Veblen Effects in a Theory of Conspiscuous Consumption

8/17/2019 Veblen Effects in a Theory of Conspiscuous Consumption

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Veblen Effects in a Theory of onspicuous onsum ption

By

LAURIE SIM ON BAGW ELL AND B . DOUGLAS B ERN HEIM *

We examine conditions under which Veblen effects arise from the desire to

achieve social status by signaling wealth through conspicuo us consum ption.

Wh ile Veblen effects canno t ordinarily arise w hen preferences satisfy a

'single-

crossing property.'' they may emerge when this property fails. In that case,

budg et brands are priced at marg inal cost, while luxury brands, though

not intrinsically superior, are sold at higher prices to consumers seeking to ad-

vertise wealth. Luxury brands earn strictly positive profits under conditions that

would, with standard formulations of preferences, yield margina l-cost pricing.

We explore factors that induce Veblen effects, and w e investigate policy impli-

cations. JELDW,

D43)

In his celebrated treatise on the leis ure

class ,

Thorslein Veblen (1899) argued that

wealthy individuals often consume highly

conspicuous goods and services in order to ad-

vertise their wealth, thereby achieving greater

social status. Veblen's writings have spawned

a significant hody of research on pr es ti ge

or st at u s good s.' In the context of this Ht-

* Respectively. Department of

Finance.

J. L. Kellogg

Graduate School of Management, Northwestern Univer-

sity.

2001 Shen dati Road. E vanston. IL 6020 8-2006 . and

Department

of Economics. Stanford Unive rsity, Stanford,

CA

94305-6072. The work reported here was supported

by the National Science Foundation through Grant No.

SES-9110211, and through a Presidential Young Investi-

gator Award. The first author would also like to

acknowledge the support of the Lynde and Harry Bradley

Foutidation

and the H oover Itistitution. The authors would

like

to thank Kyle Bagwell, Scott Brandwein. R. Preston

McAfee,

and the anonymous referees for helpful com-

ments and discus sions. Previou.s drafts of this paper w ere

circulated under the titles Conspicuous Co nsum ption.

Pure

Profits, and the Luxury Tax: Some Surprising Con-

sequences

of Perfect Com petition ' (draft dated Nov emb er

1991) and ' Conspicuous Consumption. Pure Profits, and

the Luxury Tax (draft dated September 1992).

' See , for example, Harvey Leibenstein (1950). and

more recently Robert H. Fratik (1985), Kaushik Basu

(1987), Yew-Kwang Ng (1987), R. L- Basmanti et al.

(1988). Ottmar L, Braun and Robert A, Wicklund (1989).

John

Creedy and D. J. Slottje (1991), and Norman Ireland

(1992).

More generally, other recent studies, including

George A. Akerlof (1980), Steveti R. G. Jones (1984),

Timothy Besley and Stepheti Coate (1990). B, Douglas

Bemheim

(19 94), Harold L. Cole et al (1992 ). Chaim

Fershtman

and Yoram Weiss (1992), and Amihai Glazer

erature, Ve blen effects are said (o exist

when consumers exhibit a willingness to pay

a higher price for a functionally equivalen t

Anecdotal evidence suggests that Veblen

effects may be empirically significant in mar-

kets for luxury goods. According to one mar-

keting manager. O ur customers do not want

to pay less. If we halved the price of all our

products, we would double our sales for six

months and then we would sell nothing. -*

Indeed

The Economist

(1993 ) emphasizes

that [ r j e t ai le rs can damage a glamorous

go od's image by selling it too che apl y. A

recent article in the Wall Street Journal noted

that a BM W in every drivew ay might thrill

investors in the short run but ultimately could

dissipate the prestige that lures buyers to these

luxury ca rs.

*

Econom etric evidence also cor-

roborates the existence of Veblen effects.^

Recent incarnations of Veblen's theories

simply proceed from the premise that price en-

hances utility (see. for example, Leibenstein,

1950;

Braun and W icklund, 1989; or Creedy

and Slottje, 1991 ). Yet Veblen h imself did not

• TTie following pa ssage typifies m odem disctissions of

prestige goods: Conspicuous cons um ption, or Veblen ef-

fects, are said to occur when individuals increase their

demand for a good simply because it has a higher price

(Creedy and Slottje, 1991).

' Quoted in The Economist (1993 p . 96).


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THE AMERICAN ECO NOMIC REVIEW

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endorse the view that the price of an object

affects utility directly, or that individuals seek

to pay high prices f'or the sheer pleasure of

being overcharged. Rather, he proposed that

individuals crave status, and that status is en-

hanced by material displays of wealth. Ac-

cording to Veblen , In ord er to gain and to

hold the esteem of men, wealth must he put in

evidence, for esteem is awarded only on evi-

d en ce (p. 24). By social custom , the evidence

consists of unduly costly goods that fall into

accredited canons of conspicuous consump-

tion, the effect of which is to hold the con-

sumer up to a standard of expensiveness and

wastefulness in his consumption of go ods and

his emp loyment of time and effort (p. 71).

Thus, in a theory of conspicuous consumption

that is faithful to V eblen 's analysis, utility should

be defined over consumption and status, rather

than over consumption and priees. Although the

prices that one pays for goods may affect status

in equilibrium,

this relation should be derived

not

assumed.

Moreover, since Veblen argued

that individuals engage in conspicuous con-

sumption to advertise and provide evidence of

wealth, the equihbrium relation between price

and status should result from signaling.

Tbe details of Veblen's arguments naturally

invite the interpretation that conspicuous con-

sumption reflects signaling. In particular, Veblen

distinguished between two motives for consum-

ing conspicuous goods: invidio us compari-

so n and pecuniary em ulation. Invidious

comparison refers to situations in which a

member of a higher class consumes conspicu-

ously to distinguish himself from members of

a lower class. Pecuniary emulation occu rs when

a member of a lower class consumes conspic-

uously so that he will be thought of as a mem-

ber of a higher class. In modem terms, these

motives are the essence of the incentive com-

patibility conditions that form the basis for sig-

naling. Members of higher classes voluntarily

incur costs to differentiate themselves from

members of lower classes (invidious compar-

ison), knowing that these costs must be large

enough to discourage imitation (pecuniary

emula t ion) .

Once the need to derive an equilibrium

signaling relation between price and utility

of conspicuous consumption would generate

Veblen effects. There is no particular reason

to believe that wealth is most effectively sig-

naled by paying excessive prices for conspic-

uous goods. Instead, one might prefer to

purchase a larger quantity of conspicuous

goods at a lower price, or a higher quality of

conspicuous good at a higher price.*'

This paper investigates the conditions under

which Veblen effects, defined as a willingness

to pay a higher price for a functionally equiv-

alent good, arise from the desire to signal

wealth. We examine a model in which each

individual's status depends upon perceptions

of his wealth among social contacts. Consum-

ers have private information about the value

of their assets, and attempt to signal their

wealth by consuming a conspicuous good.

The sellers of this good have access to iden-

tical production technologies, and compete

under conditions that would yield marginal-

cost pricing under standard formulations of

preferences. The model does

not

constrain

consumers to signal wealth by oveq^aying for

visibly labeled conspicuous goods: it is also

possible to signal by consuming large quanti-

ties of the good at a lower price, and/or by

selecting bigher quality. Thus, to the extent

Veblen effects are present, they must be gen-

erated endogenously.

We show that Veblen effects do

no t

arise

when the mod el satisfies the standard sin gl e-

crossing pro pe rty (wh ich, in this context

states that the marginal cost of consuming the

conspicuous good is higher for individuals

with lower wealth, so that the indifference

curves of consumers with different levels of

wealth cross at most once).^ However, when

Certain social customs in Thailand illustrate the prac

tice of advertising wealth through quantity, rather than

price. According to Philip Shenon (1991). H is consid

ered acceptable, even by some Western-educated Tha

women who would otherwise describe themselves as fem

inists, for a man to lake one or more mistresses and even

to be seen with them in public, so long as all of the women

and their children are provided tor financially . . Mis

tresses are to some de gree a demonstration of wealth, and

as a rule, the more mistresses, the wealthier Ihc man. A

handful of Bangkok's flashier millionaires are said lo have

10 or more extramarital com pan ion s (p. A4].

' Use of ihe single crossing (or Spence-Mirrlees sort


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BAGWELL AND

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351

the single-crossing properly fails in a particu-

lar way , and preferences satisfy a tan ge nc y

pro per ty, Veblen effects may em erge. In par-

ticular, the resulting equilibria are character-

ized by the existence of b ud g et brands

(sold at a price equal to marginal c os t), as well

as lu xu ry brands (sold at a price above

marginal cost). Luxury brands are purchased

by consumers who seek to signal high levels

of wealth. It is important to emphasize that, in

equilibrium, the luxury brands are not intrin-

sicaHy superior to the budget brands—they

are simply goods of identical quality, sold at

a higher price. The manufacturers of these

brands earn strictly positive economic prof

its even under conditions that would, with

standard formulations of preferences, yield

marginal-cost pricing, and despite the ability

of firms to vary both price and quality.

The theoretical plausibility of Veblen ef-

fects therefore depends upon the plausibility

of the single-crossing property. In the simplest

models of conspicuous consumption (for ex-

ample, Ireland, 1992), the single-crossing

property is satisfied. Since consumption of

conspicuous goods reduces expenditures on

other goods., declining marginal rates of sub-

stitution imply that conspicuous consumption

is more costly for households witb less wealth.

As a result, overpayment for these goods does

not arise in equilibrium. Thus, one reading of

our results (one that is based on the premise

that the single-crossing property holds) suggests

that Veblen effects are difficult to rationalize.

However, we also exhibit several slightly

more elaborate models in which the single-

crossing property fails, and where this failure

gives rise to Veblen effects. For example, we

demonstrate that the tangency property is sat-

isfied in the presence of bankruptcy con-

straints. Tbis follows from the fact that the

marginal cost of conspicuous consumption is

inversely related to wealth at low expenditure

levels,

but positively related to wealth at high

expenditure levels. Remarkably, when Veblen

effects emerge, bankruptcy constraints do not

bind in equilibrium, and so appear to be irrel-

evant, despite the fact that Veblen effects

would not exist without them. Two other fac-

tors that can produce the requisite breakdown

sympathetic to the role of any of the factors

considered here) suggests that Veblen effects

are naturally rationalized within a signaling

context.

The existence of Veblen effects in the con-

text of our model has some provocative im-

plications for public policy. Since supranormal

profits result from the characteristics of de-

mand rather than from the nature of strategic

interaction among firms, evidence of high

profitability does not necessarily support in-

ferences of either collusion or oligopolistic

forbearance. This observation also has impli-

cations for tax policy. Within our model, the

equilibrium prices of luxury brands are de-

mand driven, rather than supply driven—that

is,

luxury brands are sold at the consumer's

preferred price, which is tax inclusive, and

does not vary with the tax rate. Thus, as long

as the tax per unit does not exceed the differ-

ence between the consumer's preferred price

and marginal cost, an excise tax on luxury

brands amounts to a nondistortlonary tax on

pure profits.

This observation is of particular interest in

light of the Omnibus Budget Reconciliation

Act of 1990. which, for a time, established

substantial federal taxes on the sale of various

conspicuous goods, including expensive au-

tom obiles, yachts, jewelry , and aircraft. One

should not conclude from our analysis that

these taxes were nondistortionary; whether the

demand for luxury items is characterized by

Veblen effects is a question that can be settled

only through empirical analysis.

However, it should be noted that several

predictions of our model are consistent with

anecdotal evidence. First, many individuals

appear to consume conspicuous goods to ad-

vertise affiuence. According to Daniel Piette,

vice-president of LVMH (a French conglom-

erate that owns Louis Vuitton, Moet et Chan-

don, and Christian Dior perfumes), for many

individuals buying luxury good s is all about

demo nstration. ' * According to The Econo-

mist the most famous (example) was Ralph

Lauren, whose Polo brand was positioned to

appeal to American yuppies pretending to be


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THE AMERICAN ECONO MIC REVIEW

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Edwardian toffs (p . 92 ). Indeed, The Econ-

omist

conclud es that pri ce is ... a powerful

signal of exc lusiv ity (p . 98 ). This motivates

marketing strategies that appeal to status con-

sciousness. For example, a recent Jaguar ad-

vertisement reads: ' 'If you could drive one car

to your high school reunion, this would be it.

As you swing into your alma mater in a beau-

tiful new Jaguar XJS convertible, you can al-

most see the heads turn as your classmates ask,

'Isn't that ...?

Second, brand-name producers apparently

charge high premia on many status goods. In

some cases, these premia persist even though

the good is easily imitated.'' As a result, man-

ufacturers of status goods tend to earn supra-

com petitive returns. ' This is most cleariy

illustrated by cases in which nearly Identical

versions of the same good are sold at vastly

different prices. Marshall Schuon (1993)

notes that less expen sive cars are often vi r-

tually identica l clones of pricier models. For

exam ple, If you do n't mind a different grille

and headlights, opting for the long-wheelbase

Bentley Brooklands at

152,400 rather than its

twin, the $178,200 Rolls-Royce Silver Spur

m , can save $25,800 (p. 20) .

Third, there is some evidence that the tax-

inclusive p rices of certain luxury goods were un-

affected by the luxury tax. Specifically, Rolls

Royce. Jaguar, and BMW have each run pro-

motional campaigns in which they oifered to re-

imburse customers for the full amount of the

luxury tax. A 1991 advertisement for Rolls Royce

reads:

If the luxury tax is all that separates us.

it's time to talk. From today through December

31.

1991, Rolls-Royce Motor Cars Inc. will re-

imburse you for the full amount of the federal

luxury excise tax incurred when you purchase

or lease a new Rolls-Royce or Bentley . Tbis

offer was still in effect through

1993.

'Ireland (1992) describes an interesting case of this

involving a very expensive brand-named basketball shoe:

The shoes became so much a passport lo social success

among poor urban teenagers Ihat a campaign to limit their

commercial promotion and advert ising was ini t iated

(p.

2).

'

A number of examples are cited in

The Economist

(1993).

The paper is organized as follows. We

describe the model in Section I. Section II

examines signaling equilibria under the as-

sumption that the single-crossing property is

satisfied. Section III analyzes cases where the

single-crossing property fails to hold. The

plausibility of the assumptions required to

generate V eblen effects is discussed in Section

IV. Policy implications and other conclusion

are considered in Section V.

I. The Model

This section presents the model. Sections A

B .

and C describe the choices to be made by

households, social contacts, and producers, re

spectively. The sequence of decisions in the

game and the conditions for equilibrium are

presented in Sections D and E. respectively

Section F defines the single-crossing property

in the context of our model.

A. Households

Consider a household that must allocate re

sources over two types of consumption goo ds

One type is co ns pic uo us , in the sense tha

its characteristics, as well as the quantity con

sumed, are publicly obsen/ed. The character

istics of the conspicuous good include quality

q, where q E [g,q].The second type of goo

is inc on sp icu ou s, in the sense that it i

consumed privately, and not observed by oth

ers. Because of our assumptions about ob

servability, only conspicuous consumption

can potentially serve as a signal of wealth

The inconspicuous good is assumed, for sim

plicity, to be of fixed quality. We will use th

inconspicuous good as the numeraire.

Tbe household is endowed with resources

R,

wbicb it allocates to tbe consumption of th

conspicuous and inconspicuous goods. Le

x{q) denote theq uantity purchased of tbe con

spicuous good with quality

q..

and let

s

deno

your Jaguar dealer and we'll send you a reimbursemen

check equal to the luxury tax based on the manufacturer

suggested retail price. ' It is interesting to note that Jagu

did no t offer this deal on the XJ-6. which is ils least e


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BAGWELL AND BERNHEIM: VEBLEN EFFECTS

35 3

total conspicuous expenditures. Since the in-

conspicuous good serves as the numeraire, we

use

z

to denote both the total inconspicuous

expenditure and the quantity purchased.

There are two types of households (H and

L ) , differing according to their levels of re-

sources (/?H and /?L, with /?,_


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THE AMERICAN ECONOM IC REVIEW

JUNE 1996*

divided into two groups. The first group con-

sists of F incumbents, indexed / G [1 , .. . ,

F].

Tbe rest of the firms are potential entrants. All

firms can produce the same range of qualities.

*? G [


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BAGWELL AND BERNHEIM VEBLEN EFFECTS

35S

form inferences about each household 's

wealth, and react accordingly {by choosing

p).

The payoff to each ho usehold is given by

{x, z, p). Social contacts receive payoffs of

p) , where R is the household's actual

resources. Firm's payoffs are given by profits

(revenues minus costs).

E. Equilibrium Conditions

Our game is divided into two main phases.

In the first phase (stages 1 and 2 ) , firms com -

pete by naming prices and qualities. In the sec-

ond phase (stages 3 and 4). households select

consumption bundles and social contacts draw

inferences about households' characteristics.

The second phase is recognizable formally as

a signa ling ga m e, in the sense of Jeffrey S.

Banks and Joel Sobel (1987) or In-Koo Cho

and Kreps (1 98 7) . In particular, the household

is the se nd er , and possesses private infor-

mation concerning its type, R. The ex ante

probability distribution over (/?, , ? H } is com-

mon kno wled ge, and is sum marized by a. Af-

ter the household learns its type, it sends a

m es sa ge , in this case {x, s), to the social

who play the role of re ce iv ers . In

response to this message, the social contacts

select a res po ns e. p. The payoffs to the

tact) depend upon the sender's type {R), the

message {x, s), and the response (p) .

We reduce the set of equilibria through the

use of a refinement that is similar in spirit to

subgame perfection: for any outcome of the

first phase, actions and inferences constitute a

separating equilibrium in the second phase,

(198 7) intuitive criterion, which is equiv-

* For the receiver, dependence on the message itself is

Equilibrium with comp leie pooling can be ruled out

sideration of these equilibria

It is useful to describe the second-phase

equilibria in a bit more detail. Let Q denote

the set of quality levels named by firms in the

first phase. For each q e QA i P{q) denote

the set of prices announced by firms for con-

spicuo us prod ucts of quality ly. Define p{q) =

min P{q), a.ndp{q) = max P{q). FoFa con-

spicuous good of quality q and price p, we

define the qua lity-w eigh ted price, pi^{q);

this corresponds to the price of a quality-

weighted unit of conspicuous consumption

(that is, a unit of .v, rather than of J : ( ^ ) ) .

In l ight of equation (2) , households would,

in the abse nce of informational imp erfec-

t ions,

choose the conspicuous good with the

lowest quali ty-weighted pr ice. Let p =

min^^^,[j{q)/fiiq), and p = max^aQPiq)/

fi(q). In other words, p ( p ) is the lowest

(highest) quality-weighted unit price quoted

in the first phase.

Note that, unless p = p ; an individual's quality-

weighted conspicuous consumption, x, does not

uniquely determine his total conspicuous expen-

diture, .s. Depend ing upon which brands he se -

lects, he may spend as little as p ^ , or as much

as px. In fact, for any s satisfying px ^ s ^ px,

it is possible to purchase x quality-weighted units

of the conspicuous good for exactly 5.'

No rational consumer would ever spend

more than the minimal amount needed to ac-

quire a given quantity of the inconspicuous

good. However, a consumer may be willing to

spend more than £x to acquire x units of the

conspicuous good. Since others can observe

his level of consumption, x(q), his selection

of brands, brand prices, and brand qualities,

they can infer his total expenditure, s, and

quality-weighted consumption, x.

Formally, a separating equihbrium consists of

total conspicuous quality-weighted quantity and

expenditure choices {xi_, 5 ,, x^ , .?•„), with

(J:,

,

Si_ =f=

(xn,

Sti),

satisfying incentive compatibility.

( 4 )

(5 )


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THE AMERICAN ECONOMIC REVIEW

JUNE 199

and feasibility.

(6 ) P ^ - ^

7

P ^

Xi

Moreover, social contacts form beliefs, rep-

resented by a function 7r map ping the m essage

(x , 5) to a subjective probability that the

household is type H. This function must satisfy

the restrictions that 7r(XL, ^L) = 0 and

Hxn,

SH) = 1- Finally, the choices (.tj, 5L) and (XH,

SH) must be optimal (for type-L and type-H

households respectively) given the relation be-

tween inferences and actions that is implied by

the combination of n and r(7r).

Our description of a separating equilibrium

is incom plete in the following sense: although

we have specified total conspicuous con-

sumption (xi. and xu) as well as total con-

spicuous expenditure (5L and ^ H ) we have

not indicated which brands are purchased.

There may well be an infinite number of con-

spicuous consumption bundles containing x,

quality-weighted units, and requiring an ex-

penditure of exactly .?, (i = L, H ). ' Fortu-

nately this is immaterial, since consumers do

not care about brand selection, except insofar

as it affects total cost. Indeed, consumers are

completely indifferent between all conspicu-

ous consumption bundles containing the same

total number of quality-weighted units that re-

quire the same total expendittires. Though we

have made several assumptions to resolve con-

sumer indifference, our results do not depend

on the specifics of these assumptions.

It should be noted that, given our assump-

tions so far, Veblen effects might arise simply

because it is

impossible

to deter imitation by

type-L households except by paying inflated

prices for the conspicuous good. If, for ex-

' *

Suppose, for example, that there are three brands. ^4.

B.

and C. of qualities q, {j = A, B. C). sold at prices

/»,.

where

pJp-iRA) < PH/ti(qn) < PrffJigr). and suppose that pJ

f^tjA) < itx, <

Pc-Ifiiqr)-

Then there is an infinite number

am ple. 5, the absolute limit on conspicuous ex

penditures, is sufficiently low, then it may b

impossible to deter imitation by consumin

high quantity or quality. For the moment, w

will assume that sufficiently high quantity o

quality does suffice to deter imitation, so tha

the existence or nonexistence of Veblen ef

fects depends upon a comparison of the desi

ability

of signaling through price, quantity, o

quality, rather than on the feasibility of deter

rence. We retum to this issue in Section II.B

where we discuss factors that affect the po

.sibility of deterring im itation through hig

quantity or quality.

To state this assumption formally, we mus

first develop some additional notation, an

state one preliminary result. Define xl(p) a

the solution to max,Wi_(x, px, P L) where, fo

simplicity, we assume that this solution i

unique), and let Wl{p) denote the corre

sponding optimized value of the objectiv

function. We then have the following.

LEMMA 1: For any separating equilibriu

of the subgame beginning in stage 3, al

type-L househo lds purcha se x^(p) quality

weighted units of the conspicuous good at

total cost of pxy^ip).

The argument here is a standard one. In th

separating equilibrium, the L's are correctl

identified. Therefore, they cannot (in a se

quential equilibrium) induce social contacts t

reduce p below p, by deviating from their pr

scribed choice. Their optimal choice is then t

select feasible levels of consumption whic

maximize their intrinsic utility. Consequentl

if there is another J: ^ 0 and feasible s th

raises the value of W, (x , s, P L ) , it must mak

them better off. This contradicts the suppos

tion that an equilibrium prevails.

We are now prepared to provide the follow

ing sufficient condition for the feasib ility of d

terring imitation without paying inflated price

for the conspicuou s good: for all p ^ c'^.

(8 )

This condition states that type-L household

would choose not to imitate type-H house


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86 fio. 3

BAGWELL

AND BERNHEIM:

VEBLEN EFFECTS

357

FIGURE

I.

SINGLI; CROSSING AND THK

ABSKNCt

OI V K B L K N hftifTS

price

p.

Consequently, type-H households

could,

if

desired, differentiate themselves

by

selecting high quantity

at the

lowest available

price, rather than by overpaying for a lower

F. The Single-Crossing Property

As discussed

in the

introduction,

our

objec-

is to

determine whether V eblen effects

as a

consequence

of

signaling.

As we

the existence of Veblen effects

on the

properties

of

the househo lds'

in-

in the (x, s)

plane.

A condition known as the single-crossing

perty often plays

an

important role

in

I

in the

(x. s) plane

( / L ,

corresponding

to a

of

Wi_ix, s, p))

and for

type-H

/ H , corresponding

to a

constant

of VVH Jî i .Si P))

that satisfy this prop erty.

the

curves

In and

i\ cross only once,

at the

cros.sing.

the

slope

of /„ is

the

slope of / L .

TO

appreciate

the

of

this property, define

the

as the ratio of the utility gains

of the

conspicu-

to the

utility losses associated with

of

conspicuous expenditure.

the

single-crossing property holds,

the

is always higher for households

the

single-

Definition:

Preferen ces satisfy

the single-

crossing property

if, for any

feasible (x, x , s,

s\ p)

with

0 ^ jt W^ix, s, p).

Example: Sup pose that hou seho ld utility

is additively separable

in

.v,

c, and p, and

that

the resource co nstraint is given by z ^ R s.

Then

9) W,ix,s.p = u{x)

w{p

In that case, Wiix , s , p)

s

W^x, s, p)

im-

plies

u(x ) - u{x) >

u(/? |.

- s) - u /?L -

s ).

But as

long as

i;

is

strictly c oncav e,

v{Ri -

s )

-

v ( R y _

-

s )

> v{Rt, - s )

-

v(Rn ~ s ) .

Combining these statements gives

us Wy^{x ,

s\

p) > Wu{x, s, p). Consequently, this

ex-

ample satisfies

the

single-crossing property.

Section

II

dem onstra tes that Veblen effects

cannot emerge

in our

model when

the

single-

crossing prop erty holds. Section

III

establishes

that, in contrast, Veblen effects do emerge un-

der altemative assumptions concerning house-

hold preferences.

II . Equilibrium with the Single-

Crossing Property

In this section,

we

ch aracterize

the

separat-

ing equilibria

of

this model when

the

single-

crossing property holds. Section

A

demo nstrates

that the model cannot generate Veblen effects.

Section B considers the robustness of this finding.

A.

Analysis

of

Veblen Effects

The following result demonstrates that

Veblen effects cannot arise when

the

single-

crossing property

is

satisfied.

T H E O R E M

1; Suppose that ihe single-

crossing property holds, and that, entering

stage

3, p^^ c .

Then every equilibrium

for

the continuation game has the property that

all households purchase the conspicuous

good

at the

quality-weighted price

p. Fur-

thermore, on the equilibrium path for the en-


10/26


)UNE

A formal proof of Theorem I appears in the

Appendix. The intuition for this result is as fol-

lows.

The fact that lype-L households buy the

conspicuo us good at the quality-weigh ted price

p

follows directly from Lemma I. It is certainly

possible for type-H households to discourage

imitation by choosing

(A,I, S^)

with ,Sn >

pxu.

But in that case, type-H households could also

consider signaling by purchasing a larger

quality-weighted quantity at a lower quality-

weigbted price. If the single-crossing property

is satisfied, then the benefit ratio is higher for

type-H households, which makes it possible to

choose an increase in quantity and a decrease in

effective price thai makes type-H households

better off, while leaving type-L imitators worse

oif. The intuitive criterion then guarantees that,

upon observing this deviation, social contacts

would infer that the deviator was of type H, and

respond accordingly. But in that case, the equi-

librium with ill > pxn would be undermined.

The second half of the theorem (conspicuous

goods of quality q are available at price p ^

c^) then follows from standard Bertrand-style

arguments.

The central idea of the theorem is illustrated

graphically in Figure 1. If type-H households

choose some (.I:H,-5H) with XH''-^H > c ' , s ingle-

crossing implies that the shaded area is

nonempty. Thus, it is possible for type-H

households to increase their utility, without in-

ducing imitation, by purchasing more of the

conspicuous good at a tower price. More gen-

erally, it should be evident from this figure that

efficient signaling is ordinarily inconsistent

with prices in excess of marginal cost unless

there are no points above /u, below /H , and

above the line

s

-

c ^x.

which would require

the indifference curves to be tangent at (x^,

Su)- This observation anticipates the main re-

sult of the next section.

Although Theorem I does not establish the

existence of an equilibrium satisfying the in-

tuitive criterion where

s^

=

C XH.

this follows

from standard arguments. Thus, our analysis

establishes thai, when the single-crossing

property h olds, there can be no Veblen effects:

no household would choose to pay a higher

price in order to enhance its status. To the ex-

tent signaling distorts the choices of type-H

good consumed (as in Ireland, 1992). rather

than by the prices or qualities of the brands

chosen.

B. Robustness

We now establish the robustness of the re-

sult obtained in Section II.A by examining the

roles of several potentially important, and

possibly objectionable, assumptions. The firs

of these concerns the nature of competition

among the producers of the conspicuous good

From the statement of Theorem 1. it should be

evident that the absen ce of Veblen effects does

not depend upon the nature of competition

among firms. Note in particular that, in every

continuation game, all households purchas

the conspicuous good at the lowest available

quality-weighted price,

p.

A different mode

of competition among producers of the con

spicuous good might produce an equilibrium

price other than

c ,

but would [lot alter th

nature of any continuation game.' ' Thus, re

gardless of the process generating price and

quality choices, when faced with a choice be

tween a higher-priced brand of the conspicu

ous good and a lower-priced brand of the sam

quality, households will always choose th

lower-priced brand.

In deriving Theorem 1. we h ave also as

sumed that the quantity of the conspicuou

good is variable. This assumption is appropri

ate even if conspicuous goods are discrete ob

jects that are used one at a time, such a

watches, cars, and silk ties. Someone possess

ing many expensive watches can w ear a Role

on Monday, a Patek Phillipe on Tuesday,

Cartier on Wednesday, and so forth. Similarly

there are well-publicized examples of wealth

- With other specifications of utility. type-H hous

holds might signal wealth through their choices of bot

quantity and quality. However, as long as the singl

crossing properly holds, they would never choose to ove

pay for a conspicuous good.

-' While we have constructed a Berlrand-style game i

which equilibrium prices are driven to marginal cost, o th

models of the competitive process might well produc

higher prices (for example, when entry barriers are hig

and producers sei capacity prior lo choosing prices, as


11/26

¥0L S6 NO. S

BAGWELL AND BERNHEJM: VEBLEN EFFECTS

359

celebrities who accumulate sta bl es of ex-

pensive automobiles. Although these individ-

uals wear only one watch at a time and drive

only one car at a time, they manage to display

quantity through ostentalious variety. More-

over, even when variety across time cannot be

observed (for example, if social contact is in-

frequent), the ability to select an array of con-

spicuous goods serves the same role as

variable quantity. If ownership of an Armani

suit does not suffice to differentiate the

wealthy from pretenders, those who wish to sig-

nal may add a Rolex watch; if that fails to do

the trick, they may also brandish a Mont Blanc

fountain pen, and a Hermes tie or scart. As long

as the single-crossing property is satisfied, ar-

gum ents analogous to those used in the pr(K)f of

Theorem I imply that households will prefer to

signal with greater variety (quantity of difler-

entiated conspicuous items), rather than by

overpaying for less variety.

Finally, as we now demonstrate, even if

quantity and variety are both fixed, Veblen ef-

fects still cannot arise in equilibrium, as long as

firms are free to vary quality.-' We modify the

model by assuming that each household pur-

chases either one unit of the conspicuous good

from a single firm at a single price and quality,

or none. A separating equilibrium for die sec-

ond phase of the game consists of

{q^, p\. q^,

PH ) with iq i , p, ) * ((?„,/?„) such th at ' '

10

and

( l l :

., P I ) •

Moreover,

pi

and

pi,

must be prices actually

named by firms in the first phase of the game,

and (/i and f/n must be qualities actually named

by firms in the first phase of the game.

Define

q^

as the solution to

maK^Wi_{ti{q),

c(q), Pt ) , and let W i_ denote the correspond-

ing maximized level of utility. We will assume

for simplicity that qi_ is unique, and that Wi >

W L ( O .

0, p ,| ), so that type-L households will

actually purchase the conspicuous good. We

will also assu m e ^'

12

Condition (12) lakes the place of condition

(8) (for the case of variable quantity) as

a sufficient condition for the feasibility of

deterring imitation without paying inflated

prices for the conspicuous good. '' In particu-

lar, type-L hou seho lds will not imitate type-H

households if type-H households purchase the

highest quality conspicuous good at a price

equal to marginal cost. W ith these changes , we

have the following theorem.

T H EO R E M 2: Supp ose that the single-

crossing property holds, and that each house-

hold buys at most one indivisible unit of the

conspicuous

good

Then

p , =

c(qi ) andp^

=

It is important to realize thai this conclusion does not

follow directly from Theorem 1 Even though quality is.

in our model, a perfect substitule lor quantity trom the

perspective of households, control over available qualities

reside.s with firms, rather than households. Since house-

hold.s must choose among the products that are actually

otfered. ihe case of lixed quantity and variable quality give

household.̂ much less discretion than the case ot variable

quantity.

-' It is conceivable that one might also construct a .sep-

arating equilibrium in which some households purchase

none of the conspicuous good. This would necessitate

modification of the incentive con.straints (10) and (It).

However, subsequent assumptions will rule out the pos-

A

proo f of this result is contain ed in the Ap-

f>endix. The intuition is similar to that given

for Theorem I. The fact that there is no

markup over marginal cost on units of the

conspicuous good sold to type-L households

Technically, with indivisibilities, we must also as-

sume that c(q) s .f, so that it is feasibie to purch ase one

unit of a conspicuous product with quality ^ at a price

equal to the marginal cost. This is not restrictive, since, in

the quantity-constrained modet, we could simply define

q

as c

' ( . D .

In some sense, condition (12) is less restrictive than


12/26

36 0

THE AMERICAN ECONOM IC REVIEW

JilNh. 199

follows from standard Bertrand-style argu-

ments; competition among producers will

make quality q^, available at price

c{qv_).

It is

certainly possible to construct an equilibrium

in which type-H households discourage imi-

tation by choosing {c/n. At) with pH >

ciq^).

But in tbat case, the single-crossing property

guarantees the existence of an alternative offer-

ing with higher quality and a lower markup, such

that typc-H households would strictly pre-

fer this alternative, while typc-L households

would strictly prefer {q^_, pi). The intuitive

criterion then implies that, if this alternative

was offered, and if a household selected it., so-

cial contacts vi/ould infer that the deviating

household was of type H. and respond accord-

ingly. Consequently, if the alternative is of-

fered. type-H households will select it. But this

undermines the equilibrium, since an entrant

would then have an incentive to offer this

alternative.

Notice that Theorem 2 is weaker than The-

orem 1, in the sense that it only describes

behavior on the equilibrium path.' ' ' In equi-

librium, households never purchase an exces-

sively priced conspicuous good, so Veblen

effects do not arise as an equilibrium phe-

nomenon. However, off the equilibrium path,

type-H households may well elect the more

expensive of Iwo equivalent brands, for the

simple reason that no other alternatives are

available, and acquisition of the less expen-

sive brand would not be sufficiently costly to

deter imitation by type-L households. Al-

though Veblen effects can therefore arise out

of equilibrium, it is important to reiterate that

even this is a fragile result. The existence of

even a single conspicuous good with flexible

quantity, or the existence of a large variety of

conspicuous goods (such as watches and

cars) each with fixed quantity, effectively

brings us back to the variable-quantity case,

and eradicates Veblen effects both on the

equilibrium path and out of equilibrium.

For completeness, it is worth mentioning the

case where both quantity ««(/quality are fixed.

It should be noicd thai this is

no t

anribulable to the

difference between cundilions (12) and (8) described in

Let q = 1 deno te the single feasible leve l o

quality. Once again, a standard Bertrand-styl

argument implies that some firm will sell th

conspicuous good at price p = c \), and tha

type-L households will purchase this brand

Define p^ as the solution to '

( 1 3 ) l V L ( M n . c ( l ) . p , _ )

It is easy to verify that, in any equilibrium sa

isfying the intuitive criterion, some firm wi

offer the conspicuous good at price pn, an

type-H households will purchase this brand

despite the availability of an equivalent prod

uct at the lower price, c(l ). Thus, the fixed

quantity, fixed-quality case gives rise to Veble

effects even in equilibrium. This is the es

sence of the signaling equilibrium describe

by Wolfgang Pesendorfer (1995), It shoul

be evident, however, that Veblen effect

when generated in this way, are highly fragil

and depend on a variety of tenuous assump

t ions, including (i) households cannot var

quantity (either by changing the amount use

at one time, or by using distinguishable uni

at different points in time), (ii) firms cann

vary quality, (iii) there are no other conspic

uous goods with either variable quantity o

variable quality, and (iv) there exist rela

tivety few categories of conspicuous good

so that households cannot display wealt

through ostentatious variety.

III.

Equilibrium Without the Single-

Crossing Property

In the last section, we demonstrated th

Veblen effects cannot arise when the singl

crossing property holds if quantity, qualit

or variety is variable. However, signalin

equilibria may exist even when the single

crossing property is violated. This observatio

suggests that it may be possible to genera

Veblen effects under less standard assump

tions.

In this section, we focus on cases

which the violation of the single-crossin


13/26

VOL 86 NO. J

BAGWELL AND BERNHEIM: VEBLEN EEEECTS

FIGURE 2. TH I; TANGKNCV

property lakes a particular form, which we re-

fer to as the tangency property. At this point,

we introduce this property as a technical con-

dition, and explore its implications. In Section

IV. we identify more primitive conditions

from which this property can be derived.

Definition:

Preferen ces satisfy the

tan-

gency property if there exists a con tinu ous

function s*{x) such tha t for any (.v, x , s )

(with s ^

s*ix)),

WiXx , s , PH) = W^ix,

s*{x), PH) implies Wiiix , s , pn) < W^ix,

S*(X),PH).

We illustrate this property in Figure 2. No-

tice that the indifference curves /, and lu

(which presupposep = p,,) are tangent to each

other where they cross the function .V*{.Y).

This could occur, for example, if the benefit

ratio (defined in Section I.F) is higher for

households with greater resources when total

conspicuous expenditures are less than 5*(.v),

and lower when conspicuous expenditures ex-

ceed 5*(.r) .

When the tangency property is satisfied,

mutual nonimitation may be infeasible. We

therefore use the following additional condi-

tion to guarantee the existence of separating

equilibria.

Definition: Separation is feasible if there

exists(.rH,.v,,)

^ l.xT{c ), c xlic ))withsn/

Xu ^ c such ihaHxtW ), c xfAc ), XH, su )

satisfies expressions (4) and (5) (incentive

compatibi l i ty ) .

The remainder of this section is organized

as follows. Section A dem ons trates that

separation is feasible). ** In equilibrium, some

firms market bu dg et brands (which are

sold at a price equal to marginal cost), while

others sell lu xu ry brands (which are sold

at a price above marginal cost, despite the fact

(hat producers are perfectly competitive).

Luxury brands are not intrinsically superior

to budget brands but are purchased by con-

sumers who seek to signal high levels of

wealth. Section B examines the robustness of

this finding.

A. Analysis of Veblen Effects

To analyze the characteristics of equilibria

when the tangency property holds, we require

some additional notation. Specifically, let jf*

denote the solution (if any) to the equation

(1 4 ) W , (x * , J * ( ^ * ) , P H ) = Wlic ).

We illustrate this solution in Figure 3. where

we have superimposed the indifference curve

desc ribed by the equation W, (.v, s, p^) =

W*{c on .S '* ( J : ) . The point x* corresponds

to the intersection of this indifference curve

an d

s*(x).

It is, of course , possible that .v*(.v)

could He everywhere below, or everyw here

above, the indifference curve of interest, in

which case there would be no intersection. For

our central result, we will simply assume the

existence of a unique intersection.'' ' In Section

IV, we discuss conditions under which this as-

sumption is satisfied.

It is easy to verify that the indifference curve

of interest must lie strictly above the line s =

c ^x at the point jt* (f ' ).^ Thu s, depending on

**

Veb len effects may arise wh en ihe liingle-crossing

property fails to hold, even when the tangency property is

no t satisfied. How ever, ihc analysis of equilibHn is partic-

ularly tractable when the tangency property holds.

Once existence is assumed, it is easy to establish Ihat

the intersection musi be unique. Specifically, if a type-L

indifference curve crosses .^*(,v) more than once, it must

be tangent to the same type-H indifference curve at each

crossing (otherwise lype-H indifference curves would

cross) .

But this contradicts the strict inequality in the def-

inition of ihe tangency property.

'Consider s solving W.j.xtic -), s, pn) = Wu(x*.

s*{x*).

/?„). Since 1V,(J*, .V*(A*). p^,) = WyixTic ),


14/26


JUNE 199

the location of ,?*(.r), it is certainly possible

that 5*(.v*) would exceed f'^.v*, as shown

in Figure 3. The following result demonstrates

that Veblen effects do arise in equilibrium for

this case.

THEOREM 3 :

Suppose that the tangency

property holds, that separation is feasible,

and that s *{x*}/x

= / ?* > c^ . Then(i) (x^.

sO= (x


15/26

VOL.

86 NO. 3


36 3

returns to scale technology, and Bertrand-

style pricing—conditions that would yield

marginal-cost pricing (even when indiffer-

ence is resolved in favor of incumbents) with

ordinary formulations of preferences.

B.

Robustness

We now establish the robustness of Veblen

effects when the tangency property holds by

examining the roles of several potentially im-

portant assumptions, including those high-

lighted in Section II.B.

Once again, it is evident that different as-

sumptions about the nature of competition

among producers of the conspicuous good

would not qualitatively alter our result. Our

analysis of signaling equilibria for the second

phase of the game implies that, regardless of

the process generating p and p , type-H house-

holds will, in a wide range of situations, select

a higher-priced brand over a qualitatively

equivalent lower-priced brand.

Vebien effects are also robust with respect

to the altemative assumption that quantity is

fixed (at one unit). For the same reasons as in

Section II.B, competition among producers

will make quality

171,

available at price c{qi_)

(where the definition of ^ 1 is unchange d). De-

fine

(7*

as the solution to

1 5

The term q* serves a role analogous to that of

X* from the variable-quantity case (see equa-

tion (I 4 )i n Section III .A). Using an argument

completely analogous to that given in the

proof of Theorem 3, it is possible to show that.,

a s l o n g a s 5 * ( / x ( ^ * ) ) > c ( ^ * ) , type-H house-

holds purchase quality q^ = q* at price p^ =

s*{fi{q*)),

and that the othe r features of Th e-

orem 3 are unchanged. Naturally, Veblen ef-

fects also arise if both quantity and quality are

fixe

Anotherfeatureof equilibrium with variable

quantity described in Theorem 3 is that all

firms choose to produce the first-best quality,

q . Thu s, despite the imposition of assu mp -

tions that would yield marginal-cost pricing

under standard formulations of preferences,

cific choice of q is a somewhat special

consequence of assumptions about functional

forms. H owe ver, the finding that firms will not

dissipate profits through quality competition is

quite general, and holds even when quality is

not a perfect substitute for quantity. To clarify

this point, consider the equilibrium described

in Theorem 3, where type-H households pur-

chase x*lpiq ) units of a quality q*^ conspic-

uous good at a total cost of ,?*(.«*). Now

suppose that some firm can. through some

costly activity (for example, advertising or in-

novation), enhance the value of its product. If

it undertakes this action without changing

price or quality, it will not succeed in luring a

single buyer away from its competitors. The

reason is that the activity would also enhance

the value of the product for type-L hou sehold s,

who would then prefer this enhanced package

to ( . i :*(c ' ) , c^xtAc )). Thu s, the enhanced

package would not function as a signal of

wealth, and thereby attract type-H households,

unless the producer simultaneously raised

price and/or lowered quality.*-

A final robustness issue concems our as-

sumption that there are only two types of

households. When the single-crossing prop-

erty is satisfied, the extension of our model to

an arbitrary number of types is completely

standard. Although standard argum ents do not

apply when the tangency property holds, a

somewhat stronger version of this condition

permits the introduction of additional types

with little added com plex ity.' ' S uppose in par-

ticular that there are / + types of households

indexed / = 0. 1 .2, ... , / , with resou rces /?,

(Rj < Ri for j 0, we

will assume that there exists a continuous

function sf {x) such that for any {x, p,x , s ,

p ' ) w i t h s ' * s*(x), Wu{x ,s ,p ) = Wn{x,

s*(x), p) i m p l i e s W^x , s , p ) < W^ix,

'" In an earlier versio n of this paper (B agw ell and

Bemheim, 1992), we considered a model with advertis-

ing in which advertising enhanced ulilily. but. unlike

quality in the current model, did so in a way that was not

a perfect substitute for quantity. We demonstrated that

firms would not dissipate profits through competition in

advertising.

" This analysis extends that of Bemheim (1991), who,

in a much different context, analyzed signaling equilibria


16/26

6


JUNE 199

sf (x), p).^* We u.se ,Y,* to denote the solution

to

W,> xf.

5 ,*{-r*) , p,) = W , t ( t ' ) ( w h er e

W *ic ̂ ) is defined analogously to W l{c )).

To construct the equilibrium, we assign type-0

households the bundle (x*(c ), c x*(c ))

(analogously to type-L households in the two-

type ca se ), and type-/ > 0 households the bun-

d le (x f , s*(x*)). In other word s, we select

the bundle for each type-/ > 0 household to

deter imitation by the lowest type, rather than

(as in the standard case) by its next lowest

type. With a pair-wise analog of feasible sep-

aration between type 0 and each type /. this

assures us of mutual nonimitation for each

{0 , /) pair. Note that W^ixf . s* (x? ) , p , ) =

pair (with i, j > 0). It follows immediately

from this observation and the modified tangency

condition that mutual nonimitation is satisfied

for (/,y) (strictly iis* {x* ) # .s*{.x*)).

IV. Are Veblen Effects Plausible?

Our analysis has isolated theoretical condi-

tions that allow us to rationalize the existence

or nonexistence of Veblen effects. However,

the fact that it is possible to produce Veblen

effects under some appropriate set of assump-

tions does not necessarily imply that one is

likely to observ e these effects in practice . In-

deed, the conditions required to generate

Veblen effects may strike the reader as im-

plausible. In this section, we examine the

plausibility of the tangency property. We

then discuss in greater detail the effective-

ness of conspicuous expenditures as a signal

of wealth.

A. Justifications for the Failure of the

Single-Crossing Property

In this section, we demonstrate that the tan-

gency property can be derived from more

primitive assumptions. Three separate exam-

ples are considered.

Note [hat. under this assump tion, the locus of tan-

gencies between inditference curves is independent of p.

Example 1: Personal Bankruptcy. Con

sider a modified version of the game, in whic

consumers must borrow to finance conspicu

ous expenditures, and where loans to house

holds are potentially risky, since household

may choose to default. The game unfolds i

five stages rather than four, with the set o

agents expanded to include a large number o

potential creditors, who can borrow and len

money at the riskless rate /* (their opportunit

cost of funds). First , each incumbent / a n

nounces quality q and price, pf, for the con

spicuous good, and each creditor n announce

an interest rate, r,,. Second, potential conspic

uous good producers observe these qualities

prices and interest rates, and then decid

whether to enter. If a firm chooses to enter,

announces a quality and price for the conspic

uous good. Third, consumers observe all an

nounced qualities, prices and interest rate

and determine the amounts of the conspicuou

good to be purchased from each firm. Sinc

incom e is not received until stage 5. these pur

chases must be financed through borrowing.''

We assume for simplicity that creditors can

not monitor the total indebtedness of any cl

ent. Thus, households can obtain any desire

loan at the prevailing rate market of interes

rS: r*. Fourth, social contacts observe hous

holds ' b randed consp icuous-consumpt io

bundles, form inferences about household

resources, and react accordingly (choos

/?). '

Social contacts do not observe hous

holds '

choices of lenders. Fifth and finall

income (R ) is received and loans matur

Each household has the option to default o

its loan, in which case creditors receive a

'^ Nothing would change if households received a po

tion of their incomes prior to stage 3. The extreme a

sumption that all income is received in stage 5 is made f

simplicity only.

Note thai inferences are draw n in stage 3. prior lo t

lime at which bankruplcy may be declared. We have ther

fore assumed implicitly thai a deciaralion of hankniplc

would not affect status (possibly it is uno bservab le). How

ever, this assumplion is not essential. Even when a de

laration of bankruptcy negatively affects stalus, th

marfiinal cost of conspicuous spending will be higher f

higher-income households pasl the point where the ban

ruptcy con.straint binds for lower-income household


17/26

VOL. 86 NO. 3

BAGWELL AND BERNHEIM VEBLEN EFFECTS 36 S

enforceable claim against the household's

income. Since bankruptcy protection allows

the household to retain resources of the

amount z, independent of type, a declaration

of bankruptcy leaves the household with re-

sources equal to max [z, R - {\ + r)s}. W e

assume that the household's conspicuous

consumption is unaffected by bankruptcy (in

other wo rds, the conspicu ous good cannot be

repossessed) ." All residual resources are

spent on the inconspicuous good at the end

of stage 5. As in the example in Section I.F.

utility is additively separable, U,ix, s, p) =

u{x) + vis) + wip).

Once creditors have selected interest rates,

the game is merely a special case of the model

considered in Section III. The utility of the

household is described by equation ( 3 ) , where

(1 6 ) y(s.R,) = max {z,R - (1 + '•).v .

Indifference curves in the {.r, s) plane for

type-L households, /, , and for type-H house-

holds, /H , are depicted in Figure 4. It is easy to

verify directly that, given appropriate ch oices

of

c

and .v̂ , Ihe tang enc y prop erty ho lds for

this model (including the stronger version of

the condition introduced in our discussion of

multiple types), as shown in Figure 2. In ef-

fect, the marginal cost of conspicuous con-

sumption is higher (and the benefit ratio is

lower) for type-L households as long as total

expenditures do not exceed s* = (/?L ̂ z) /

(I -I- r). However, for higher levels of con-

spicuous spending, the marginal cost is higher

(and the benefit ratio lower) for type-H house-

holds."* Since, in this example, 5* is indepen-

dent of .V, we abbreviate

s*{x)

as

s* .

^ This assump tion requires some Justification. Between

the purchase of a conspicuous good and a declaration of

bankruptcy, some or all of that good may be consumed or

depreciated Mo reover, bankruptcy courts often allow in-

dividuals to retain expensive possessions (see, for exam-

pie,

Kirstin Downey, I99l:or Richard Hylton, 1991). One

could, at Ihe cost of introducing considerable analytic

complexity, instead assume that, in the event of bank-

ruptcy, a household consum es some fraction \ (0 < \ <

1) of its conspicuous possessions, while the remainder,

(1

—

\)x. is reposse ssed. It does not appear that this would

disturb the qualitative features of our analysi.s.

" 'F or ,v C ' J : * ( C ' ^ ) ,

their bankruptcy constraint does not bind.

Since type-H households spend the amount

s* = (/?L ^

z)/{

I + /•*) on conspicuous con-

sumption, their bankruptcy constraint does not

bind either. Hence, (he casual observer would

conclude that bankruptcy constraints are irrel-

evant. But this is certainly not the c ase — w ith-

out the bankruptcy constraint. Theorem 1

applies, and no Veblen effects emerge. The

key to this apparent puzzle is that type-L

households are influenced by the fact that they

""Since ,?,*(.«:*) = s*{x ) = .i* fo r/ ,) > 0, it does not

follow that the mutual nonimitation constraints hold

strictly. Indeed, while each type

i >

0 strictly prefers to

differentiate itself from type 0, all other incentive com-

patibility conditions hold with equality. If income was un-

certain as in Bagwell and Bemheim (\ i92]..s*(x*) would


18/26

366


JUNE 99

would

confront a binding bankruptcy con-

straint // they attempted to imitate the type-H

households. Furthermore, with the introduc-

tion of income uncertainty, default does occur

with positive probability, while the other

features of the equilibrium remain qualita-

tively unchanged (see Bagwell and Bemheim,

1992) .

This is consistent with evidence that

many wealthy individuals are at significant

risk of bankruptcy (see, for example, Michael

Allen, 1991), and that this risk is often asso-

ciated with the acquisition of costly, conspic-

uous possessions. '

Example 2: Taxation. Supp ose that, as in

Exam ple 1, utility is additively separable. Sup -

pose also that some conspicuous expenditures

(such as lease payments on luxury automo-

biles,

or mortgage payments on expensive

homes) are deductible expenses for the pur-

pose of computing personal income taxes, and

that marginal personal income tax rates de-

cline with taxable income over some range

(we note that the U.S. tax code has satisfied

this condition since 1986 due to the ta ke

ba ck of personal exemptions and itemized

deductions). More specifically, suppose that

taxabje income is given by Y = R s, that the

first Y dollars of taxable income are taxed at

the rate r,, and that additional taxable income

is taxed at the rate_T2, with T, > T2. Assume

further that

R^

>

Y.

Then

(17 )

+

( r , - r . ) m a x { 0 , / e

- s - ?}

In this case,

s* = Ri_ -

K( which is indepen -

dent of .V, as in Exam ple 1) . It is easily verified

that, as long as either the curvature of v is not

too great, or R ̂ -

Ry^

is relatively small, then,

under appropriate choices of t'^ and J, the tan-

gency property holds (including the stronger

One reporter recently summarized this relation as fol-

lows:

' In the 1980s, people lived out their materialistic

dreams, overspending on BMWs, huge boats, Caribbean

vacations and dream condos, bankruptcy lawyers say.

Then came the real estate crash and the job layoffs. Now ,

version introduced in our discussion of mul

tiple types).

Example 3: Intrinsic Utility. Suppose tha

utility is given by the expression

(18 )

w p

for / = L, H. where ^L > ^H > 0. In othe

words, assume that type-L households receiv

greater intrinsic utility from consuming luxury

goods, perhaps because of no ve lty value

or because of personal satisfaction derived

from ac tin g rich. Assum e also that the

household faces the budget constraint z = R ~

s. For simplicity, assume that

uix) = x.

It i

then possible to verify that, under appropriate

choices of c' ' and s' , the tangency propert

holds i f v'{Ri,)/v'(Ri) < 9^19 ^,, and i

v'iRn - s)lv'(R\_ - 5) declines with 5.- Thi

final property requires v'


19/26

VO L H NO 3


367

little or no attempt to observe it), and it must

be interpreted as evidence of substantial re-

source dissipation. Thus, one can certainly de-

stroy substantial resources by burning dollar

bills on one's front lawn, but relatively few

peop le will observ e this activity since it is both

brief and localized. It is also possible to waste

substantial resources in numerous small incre-

ments during the normal course of social in-

teraction, for example by tipping excessively

at every opportunity. H owever, since other in-

dividuals observe this behavior only at isolated

moments, tipping serves as an effective signal

only if others believe that current behavior is

representative. In contrast, expensive durable

goods, including one's automobiles, jewelry,

and clothing are all ob.served regularly by

numerous other individuals during the nor-

mal course of social interaction, and pro-

vide durable emblems of substantial resource

dissipation.^'

The predisposition for signaling wealth

through the purchase of expensive, conspicu-

ous, durable goods does not completely re-

solve the issue of indeterminacy. While we

have focused on the case of a single conspic-

uous good (with many brands), the extension

of our analysis to an arbitrary number of con-

spicuous goods is straightforward and yields

essentially identical conclusions, except thai

the distribution of demand across conspicuous

goods is indeterminant. Thus, our theory does

not explain which durable, conspicuous goods

households will choose as signals. Given the

diversity of actual behavior, we regard this as

a virtue, rather than a difficulty.

One might also wonder why households do

not simply publish tax returns or audited asset

statements. If one takes our theory literally, it

is also difficult to understand why consumers

•- The observation that agents can bum money in a va-

riety of different ways is troublesome in other contexts,

such as financial market signaling. Since investors have

strong incentives to leam all relevant information about

stocks, the firm need not undertake dissipative activities

thai investors w ill observe w ith little or no effort, nor need

they seek durable emblems of dissipation (since potential

investors can always review fmancial records). Thus, one

can entertain general doubts about models with money

remove price tags from their conspicuous pos-

sessions. Obviously there are other important

considerations that influence the choice of a

signal; completely transparent exhibitions of

wealth seem socially unacceptable. An exam-

ple of tbese kinds of concerns has been de-

scribed by The Economist (1993 p . 98 ) : M en

flocked to the likes of Patek Philippe and Ebel,

apparently because watches are the one sort of

luxury good that has what the marketers at

Cartier smilingly describe as a 'functional

alibi ' . '

C .

The Observability of Price Concessions

Another assumption implicit in the analysis

of Sections II and III.A is that firms cannot

make a secret price concession to any given

buyer. If secret concessions are possible, then

the equilibrium described in Section III.A will

break down: type-H agents prefer to buy the

conspicuous luxury good at a lower price, as

long as they still get credit for purchasing it at

the higher priee.'*^

There are many possible solutions to this

problem. Each luxury brand producer clearly

has an incentive to comm it him self to a policy

of making no secret concessions. Indeed,

the argument in the preceding paragraph im-

plies that the signaling value of conspicuous

consumption is present only if the producer

has made a credible commitment of this sort.

One approach is to rely on intermediaries. By

selling products to intermediaries (for example,

car dealerships) at publicly observable prices

that exceed marginal cost, the manufacturer

places a lower bound on secret price conces-

sions (equilibrium prices cannot be less than

dealer invoice'). Another possibility is that

manufacturers will rely on reputations. Once a

luxury brand acquires a reputation for being

sold at heavy discounts, the sn ob va lu e as-

sociated with its purchase may be eroded.

In practice, manufacturers of luxury goods

do indeed adopt these kinds of mechanisms in

order to maintain high prices. According to

The Economist

(1993 p . 98) :

This motivates manufacturers to thwart the distribu-


20/26

368


JUNE 1996

Recently a fight broke out between big

pertume houses and a clutch of British

retailers who , having bought such brands

as Chanel No. 5 on the grey ma rket ,

were then reselling them for 60% below

the recommended price. For some com-

panies, like Vuitton, the solution is to re-

strict sales outside their own boutiques.

Those that use specialist distributors

must monitor them closely. Cartier has

one person in Paris whose sole respon-

sibility is to keep tabs on its watches

once they leave the workshop.

V. Policy Implications and Conclusions

The existence of Vebien effects in the con-

text of our model has some provocative im-

plications for public poliey. Since supranormal

profits result from the characteristics of de-

mand rather than from the nature of strategic

interaction among firms, evidence of high

profitability does not necessarily support in-

ferences of either collusion or oligopolistic

forbearance.

The implications for tax policy are equally

controversial. Within our model, the equilib-

rium prices of luxury brands are demand

driven, rather than supply driven—that is, lux-

ury brands are sold at the co nsu m er's preferred

price, w hich is tax inclus ive, and does not vary

with the tax rate. Thus, as long as the tax per

unit does not exceed the difference between

the consumer's preferred price and marginal

cost, and as long as the tax does not fall on

budget brands, an excise tax on conspicuous

goods amounts to a nondistortionary tax on

pure profits.

Consider, for example, tax-price relations of

the form

rip)

= max {0,

t(p - k)].

whe re the

parameters / and k satisfy 0 < / < I and k ^

c(q )

(so that, in equilibrium , the tax falls

only on luxury brands).* It is easy to verify

that equilibrium quantities and prices are in-

variant with respect to /, and that the tax is

therefore equivalent to a nondistortionary levy

on pure profits. This family of tax schedules is

of particular interest, since it includes the fed-

^ The analysis proceeds similarly as long as rU iq }} =

eral luxury taxes created by the Omnibus

Budget Reconciliation Act of 1990 (OBRA).

In particular, this Act imposed a 10 percent

excise tax (r = 0.1 ) on the portion of the retail

price of certain items that exceeds a product-

specific threshold

(k).

The thresholds were

$30,000 for automobiles, $100,000 for boats

and yachts, $250,000 for aircraft, and $10,000

for jewelry and furs.^

It is worth emphasizing that traditional

modes of analysis would produce highly mis-

leading conclusions within the current context.

Suppose that the inconspicuous good, ~, is

nontaxable. Assuming that the planner's ob-

jective is efficiency, rather than distribution,

the preceding analysis implies that only luxury

brands should be taxed (as long as revenue

requirements are not too high). In contrast,

since the demand for luxury brands in our

model is highly price elastic, the application

of traditional Ramsey-style optimal tax for-

mulas would suggest that the government

should raise a significant fraction of its reve-

nue by taxing budget brands. ^^

We mentioned in Section IV.B that, in a

model with many conspicuous goods, the dis-

tribution of demand across conspicuous goods

is indeterminant. This implies thai the re-

sponse to an increase in the luxury tax rate on

some specific conspicuous good is also inde-

terminant. It is possible, for example, that

prices could simply adjust so Ihat profits shift

to a more lightly taxed industry (with side-

payments among firms, one might even expect

this to occur). Thus, there may be advantages

to adopting a reasonably broad-based luxury

tax, such as the one originally envisioned in

OBRA.

Our results on luxury taxation stand in sharp

contrast to those of Ireland ( 1992) and Ng

( 1 9 8 7 ) . Ireland considers a signaling model

of conspicuous consumption that satisfies the

single-crossing property (and which, there-

fore,

does not give rise to Veblen effects). In

his model, a tax on luxury goods does dis-

• The 1994 threshold for automobiles was $32,000,

wbiie the luxury tax on all other goods has been repealed

effective January 1993,


21/26

VO

NO i

BAGWELL AND BERNHEIM: VEBLEN EFFECTS

36 9

tort behavior. However, since equilibrium

involves excessive consumption of the con-

spicuous good, the tax may actually be wel-

fare improving. Ng studies optimal taxation of

a special class of commodities, which he labels

diamo nd good s, for which consumers

pref-

erences are defined over the amount of money

spent on acquisition, rather than over amounts

consumed. Since a change in the price of a di-

amond good does not alter the utility received

by consumers, the optimal rate of taxation for

a diamond good is infinite. The contrast be-

tween our results and those of Ireland and Ng

therefore reveals the .sensitivity of policy im-

plications to the particular formulation of the

demand for luxury goods.

APPENDIX

PROOF OF THEOREM 1:

To prove the first part of this iheorem, we

begin by applying Lemma I, which tells us

that all type-L households purchase .xfip)

quality-weighted units at p. Next, we claim

that type-H households will also purchase all

conspicuous units at the quality-weighted

price p. We establish this claim by supposing

that, on the contrary, s^/Xif > p, and inducing

a contradiction. The argument leading to the

contradiction consists of four steps.

Step I: The incentive com patibility con-

straint binds, that is,

( A l ) W L(-rH.VH,pH)= WUP)-

Suppose on the contrary that this is not the

case. Then the right-hand side of ( A l ) must

exceed the left-hand side (otherwise incentive

compatibility would be violated). Consider

(.XH, S H), with s u slightly less than .^H, and

X H = x^^,

such that

.V|'|/-VH ^

£, and such that

incentive compatibility still holds with strict

inequality. Then type-L households prefer

their equilibrium

payoff,

W * ( £ ) , to

(.v, ,, 5 H,

p) for all p G [pi_, p,il- In contrast, there are

some values of p e [pu, pul (specifically, p n)

for which type-H households prefer

(JCH,

^ H ,

p) to their equilibrium outcome, (.Vn, .VH- PH)-

Thus,

by the logic of the intuitive criterion,

social contacts must infer R = R^ upon ob-

s ,i,

Pn) in particular to their equilibrium out-

come.

(AH, .VM.

PH)- Thus, the candidate equi-

librium fails the intuitive criterion. This

establishes that (AI ) must hold.

Now we define x as the maximum value of

X G

[J :II,

sip] satisfying

( A 2 )

W, x,px,pn)=

W^Ap).

Step 2:

V

is well defined, x >

,Vn,

and ^.v <

s. First, note that T ^ Si, > p.x^i, so x,i < s lp,

implying that the feasible set is nonempty. N ext,

note that

(A3) H/,,(.V,

and

( A 4 )

(where the last inequality follows from (8)).

( A 3 ) ,

(A4), continuity, and the intermediate

value theorem give us existence oix. x =/= x^

(and therefore

.x >

.VH) follows from (A 3 ).

Finally, since x < s^/p (.x ^ Jlp^ follows from

(M)), px WH (;CH, AH, PH )-

This follows from the single-crossing prop-

erty, since .x > x^ and IV, ( i , p^x, pn) =

W*{p^) = WL(XII,

.9,),

P H )

(which in turn im-

plies /).v > .TH, since x > Xu).

Step 4: The re ex ists .r,',, .vf, with si, =

px u such that IV,

(.v, ,. .VH,

pa) < W tip) an d

P

let

x n

= i 4- e and

s\\ = pxi,.

For e > 0

sufficiently small, {x{,. s u) necessarily satisfies

the required properties (recall that .x is defined

as the largest value of x satisfying (A2)).

Now we assert that the candidate equihbrium

fails the intuitive criterion. This follows from

step 4 through an argument completely antilo-

gous to thai given in step 1 above. Thus, we have

the desired contradiction, and we conclude that

type-H households must purchase all conspicu-

ous units at the quality-weighted price p.

The second part of the theorem is an im-

mediate corollary of the first part. The free

entry assumption, combined with the usual


22/26


JUNE 1996

and sell their products at price c{q ) =

/i(f7^)c^ Clearly, only conspicuous goods

of quality q will be available at quality-

weighted price c ' . so only these will be

produced.

PROOF OF THEOREM 2:

We begin by establishing that, in equilib-

rium, some firms offer, and type-L households

purchase, a conspicuous product of quality q^

at price C ( ^ L ) - Suppose on the contrary that

{?L.

P\^ ^ iqi.> c{q\_)).

Since firms cannot

lose money in equilibrium, either C/L =̂ q\_ and

Pl. ^ c{qi), or ^L = qL a n d P > c{qi_). In

either case.

( A 5 )

choose this alternative regardless of socia

contacts' inferences, while type-H households

would choose this alternative for some infer-

ences, for example, p,,). Consequently, if this

alternative is offered, type-H households wil

select it. Knowing this, it is in the interest of

an entrant to offer (f/n, pit), which under

mines the equilibrium.

Now define q as the m aximum value of ^ G

[qn,if] satisfying

( A 7 )

Step 2 : lj Is we ll-defined, and q > q> q\\

Since, by supp osition,pn >

( A 8 )

for some small ^. Suppose then that an entrant

offered ^,. at price c\qy) + e. For any house-

hold electing the ent ran t's offering, social con-

tacts must respond with

p ^

p]_. Therefore, by

( A 5 ) ,

all type-L households will purchase the

conspicuous good from the entrant. This im-

plies that the entrant w ould eam a profit, which

contradicts the supposition that an equilibrium

prevails.

Now we establish thatpH = c{qn). Suppose

on the contrary that /?,, > c{qn) (this is the

only other pos.sibility, since, in equilibrium,

price cannot be less than marginal cost). We

induce a contradiction through four steps (the

argument here is analogous, but not identical,

to that used in the Proof of Theorem 1).

Step I: The incentive compatibility con-

straint binds, that is

( A 6 )

Suppose on the contrary that this is not the

case. Then the right-hand side of (A6) must

exceed the left-hand side. Consider ( qw) follows from

( A 8 ) . q * ^(and therefore q < q) f

Documents

Veblen Effects in a Theory of Conspiscuous Consumption