 if tH > 0

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44 S.J. Holland / The Journal of So

∂EUD

∂tM= ˛q(M − �V ) − (˛ + ˇ)q(tM − �t) ≤ 0, but = 0 if tM > 0

∂EUD

∂tL= ˛r(L − �V ) − (˛ + ˇ)r(tL − �t) ≤ 0, but = 0 if tL > 0

here �t = ptH + qtM + rtL.It can be shown that under these conditions tL = 0. Using

his result and manipulating ∂EUD/∂tH yields tH = ˛(˛+ˇ)

(H−�V )(1−p) +

q(1−p) tM . Substituting this result into ∂EUD/∂tM and solving for tM

nd tH results in the optimal tipping scheme:

∗H = ˛

(˛ + ˇ)(H − L) > 0; (4)

∗M = ˛

(˛ + ˇ)(M − L) > 0; (5)

∗L = 0 (6)

Notice that for consistency Eq. (6) could be interpreted as t∗L =

/(˛ + ˇ)(L − L). The second order conditions are:

∂2EUD

∂t2H

= (˛ + ˇ)p(p − 1) < 0,

∂2EUD

∂t2M

= (˛ + ˇ)q(q − 1) < 0,

nd

∂2EUD

∂t2L

= (˛ + ˇ)r(r − 1) < 0

nd are also satisfied.

. Outcomes

The results of this model, specifically Eqs. (4)–(6), imply behav-or that is consistent with intuition and practice. To summarize:

.1. Tipping is rational

A tipping scheme that involves a diner paying a positive amounto her waiter is optimal whenever the diner is risk-averse (˛ > 0)nd the quality of the meal is uncertain (e.g., H > L). Tipping shiftsisk from the diner to the waiter by increasing the variance of theaiter’s compensation. The diner’s expected utility improves rel-

tive to a world without tipping and, because of the competitivearket constraint in Eq. (2), the waiter is no worse off than before

ipping took place. The optimal tipping scheme in Eqs. (4)–(6)llows for an allocation of risk that is Pareto superior to that whichould result from the market only.

In fact, a positive tip is optimal even if the quality of the din-ng experience is independent of the waiter’s effort. This papers not meant to suggest the monitoring problem is irrelevant. Inact, this result strengthens the theory that tipping is an effectiveubstitute for firm monitoring. In Azar (2004a) it was shown thatncreased tipping increases incentives for servers to provide highuality service and reduces the need for firm monitoring. In thattudy, however, it was assumed that a social norm or “repeated-nteraction scenario” caused the tip to increase linearly with service

uality. By analyzing tipping as a risk sharing mechanism we areow able to explain why tipping increases with the quality of theining experience. Although this paper assumes waiter effort haso impact on quality, it is not inconsistent with such a finding. Ofourse, further study integrating risk and waiter effort would benteresting.

onomics 38 (2009) 641–647

3.2. Tips increase as the quality of the meal increases

If H > M > L it follows from Eqs. (4)–(6) that t∗H > t∗

M > t∗L .

3.3. Tips increase as the variability in meal quality grows

If tipping is, in fact, a response to risk, then an increase in thevariance of the meal quality should increase the level of tipping. Theoptimal tipping scheme reveals that as (H–L) and (M–L) increase, sowill the respective tips. This confirms that a wider range of possibleoutcomes causes the diner to increase tipping.

3.4. Tips increase with ˛, the diner’s coefficient of risk aversion,and decrease with ˇ, the waiter’s coefficient of risk aversion

Eqs. (4)–(6) illustrate the importance of risk aversion to tip-ping. Taking the partial derivate of t∗

H with respect to each of thecoefficients of absolute risk aversion reveals:

∂t∗H

∂˛=

[1

˛ + ˇ

(1 − ˛

˛ + ˇ

)](H − L) > 0

and

∂t∗H

∂ˇ= −

(˛

˛ + ˇ

)(H − L) < 0

The optimal tip increases with the diner’s risk aversion anddecreases with the waiter’s risk aversion. Similar results would holdfor t∗

M .This confirms the earlier observation that tipping is a method to

shift risk from the diner to the waiter. A more risk-averse diner willattempt to shift more risk to the waiter through increased tipping.If the waiter acts in a fairly risk neutral manner due to the factthat aggregate tips over the course of a day or a week are fairlyconsistent, then average tips will rise. A more risk-averse waiter, onthe other hand, will resist more uncertainty in his compensationand demand smaller wage reductions as the tips grow. Therefore,higher waiter risk aversion increases the diner’s cost of shifting riskand reduces the optimal level of tip.

3.5. Tipping a percent of the bill is a reasonable proxy for theoptimal tipping scheme

Thus far, the tip has been modeled as an absolute amount thatis added to the restaurant bill but the actual practice, at least inrestaurants, is to tip a percent of the bill. I will show that these twoapproaches are consistent if we assume that a restaurant’s pricesare positively correlated with its quality.

We can define the average percent tip by dividing the averageabsolute tip by the price of a meal (W + C). The average absolute tipis:

�t = pt∗H + qt∗

M + rt∗L = p

˛

(˛ + ˇ)(H − L) + q

˛

(˛ + ˇ)(M − L)

= ˛

(˛ + ˇ)(�V − L).

Therefore, the average percent tip is:

%tip = ˛

(˛ + ˇ)(�V − L)(W + C)

(7)

Suppose we define a higher quality restaurant as one in which theexpected value of V (�V) is higher than in a low quality restaurant.

This would occur, for example, because p, the probability of gettingV = H, is greater.

Now suppose that the price of the meal in the high qualityrestaurant rises proportionately to its expected quality–in otherwords, �V and (W + C) increase by roughly the same percentage.

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S.J. Holland / The Journal of So

his might be because the cost of ingredients is higher, the rent offancier space is greater, or staff wages are higher because of theeed for greater skill. The average tip in a high quality restaurantill be larger in absolute terms (due to the increase in �V), but ifand � are fixed and L is small the tip measured as a percent of

he meal price (Eq. (7)) will stay relatively constant. The percent tipill not, of course, remain perfectly constant because quality andrice are not likely to rise at exactly the same rate, L /= 0, and there

s downward pressure on W when the average tip increases. How-ver, the average percent tip is likely to be stable enough to serve asconvenient, if not fairly accurate, proxy for the optimal absolute

ip (t*).

. The commitment problem

Thus far I have shown that tipping is rational for diners. Dinersre willing to pay a little more when they eat out in exchange foress risk, and waiters are willing to accept a more variable com-ensation package so long as the expected value of that package

ncreases. However, what is to prevent a diner from proposing theptimal tipping scheme described in Eqs. (4)–(6), benefiting fromhe resulting drop in waiter wages, enjoying her meal, and thenlipping out without leaving the promised tip? In other words, ishe optimal tipping scheme enforceable?

While I have been treating tipping as a contract, it is importanto remember it is an extra-legal one. There are no police or courts tounish those who violate the contract by under-tipping. This situ-tion would seem to create the well-known commitment problem.s an illustration, suppose a diner orders and consumes a superb,igh-value meal (V = H). After desert, the diner has the choice of

eaving a tip of t∗H as she promised in the contract, or leaving no

ip at all. Tipping gives the diner a payoff of (H − W − C − t∗H) and

eaving no tip gives her a payoff of (H–W–C). Obviously, it is in theiner’s short-term best interest to leave the restaurant without tip-ing. If all diners act this way, wages will rise and the practice ofipping will unravel. Fortunately, there are a number of reasons aational diner will not act opportunistically.

.1. Repeated interactions

A diner who frequents the same restaurant faces a repeatedame in which it is rational to abide by the terms of the tippingcheme. A simple numerical example illustrates the self-enforcingature of infinite repetition in this context. Suppose ˛ = ˇ = 0.5,= (8,10,12), p = q = r = 1/3, C = $0 and S = $6.00. Then, applying Eqs.

2) and (4)–(6), the optimal tipping scheme is t∗ = (0, 1, 2) and theage is W = $5.25. A diner who enjoys a high value meal (V = 12)ill leave no tip in a one-shot game because this would result inpayoff of $6.75 rather than the lower payoff of $4.75 that would

ome with abiding by the contract. However, a waiter who receiveso tip from this diner and other diners like her will not continue toait tables very long unless his wage rises to that of a comparable

ob, or $6.00.If the loss of utility in the future outweighs the short-term gain

f deviating from the promised tip, then the diner will not deviate.f we assume that wages adjust immediately to reflect the absencef tipping, then deviating from the promised tipping scheme in thisxample gives the diner a payoff of $6.75 in the current period plushe discounted value of EUD = E(V − S) − (˛/2) Var(V − S) = $3.00oing forward for an infinite number of time periods. A diner who

bides by the contract receives $4.75 in the current period plus theiscounted value of EUD = E(V − W − t) − (˛/2) Var(V − W − t) =3.50 in the future. In this case, a rational diner with a discount ratef ı will adhere to the promised tipping scheme, despite the short-erm benefit of deviating, if

($4.75 + $3.50

ı

)>

($6.75 + $3.00

ı

)or

onomics 38 (2009) 641–647 645

ı < 0.25. In other words, if the discount rate is sufficiently low andthe diner fears a lack of tipping will lead to higher wages, thena rational diner will realize the long-term costs of deviating fromthe promised tip exceed the short-term gains. If diners eat out fre-quently and wages respond quickly to changes in tipping practicesthis is likely to be the case and we can expect the tipping contractto be self-enforcing.

4.2. Social norms

Customers who rarely or never return to the same restaurantdo not face a repeated game, so opportunistically “stiffing” thewaiter would still seem to be the optimal strategy. However, moreoften than not diners leave a tip even when there is no intentionof ever returning. A risk-based approach to tipping, alone, does notexplain this. Here, recent work on social norms is important (see, forexample, Azar, 2005a). Opportunistic behavior arises in this contextbecause there are no future costs to offset the benefits of not leavinga tip today. However, since tipping has become a social norm, theembarrassment and sense of unfairness that comes with violatingthe norm imposes a cost on a diner who stiffs the waiter. The costs ofviolating the norm take the place of the future costs of opportunismwe saw in the repeated game and appear to be substantial enoughto make the implied contract to tip self-enforcing. This paper but-tresses Azar’s argument that tipping is a welfare enhancing practiceof the type that often leads to a social norm.

5. Applications

5.1. Why retail workers and bus drivers are not tipped: the role ofrisk and asymmetric information

Current theories do not fully explain why workers in some occu-pations routinely receive tips while other workers in seeminglysimilar jobs do not. Azar (2005b) addressed this question and found,among other things, empirical support for a positive correlationbetween tipping and the psychological desire to show gratitudetoward low-income workers. While a useful finding, it cannot fullyexplain inconsistent tipping practices across low-income occupa-tions.

For example, the service provided by a restaurant worker(answering questions about the food and delivering it to the tablein a timely manner) is similar to that provided by a retail worker(answering questions about the merchandise and helping the cus-tomer pay for it in a timely manner). Taxi drivers and bus driversprovide similar services as well. Yet, restaurant workers and taxidrivers are tipped while retail workers and bus drivers are not. Inall of these cases the worker receives modest wages, the cost oflabor makes up a substantial portion of the price of the service, andit is much more difficult for the employer to observe the worker’seffort than it is for the customer. So how can the disparate tippingpractices be explained?

Understanding tipping as a response to customer risk helpsresolve this problem. Consider the customer at a restaurant. Shemust make her decision about what to eat based on a short descrip-tion of the meal. She cannot taste, touch or smell the meal todetermine its quality before she commits to paying for it.5 This type

5 Most of us try, however. This explains why a tray full of hot food being deliveredto a table draws so much interest from the customers who are deciding what toorder.

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46 S.J. Holland / The Journal of So

A customer in a department store, on the other hand, faces a dif-erent situation. Often, she can look at the merchandise, read aboutts features, and even try it on. These are considered “search goods”ecause the quality can be determined through the search processrior to purchase (Darby and Karni, 1973). The risk of purchasingsearch good is minimal because the customer can gather nearlyerfect information and can simply avoid a transaction if it wouldeduce utility. For department store goods that would be consideredxperience goods, such as a dishwasher, the risk is also minimalecause the customer can usually return an unwanted item and geter money back. Even if she could not return the good, the customerould be in no position to tip at the time of sale because the good’s

alue cannot be determined until well after payment is made. Inny case, tipping does nothing to reduce risk.

When the risk of getting a low quality good is small so that theariance of the expected utility is minimal, tipping is not necessary.ecall that the optimal tip goes to zero as the range of potentialutcomes narrows. Because restaurant customers face much risknd department store customers face little risk, and because thehronology of purchase, payment and assessment vary in signif-cant ways, restaurant workers are tipped and retail workers areot.

Similarly, when a rider gets into a taxi cab he commits to payinghe fare printed on the door of the cab but has no idea whetherhe driver will drive safely, choose the fastest or shortest route, orick a radio station that appeals to the rider. A bus rider, however,nows almost exactly when he will arrive at his destination and hasmuch better idea of what to expect on the ride. The risk of getting

nto a taxi is significant and can be mitigated by tipping. The risk ofoarding a bus is negligible and tipping is unnecessary.

.2. Why lawyers and automobile mechanics are not tipped: themportance of the nature of the labor market

I have argued the risk of purchasing a service is greatest whents quality has a large variance and it is difficult or impossible tobserve the quality before committing to payment. By that stan-ard, there are few purchases that are riskier than hiring a lawyer orn auto mechanic. These are often referred to as “credence goods,”r goods and services whose quality cannot be evaluated even afterse (Darby and Karni, 1973). In each case, the range of possible out-omes is wide and the customer must sign a contract or submit tolien to secure payment before any work is done on his behalf. If

ipping is indeed a useful mechanism to reduce this risk, then theseervice-providers should be tipped. Why then is it uncommon to tipither of these professionals?

One reason is that credence goods must be paid for before theuality of the good is determined. Like the case of the dishwasher,ipping is impractical.

The structure of the relevant labor market is also likely to bemportant. The reason tipping was a cost-effective risk reductionool in the case of restaurant workers is because labor market mobil-ty caused the waiter’s wage to fall as the expected tip increased.ncreased tipping in the restaurant industry lures workers fromther industries and the wage for waiters falls until no more work-rs have an incentive to switch jobs. This logic does not hold,owever, for lawyers and auto mechanics because they have specialraining, skills, and certification. If clients began tipping lawyers,igh barriers to entry would keep accountants and college profes-ors from flocking to the legal industry in the short-term. Since

dditional tip compensation is not likely to significantly increasehe supply of lawyers, tipping will do little to reduce the under-ying cost of hiring a lawyer. Under these circumstances the costf shifting risk is very high and it is no surprise that tipping isncommon.

onomics 38 (2009) 641–647

A final reason lawyers and auto mechanics may not get tippedstems from the importance of consistently high quality work forthe reputation of the service provider. Enforceable contracts arenecessary to avoid the problems of opportunism and unexpectedcontingencies when performance takes place over time.6 As anillustration, suppose a client commits to buying legal services, suchas representation in civil litigation, which will be performed overthe course of the next year. The lawyer’s incentive in this case wouldseemingly be to shirk his responsibilities because the client hasalready committed to pay and the lawyer’s compensation no longerdepends on the provision of high quality service (which the clientcannot adequately assess anyway). This would normally be a goodplace for tipping except that lawyers and auto mechanics, more thanrestaurant workers and cab drivers, tend to rely on repeat customersand “word-of-mouth” referrals that result from work which exceedsthe customer’s expectations. It has been shown that when parties toa contract value their reputations the contract may be self-enforcingeven in the absence of legal enforcement (Bernstein, 1992). In otherwords, the need to develop a good reputation and nurture long-term business relationships causes lawyers and mechanics to do abetter, more consistent, job than a waiter. This decreases the risk tothe customers and further reduces the need for tipping.

This observation is contrary to the theory that justifies tipping asa way to induce better service in the future. A risk-based approach totipping suggests that tipping is less likely when the personal rela-tionship is ongoing because repeated business dealings with thesame person reduce the risk of poor service. It is when the relation-ship with the individual service provider is transitory (although thepurchase of the service in general is infinitely repeated) that tippingcan be most effective.

6. Conclusion

The object of this study was to explore whether uncertaintyabout the value of goods and services could provide a rationalefor tipping that is consistent with the assumption of utility max-imizing agents. The main finding is that a risk-averse customer canbenefit from tipping when the true value of the good or servicebeing sold is uncertain, the wage of the service provider is a sig-nificant part of the cost of the good or service, and that wage isdetermined by a competitive market. Under these circumstances,tipping can reduce the wage paid to the service provider andmake a portion of the price of the service discretionary. Whenthe service quality is below what the customer expected, shecan leave a smaller tip and pay a price that is closer to the ser-vice’s true value. A risk-averse service provider, on the other hand,will resist a tip based compensation package because it increaseshis exposure to risk. As a result, wages will fall less than theincrease in the expected tip. This imposes a cost on the cus-tomer, who will balance this cost against the benefits of addedcertainty.

This approach to tipping explains why rational economic agentswould engage in such behavior. It also helps to explain peculiar dis-crepancies in tipping behavior. For example, tipping in restaurantsis beneficial because of the great uncertainty over the quality ofthe food that will be served. Tipping is not useful or practical inthe case of retail workers because the quality of goods purchasedin a department store can be reliably observed before a purchase ismade. In addition, this approach suggests that when tipping is not

costly to be an effective risk reduction tool.

6 A good summary of the economic role of contracts is found in Posner (2003).

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eferences

rrow, K., 1971. Political and economic evaluation of social effects and externali-ties. In: Intriligator, M. (Ed.), Frontiers of Quantitative Economics. North-Holland,Amsterdam, pp. 3–25.

zar, O.H., 2004a. Optimal monitoring with external incentives. Southern EconomicJournal 71 (1), 170–181.

zar, O.H., 2004b. what sustains social norms and how they evolve? the case oftipping. Journal of Economic Behavior and Organization 54 (1), 49–64.

zar, O.H., 2005a. The social norm of tipping: does it improve social welfare? Journalof Economics 85 (2), 141–173.

zar, O.H., 2005b. Who do we tip and why? An empirical investigation. AppliedEconomics 37, 1871–1879.

zar, O.H., 2007a. Why pay extra? Tipping and the importance of social normsand feelings in economic theory. The Journal of Socio-Economics 36, 250–265.

zar, O.H., 2007b. Do people tip strategically to improve future service? Theory andEvidence. Canadian Journal of Economics 40 (2), 515–527.

zar, O.H., 2007c. The social norm of tipping: a review. Journal of Applied SocialPsychology 37 (2), 380–402.

zar, O.H., Yossi, T., 2008. Tipping as a strategic investment in service quality: anoptimal-control analysis of repeated interactions in the service industry. South-

ern Economic Journal 75 (1), 246–260.

en-Zion, U., Karni, E., 1977. Tip payments and the quality of service. In: Ashenfelter,O.C., Oates, W.E. (Eds.), Essays in Labor Market Analysis. John Wiley & Sons, NewYork, pp. 37–44.

ernstein, L., 1992. Opting out of the legal system: extralegal contractual relationsin the diamond industry. The Journal of Legal Studies 21 (1), 115–157.

onomics 38 (2009) 641–647 647

Bodvarsson, O.B., Gibson, W.A., 1997. Economics and restaurant gratuities: deter-mining tip rates. American Journal of Economics and Sociology 56 (2), 187–203.

Conlin, M., Lynn, M., O’Donoghue, T., 2003. The norm of restaurant tipping. Journalof Economic Behavior & Organization 52 (3), 297–321.

Darby, M.R., Karni, E., 1973. Free competition and the optimal amount of fraud.Journal of Law and Economics 16, 67–88.

Dixit, A., 2004. Lawlessness and Economics: Alternative Modes of Governance.Princeton University Press, Princeton.

Epps, T., 1981. Necessary and sufficient conditions for the mean-variance portfoliomodel with constant risk aversion. Journal of Financial and Quantitative Analysis16 (2), 169–176.

Estreicher, S., Nash, J.R., 2004. The law and economics of tipping: the laborer’sperspective. In: American Law & Economics Association 14th Annual Meeting,Article 54, available at http://law.bepress.com/alea/14th/art54.

Frank, R., 1987. If Homo Economicus could choose his own utility function, wouldhe want one with a conscience? American Economic Review 77 (4), 593–604.

Landsburg, S.E., 1993. The Armchair Economist. The Free Press, New York.Lynn, M., 2006. Tipping in restaurants and around the globe: an interdisciplinary

review. In: Altman, M. (Ed.), Handbook of Contemporary Behavioral Economics:Foundations and Developments. M.E. Sharpe Publishers, pp. 626–643.

Lynn, M., McCall, M., 2000. Gratitude and gratuity: a meta-analysis of researchon the service-tipping relationship. The Journal of Socio-Economics 29, 203–214.

Lynn, M., Zinkhan, G., Harris, J., 1993. Consumer tipping: a cross-country study. TheJournal of Consumer Research 20 (3), 478–488.

Posner, R., 2003. Economic Analysis of Law, 6th ed. Aspen, New York.