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Massachusetts Institute of Technology
Department of Economics
Working Paper Series
SHROUDED ATTRIBUTES, CONSUMER MYOPIA,
AND INFORMATION SUPPRESSION IN
COMPETITIVE MARKETS
Xavier Gabaix
David Laibson
Working Paper 05-1
April
2005
Revised October 3, 2005
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http://ssrn.com/abstract=728545
MASSACHUSETTS INSTITUTE
OF TECHMOLOGV
OCT
1
3
1
2005
LIBRARIES
SHROUDED ATTRIBUTES, CONSU^IER IvIYOPIA, AND
INFORlvJATION SUPPRESSION IN COMPETITIVE
MARKETS*
Xavier Gabaix and David Laibson
October
3,
2005
Abstract
Bayesian consumers infer that hidden add-on prices
likely to
be high
prices. If
consumers are Bayesian, firms
rium. However, shrouding
Such shrouding creates an
may
(e.g.
the cost of ink for a printer) are
will
not shroud information in equilib-
occur in an economy with some myopic (or unaware) consumers.
inefficiency,
ucating their competitors' customers.
which firms
may have an
However,
add-ons have close substitutes, a "curse of
if
incentive to eliminate by ed-
debiasing" arises, and firms will not be able to profitably debias consumers by unshrouding
add-ons.
In equilibrium, two kinds of exploitation coexist.
Optimizing firms exploit myopic
consumers through marketing schemes that shroud high-priced add-ons. In turn, sophisticated
consumers exploit these marketing schemes.
ness of sophisticates. It
non-exploitative firms.
itive
is
It is
not possible to profitably drive away the busi-
also not possible to profitably lure either
We show that
myopes or sophisticates to
informational shrouding flourishes even in highly compet-
markets, even in markets with costless advertising, and even when the shrouding generates
allocational inefficiencies.
"For useful suggestions we thank our editor and referees, Daron Acemoglu, Simon Anderson, Mark ArmAndrew Caplin, Kenneth Corts, Peter Diamond,
Avinash Dixit, Glenn Elhson, Sarah ElUson, Drew Fudenberg, Edward Glaeser, Joseph Farrell, Robert
Hall, Ah Hortacsu, Sergei IzmaLkov, Paul Joskow, Paul Klemperer, Juhe Mortimer, Barry Nalebuff, Aviv
Nevo, Ariel Pakes, Nancy Rose, Jose Scheinkman, Andrei Shleifer, Chad Syverson, David Thesmar, Jean Tirole, and seminar participants at Berkeley, Columbia, the Federal Trade Commission, Harvard, Massachusetts
Institute of Technology, National Bureau of Economic Research, New York University, Northwestern, Princeton, Stanford, Toulouse, the University of Virginia, Wharton, Yale, the 2003 European Econometric Society
meeting, the 2004 American Economic Association meeting, and the 2004 Duke-Northwestern-Texas Industrial Organization Theory conference. Nathan Barczi, David Borden, Carlos Caro, Steve Joyce, Dominique
Olie Lauga, Laura Serban, Kelly Shue and Chen Zhao provided great research assistance.
We acknowledge financial support from the National Science Foundation (SES-0099025). Emails: xgabaix@mit.edu,
dlaibson@arrow.fas.harvard.edu.
strong, Ian Ayres, Robert Barro, Douglas Bernheim,
Introduction
I.
When
consumers make mistakes, firms
competitive pressm'e
may undermine such
reveal the exploitation
consrraiers
error
first
We
this paper,
study the market
we
some markets,
identify
when such competitive
—
printer cartridges
add-ons
for
e.g.
—
proposed by Glenn Ellison [2005, section V.C], who suggests that some
do not think about add-ons when they buy a base good.
and determine when competition
Our paper
In
For example, competing firms could
exploitation.-
and win over customers. In
debiasing will and will not occur.
and develop an idea
will try to exploit those mistakes.^
We
formalize this consiuner
will lead to debiasing.
motivated by the observation that firms choose to hide information fiom consumers.
is
For example, banks prominently advertise the virtues of their accounts, but the marketing materials
do not highlight the costs of such an account which include
minimum balance
them.
Indeed,
fees, etc.
Banks could compete on these
many bank customers do
ATM
costs,
usage
fees,
bounced check
fees,
but they instead choose to shroud
not learn the details of the fee structure until long after
they have opened their accounts.
Cruickshank [2000] reports results of a U.K. Treasury survey that investigates the origins of high
fees in the
fees for
U.K. banking
common
sector.
Half of the respondents report having no information about the
financial services at their
own bank.^ The
to supply banking services to personal customers
[...]
report concludes that "In the markets
few consumers are aware of the terms and
conditions of the products they hold, pointing to significant information problems."
The
printer market operates in a similar way.
their Inkjet printers, but
that cost ten times
do not compete on the principal cost of ownership: patented ink cartridges
more than the
printer itself over the Ufe of the product.
only 3 percent of printer owners claim to
Indeed, printer manufacturers try to
A
Printer manufacturers advertise the low price of
know
make
HaU
[2003] reports that
the printing cost at the time they buy their printers.
these costs invisible.
For example, the printing cost
growing literature models markets in which sophisticated firms interact with consumers who may have psychoFor example, see DellaVigna and Malmendier [2004], Gabaix, Laibson and Li [2005], Glaeser [2005],
Heidhues and Koszegi [2005], Jin and Leslie [2003], Koszegi and Rabin [2006], MuUainathan and Shleifer [2005], Oster
and Morton [2005], Shui and Ausubel [2004], Spiegler [2004], and Ellison [forth.] for an overview.
-See Becker [1957] and Laibson and Yariv [2005].
^Respondents were asked "How accurately do you feel you know the charge for services on your account?" Response
categories included; "Exactly," "Roughly," "Not at all," and "Did not apply." About half of respondents choose
"Not at all."
'
logical biases.
of personal Hewlett-Packard deskjet printers
From each
printing.
printer's
further
is
not easily accessible on the company's
web
site.
homepage, one must follow a complex sequence of hnks to uncover the cost of
Such shrouding does not
printing costs
is
reflect
away from the
exogenous communication
printer
homepage
costs.
— using the
The information about
click
metric
— than
any
other information about the printer.
At
if
first
glance, shrouding add-on prices seems like a natural marketing strategy.
consumers are
rational (or aware), shrouding should actually hurt the
all
bank or
However,
printer
man-
ufacturer, because rational consumers will expect the worse from a firm that shrouds [Milgrom
Any
1981].
altogether
information that
—
is
is
hidden
and rmravelling
Rational consumers will infer that hidden
not likely to be favorable to consumers.
prices are likely to be high prices.
— or excluded from marketing materials
in the fine print
Such reasoning creates an incentive
of shrouding. Indeed,
all
for
information revelation
firms choose to unshroud their prices in equilibria with
rational consumers.
We
future
show that shrouding behavior
game
Some economists
tree.
will arise
if
"myopic" consumers incompletely analyze the
believe that such shrouding cannot survive [Shapiro 1995],
arguing that competitive firms should educate other firms' customers, offer those customers
pricing schemes, and consequently win their business. In contrast,
myopic consimaers creates equilibrium shrouding that
is
immune
we show that
efficient
the existence of
to such competitive pressure.
We derive conditions under which competitive price cutting and educational advertising will
occur in eqmlibrium.
We show
that debiased consumers prefer to give their business to firms with
high shrouded prices because these sophisticated consumers end
designed for myopic customers [DellaVigna and Malmendier 2004,
To develop
Suppose that
plan a hotel
add-ons
intuition for our results, consider a hotel
all
consumers are
When
visit).
like parking,
not
initially
myopic
(i.e.,
room
up with a subsidy from
policies
2005].''
that costs Hilton $100 to supply.
they do not think about add-ons
when they
such a customer stays at Hilton, she ends up paying $20 to purchase
telecommunications,
room
service, etc.
that these add-ons cost Hilton nothing to provide.
Without
loss of generality,
assume
In a competitive market, Hilton will then
advertise "Hilton's rooms cost only $80," neglecting to mention the costly add-ons that effectively
raise its revenue.
In competitive equilibrium, Hilton's costs ($100) equal Hilton's total revenues
($80-h$20).
"In DellaVigna and Malmendier [2004, 2005] cross-subsidies arise from self-control problems.
not recognize their self-control problems cross-subsidize sophisticated consumers who do.
who do
Naive consumers
Now consider another hotel chain,
parent could
tell
called Transparent, that
is
picking a business strategy.
consumers about the shrouded add-ons that consumers pay
parent could advertise, "Watch out for add-on prices at our competitors.
are
all free."
revenue.
Naturally,
An
if
Transparent did
this,
for at Hilton.^
TransTrans-
Tranparents's add-ons
they could not subsidize their room fees with add-on
aggressive transparency strategy would be to charge $100 for rooms and nothing for
add-ons.
Unfortunately, this efficient pricing scheme might not attract any customers.
Once consumers
understand the high mark-up strategy of Hilton, consumers might prefer to stay at Hilton and
simply substitute away from add-on consumption.
marked up add-ons
A
"sophisticated" customer anticipates the
and avoids buying many of them
at Hilton
she brings a
(e.g.,
cell
phone instead
of relying on the hotel phone, she takes a taxi instead of renting a car that requires parking,
etc.).
Suppose that the economic cost of such substitution
is
$10.
In this case, Hilton's newly
educated customers prefer to stay at Hilton rather than defecting to marginal cost pricing at
Transparent.
a
little
Hilton's educated customers receive a $100
are taught to substitute
and only have
for sophisticated
less profitable for
know how
incentive to pursue debiasing
many markets
in
the debiasing firm. Sophisticated consumers tend to be less
to avoid unecessary costs.
and competition
the customers of their competitors.
room
will
In such cases, firms do not have an
not lead consumers to behave rationally.
There
own customers
or even
their
Consider the illustrative example above.
for a price of $80 plus $10 of inconvenience.
consumer has no reason to defect to Transparent.
^For concreteness, assume that
a better deal
This curse occurs whenever debiasing
which firms do not have an incentive to educate
customers, get a $100 hotel
is
this example.*^
This example also illustrates the curse of debiasing.
profitable because they
Hilton
pricing.
nobody
Hence, Transparent's unshrouding/advertising campaign does not
any business. The present paper generalizes
makes a consumer
So Transparent's
After the educational advertising campaign,
though Transparent has marginal-cost
consumers.
to endure
— which seUs fewer add-ons — but helps Hilton's customers, who
away from add-ons.®
defects to Transparent, even
are
for $80
inconvenience (worth $10) to avoid buying Hilton's overpriced add-ons.
education campaign hurts Hilton
attract
room
Debiased Hilton
Hence, the debiased
Accordingly, Transparent (or Hilton) has no
all consumers receive and understand this message and assume that advertising is
However, the example works no matter what fraction
< A < 1 of consumers get the message and no matter
what it costs to place such advertisements.
Of course, Hilton would like to screen out such sophisticated consumers, but this is typically not possible.
^In the notation of section II, c = 100, c = 0, p = 0, e = 10, q = 0, A e (0, 1], p = 80, p = p = 20.
free.
incentive to educate Hilton's myopic consumers in the
for the
consumer and bad
we show that
In essence,
In turn,
Finally,
both firms.
for
Debiasing a consumer
Neither firm has an incentive to do
there are two kinds of exploitation.
when consumers become
when
place.
first
good
it.*^
Firms exploit myopic consumers.
sophisticated, they take advantage of these exploitative firms.
sophisticated consumers exist, firms cannot rid themselves of them.^
nobody has an
is
In equilibrium,
But the myopes do not know
incentive to deviate except the myopic consumers.
any better and often nobody has an incentive to show them the error of their ways.
Educating
consumer who prefers to go to
a myopic consumer turns
him
firms with loss-leader base
good pricing and high-priced (but avoidable) add-ons. Hence, education
into a (less profitable) sophisticated
does not help the educating firm.
This mechanism applies to a wide range of markets.
benefit of a $50 gift for opening an account
consumers.
An
interest charges
An
educated banking customer gets the
and avoids paying some of the
educated credit card holder gets convenience,
and
and avoids paying
late
payment
fees.-^°
for frequent cartridge
color, printing in draft
consumers prefer to
An
educated
home
myopic
and miles and avoids paying
printer buyer gets a loss-leader price
replacements (by printing in black and white instead of
mode, or printing fewer large jobs
stick
fioat,
fees that snare
at home).-^^
In such markets educated
with the firms that feature high add-on prices, since these firms have
loss-leader base-good prices,
and the educated consumer can
partially substitute
away from the
overpriced add-ons.
Our
and
analysis shows
free advertising.
why
high add-on markups will persist in markets with numerous competitors
This prediction distinguishes our model from standard search models, which
Another example of the curse of debiasing occurs in mutual funds. If a mutual fund company explains that
is not effective and that fees are the primary predictable component in risk-adjusted returns, a newly
educated consumer will decide to buy an index fund - a very competitive, and relatively unprofitable, segment of the
market. Educating the consumer transforms him into an unprofitable consumer, and for-profit companies will not
want to implement such education [Gabaix, Laibson and Li 2005].
In the example above, Hilton cannot drive away educated consumers without also losing its myopic consumers.
'°In recent years, a new shrouding ploy has emerged. For example. Chase offers
percent Annual Percentage Rate
(APR) on transferred balances. In a footnote in their ads the company acknowledges that "we apply payments to
introductory balances before balances with higher APRs
Learn more about rates, fees, and other cost information
by reviewing Pricing &: Terms." In the fine print of Pricing &; Terms, Chase reports, "You authorize us to allocate
your payments and credits in a way that is most favorable or convenient for us. For example, you authorize us to
apply your payments and credits to balances with lower APRs (such as promotional APRs) before balances with
higher APRs." Sophisticates can take advantage of this scheme by transferring a balance to Chase and never using
the Chase card to make a purchase. In contrast, myopes may fail to realize that they can only repay their new credit
card charges (which may accumulate at a high interest rate) after they have repaid their introductory balance (which
accumulate at a 0% interest rate). We thank Robert Barro for pointing out this example.
A sophisticated consumer could also purchase the add-on from a third party, at some transaction cost. This is
why base-good firms often hinder such third party transactions. See Salop [1993] and Hall [2003] for examples.
stock picking
[.
.
.
]
imply that firms have an incentive to disseminate information about their products and choose not
to do so only
if
such dissemination
We
Stahl [1989]).^-
costly (e.g., Butters [1977]; Salop
is
which firms
identify concUtions under
not compete by lowering add-on prices, even
when
with nearly costless marginal information dissemination
model with only rational consumers, firms
do so
costlessly.
will
still
Stiglitz [1977];
and
choose not to advertise and hence
will
advertising
and
This explains why industries
is free.
shroud their add-on
choose to disclose
all
prices. In a search
of their information
In our model, with enough myopic consumers, shrouding
is
the
more
if
they can
profitable
strategy.
As we have
explained, our explanation for add-on shrouding and high
presence of myopic consumers.
that explain
why
In contrast,
why add-ons have
many
high markups.
firms gratuitously shroud add-on prices.
authors have developed rational actor models
However, these rational models do not explain
Two
types of explanations for high mark-ups figure
prominently in the literature: high exogenous search
costs^"*
Ellison [2005] proposes a rational price-discrimination
firms to charge high
demand consumers
model, exogenous search costs make
markups
raise profits
markups
will not
by
it
relatively
markups depends on the
and an
model
in
inability to commit'-^.
which add-on pricing enables
more than low demand
consumers.'-^ In Ellison's
costly for consrmaers to observe add-on prices.
facilitating price chscrimination.
However, Elhson points out that high
be sustainable when information transmission
costs are exogenously small, see Stole [2005] )
.
To handle
this case,
is
inexpensive
and
We
cost including the add-on.
different degrees of competition.
take the add-on into account
work out a
(i.e.,
when
closely related
if
they anticipated
model that incorporates myopia
In our setting, unsophisticated consumers simply
when comparing products.
''This can be viewed as the key difference between modelling
search
Elhson suggests an extension that
would incorporate unsophisticated consumers who would not buy a base-good
its total
High add-on
fail
to
Hence, they only compare the prices
bounded rationaUty
as search costs [e.g., Salop and
an attribute as in our model. In the search cost
approach, if firms can costlessly educate the consumers, they will do so because consumers are Bayesian. If a firm
goes out of its way to sustain high search costs, Salop and StigUtz consumers will rationally infer that it has something
Stiglitz 1977]
and modelling
to hide. So,
advertising costs are low,
if
it
directly as failure to anticipate
all
firms reveal information to consumers.
In contrast, Ayres and Nalebuff [2003] propose that high add-on prices are partially due to myopic choices on
the part of firms, which would make more profits if they had low add-on prices and consequently developed a good
reputation.
'*
Search-cost models imply that firms choose high add-on prices because
it is
exogenously costly for consumers to
observe add-on prices before they buy the base good [Diamond 1971; Lai and Matutes 1994; Stahl 1989; Hortacsu
and Syverson 2004]. In contrast, our model generates voluntary information suppression.
'"The hterature on commitment shows that firms choose high add-on prices if firms cannot commit to add-on prices
good is sold (Borenstein et al. [1995], Farrell and Klemperer [2005], Klemperer [1987]). In our
analysis however, we consider the polar case in which firms can commit to an add-on price.
'^See Elhson and Ellison [2004] for related empirical analysis.
at the time the base
When
of base-good across firms, instead of comparing the total prices (base-good plus add-on).
add-ons are made salient
the market, but instead
II defines
demand
discrete
continuous
markets.
II.
We
through advertising
make an more informed
— our newly educated consumers do not. exit
choice
among
concludes.
IV
discusses the
All proofs are presented in appendices.
Shrouded Attributes: Definitions and a Model
might suppress information about minimum balance
will neglect to consider
shrouded attribute
is
when
a product attribute that
be nearly costlessly revealed. -^^
site is
such fees
is
fees in the bank's
picking a bank.
These shrouded
For example, a bank
by some potential customers.
attributes are not taken into consideration
on their web
this way.
measurement and regulation of shrouded
analyze a market in which firms can shroud attributes of their products.
consumers
analysis
Section III discusses extensions, including the general case with
for add-ons. Section
V
Our
the available goods.
a shrouded attribute and presents an equilibrium analysis of a market with
for add-ons.
demand
Section
e.g.
under which no firm has an incentive to educate consiuners in
identifies conditions
Section
—
marketing materials.
Some
For the purposes of our model, a
hidden by a firm, even though the attribute could
The Hewlett-Packard
decision to omit the deskjet price per page
an example of such information suppression.
Shrouded attributes may include surcharges,
fees, penalties, accessories, options, or
hidden feature of the ongoing relationship between a consumer and a firm.
We
any other
divide this
list
into
two mutually exclusive categories: (avoidable) add-ons and (unavoidable) surcharges.
The
analysis in this paper primarily discusses add-ons, the
type of shrouded attribute.
first
Add-ons are complementary goods that consumers have the option to avoid.
guests can avoid paying telephone charges
if
they instead use ceU phones.
can avoid paying for room service meals by finding local restaurants.
hotel
room
service
complement a hotel
stay.
For example, hotel
Likewise, hotel guests
Both
hotel
phone use and
Such complementary (voluntary) goods are referred
to as add-ons.
In our modeling,
we
distinguish between a "base good"
preceding example, the base good
We
is
a hotel
and the shrouded
room and the shrouded
attribute.
In the
attributes are hotel services.
assume that myopic consumers pick a base good without considering shrouded
"^More generally, communication costs need to be low enough so that unshrouding would occur
attributes.
in
^'^
an equilibrium
with rational consumers.
'*A consumer can compare prices of closely located four star hotels on a web travel
site (e.g., Orbitz),
without
Timeline and overview of (discrete demand) shrouding game
II. A.
We now
—
i.e.,
— to section
continuous demand
the discrete
Period
•
discuss a model with discrete
demand game. We
demand
We
III.B.
for the add-on.
start
Firms decide
by providing an overview of the timing of
discuss the details of the
game
to
after the timeline.
make information about the add-on shrouded
Unshrouding a price
Firms pick
prices for a base
good
{p)
or unshrouded.
we assume
and an add-on
This
is
a
To make un-
equivalent to advertising that price.
is
shrouding/advertising maximally attractive to the firm,
Period
postpone the general case
0:
binary choice.
•
We
that unshrouding
is free.^^
(p).
1:
• Sophisticated consrmiers (fraction
price into consideration.
If
a <
of the population) always take the add-on
1
information about the add-on
is
and
its
shrouded, sophisticates form
Bayesian posteriors about the unobserved add-on.
•
Myopic consumers
(fraction 1
—q
observe the add-on information.
add-on information.
When
of the population) only consider the add-on
When
the add-on
the add-on
is
is
if
they directly
shrouded, myopes do not observe the
unshrouded, fraction A e
myopes observes
(0, 1]
of
them
to substitute
the add-on information.
•
Consumers choose a
•
Consumers can
firm.
initiate costly
behavior
(effort cost e)
that enables
away
from future use of the add-on.
Period
•
2:
Consumers observe the add-on price
portunity to purchase the add-on.
(if
they have not observed
it
already)
Consumers who previously engaged
and are given an op-
in costly substitution
behavior have a lower incentive to purchase the add-on.
See Ayres and NalebufF [2003].
assumption in subsection III.D.
"
assume q < 1 because the analysis is of interest only when there are myopic consumers. Also, when q
many combinations of p and p are equivalent, as the equihbrium determines only p -|- p.
observing the hotels' add-on pricing schedules.
'
We
We
revisit this
=
1,
Details of the shrouding
II.B.
To motivate the model, we
game
will discuss the
example of a bank, but the model applies to any
setting in which firms offer add-ons to their customers.
Period
In period 0, banks set
0:
a base good, which in our example
and potentially shroud
the price of opening a bank account.
is
price of an add-on. In our example, violating the
Both p and p are chosen by each bank
p.^^
Let p represent the price of
prices.
minimum
balance
is
Without
in period 0.
Let p represent the
an add-on service with price
loss of generality,
we assume
that banks have zero marginal cost of opening an account or of having an account-holder violate
the
minimum
balance threshold.
Each bank may shroud or unshroud
minimum
p, the
hidden
minimum
balance
fee.
If
the bank chooses to shroud
balance fee will not be seen by potential consumers.
in fine print or
pubhshed
a gratuitous search cost that
Without
its
loss of generality,
is
in
an obscure
large
One can think
location.
For example, p
may be
of this action as creating
enough so that few consumers bother to see the add-on
price.
we assume that shrouding imphes that no consumer observes the add-on
price.
The bank may
alternatively costlessly advertise p, thereby revealing
<
consumers and to A fraction of myopic consumers, with
assume that A
myopes
may
We
fixed.
is
— who may not
A
<
it
Without
1.
to all sophisticated
loss of generality
we
allow A to be weakly less than unity to reflect the possibility that
initially recognize the value of
overlook that information even
when
it is
made
information about the add-on market
available.
We
define informed
—
myopes as the
myopes that have seen (and noted) unshrouded information about the add-on. Informed myopes
behave exactly
sophisticated consumers.
like
Analogously,
we
define uninformed
myopes as those
myopes that have not seen information about the add-on. Hence, when information
by one or more
firms, a fraction
— and a fraction
1
—
A of myopes
A of myopes
is
informed
''in
US
fee,
— and therefore become sophisticated
all firms.
^^
1:
banks, a typical
some minimum that
check
unshrouded
uninformed. Hence unshrouding by any firm increases the
is
sophistication of the pool of potential customers shared by
Period
is
is
minimum
strictly greater
or an insufficient funds fee.
do not have
in their accounts.
"Assuming
balance fee
than
zero.
Those
$10 and applies in months when an account balance falls below
balance fee is distinct from an overdraft fee, a bounced-
apply to cases in which customers would like to use funds that they
model discussed here applies to those fees as well.
advertising is more local would not change our results.
fees
Naturally, the
that the impact of
is
A minimum
Consumers pick a
fii'm
from which to buy the base good. Sophisticates always take the existence
when
of the add-on into consideration, forming Bayesian posteriors about the add-on
shrouded. Myopes only consider the add-on
if it is
high add-on prices can exert costly
effort e
who
For example, a consvuner
add-on.
>
Second, a consumer
in period 1
faces a high
assume that add-on
customer
is
fee
forced to pay a high
or lodge a complaint. Legal
charge. Finally,
p
is
who
First, a
consumer
anticipates or observes
balance fee could transfer balances
less likely to
be invoked.
bounded above hy p > e?^
effectively
is
is
and thereby substitute away from the
minimum
into the account or cut back withdrawals so that the fee
We
price
revealed to them.
For a consumer, taking account of the add-on generates two sources of value.
can consider add-on pricing when choosing a firm.
its
For example,
if
a
the customer might terminate her relationship with the bank
fee,
and regulatory constraints
p cotJd represent the
cost of a last
also
hmit the penalties/fees that banks can
minute consumer intervention that enables the
consumer to avoid purchasing the add-on.
We
assume that sophisticates and informed myopes are aware of the add-on
sophisticates
and informed myopes
will exert substitution effort e
if
e
<
Hence,
fee.
Ep}'^
Let Xi represent the anticipated net surplus from opening an account at bank
i
less
the antic-
ipated net surplus from opening an account at the best alternative bank (ignoring idiosyncratic
taste differences).
prices set
by other
Throughout the paper we use starred
analyze symmetric equilibria in this paper. ^^
We
firms.
variables to represent the (symmetric)
For sophisticated consumers,
^i
where
Ep and Ep*
=
[-Pi -'mhi{Ep,e}\
-
[-p* -vimi{Ep',e}]
,
are the rational expectations about the add-on price of the firm, and
petitors, respectively.
When
the add-on information
true value of the add-on price.
When
is
com-
unshrouded, expectations are equal to the
the add-on information
solve the Bayesian equilibrium to calculate
its
is
shrouded, sophisticated consumers
Ep and Ep* ?^
is unavoidable (e > p) and consumers are not all sophisticated (A < 1, a < 1) then the proof of
shows that there is a unique sequential equilibrium, which has Shrouded Prices and p = — p -I- ^, p = p"""We assume local risk neutrality throughout the paper. Also, it is important that informed myopes behave like
'^If
the add-on
Proposition
1
sophisticates.
^^Technically, our equilibrium
'^
We commit some abuse
beliefs are part of
is
a sequential equiUbrium, as detailed in the preamble of the proof of Proposition 1.
When the add-on information is shrouded, the sophisticated consumers'
of language here.
a consistent assessment
(i.e.
a strategic profile and a belief system), in particular they anticipate
perfectly the price that the firm charges in equilibrium.
10
Myopic consumers
fall
into
myopes becomes informed.
of
A
p.
firms.
myope
that
two
When
classes.
These informed myopes behave
was educated by firm
i
When
add-on information
is
in his
unshrouded, a fraction
shrouded,
is
just like sophisticates with
becomes sophisticated
However, even when add-on information
uninformed.
add-on prices are unshrouded, a fraction A
all
behavior vis-a-vis
—A
1
Ep =
of
all
myopes remains
myopes are uninformed.
For uninformed myopes,
=
Xi
-Pi +P*-
Uninformed myopes neglect the add-on when deciding where to open
their
uninformed myopic consumers do not consider exerting substitution
effort e in
bank account. Likewise,
period
Let D{xi) represent the probability that a consumer opens an account at bank
represents the average anticipated net surplus from opening an account at
bank
anticipated net surplus from opening an account at the best alternative bank.
D
is
strictly increasing,
bounded below by
a microfoundation of the
demand
function.
The demand function
the degree of competion in the industry, via the quantity
jj,
=
i
Recall that Xi
less
the average
The demand function
and bounded above by one.
zero,
i.
1.
Appendix
1
presents
allows us to flexibly parametrize
D{0) /D'
(0),
which
will
turn out
to be equal to the average profit per consumer. In particular, perfect competition corresponds to
/i
=
0.
Period
2:
Consumers observe the add-on
price
opportunity to purchase the add-on.
not purchase the add-on.
II. C.
(if
they have not observed
Consumers who have engaged
already) and are given an
in substitution in period 1
do
All other consumers purchase the add-on at price p.^^
Symmetric equilibrium
We now
characterize the symmetric sequential equilibrium of this game.^* Let
share of sophisticated consumers in the marketplace.
will
it
choose high markups in the add-on market.
The
a
represent the
following proposition shows that firms
In the Shrouded Prices Equilibrium, firms will
choose markups that are so high that the sophisticated consumers substitute out of the add-on
market.
we could assume that uninformed myopes buy the add-on in period 2 without observing the
is low enough to justify the purchase.
Proposition 1, in Appendix 2, provides the details of the strategies and behefs.
'^Alternatively,
i.e.,
"
the myopes believe that the unobserved add-on price
The proof
of
11
price:
Proposition 1 Let
= 1-
a^
(1)
e/p
and
^
=
If
the fraction of sophisticated consumers
a
in
which firms shroud the add-on
(2)
price.
D{0)/D'iO).
is less
than a'
there exists a symmetric equilibrium
,
Call this the Shrouded Prices Equilibrium.
The
prices of
the base good and the add-on are respectively:
(3)
p
= -{l-a)p + ^
(4)
P
^
P-
In this equihbrixma only myopes purchase the add-on.
substitute
The
allocation
is
inefficient since sophisticates
away from the add-on.
If
the fraction of sophisticated consumers
in
which firms do not shroud the add-on
prices of the base
a
is
greater than a'
price.
good and the add-on are
Call this the
p
=
-e
(6)
p
=
e.
all
there exists a symmetric equilibrium
Unshrouded Prices Equilibrium. The
respectively:
(5)
In this equilibrium
,
+
/x
consumers purchase the add-on, so the equilibrium
is efficient.
In each of these equilibria, the beliefs of sophisticated consiuners and educated myopes are p
for the
add-on price
at a firm that shrouds, independently of its base
profits of the industry are
The proof
is
in
p..
Appendix
2.
12
good
price.
=
p
Also, the total
Proposition
1
Shrouded Prices Equilibrium^^
characterizes a
in
which firms choose
high markups in the add-on market and choose to shroud those add-on prices. "^°
Prices Equihbrium, firms set p*
equilibrium
(see subsection
II.
D
(i.e.,
demand curve
the
competitive market with
—
—
<
or
and the base good
will
p* Ri
(1
a) p
Our model
jD*
smaU
0.
markups
easiest to see
is
highly elastic, and hence
is
p, the base
« -e <
be the
effort cost e to substitute
result that high
markups on the base good.^^ This
competitive
pay
This
is 0.
away from add-on
below).
Our model reproduces the well-known
or negative
In the Shrouded
the marginal cost of producing the add-on
inefficient since the sophisticates
is
consumption
=p, though
inefficiently
good
add-on are
when the market
p
is
is
close to zero).
by low
approximately
In a relatively
that the add-on will be the "profit-center"
'^^
also predicts equilibrium shrouding, as conjectured
by Ellison
[2005].
Other previous
authors have conjectured that the availability of inexpensive advertising would drive
market prices and eliminate shrouding.
offset
always a loss leader with a negative markup:
is
The model imphes
"loss leader."
for the
down
after-
For example, Shapiro [1995] describes the inefficiency
caused by high markups in the aftermarket and then observes that competition and advertising
,
should drive them away.
Furthermore, manufacturers in a competitive equipment market have incentives to
avoid even this inefficiency by providing information to consumers.
could capture profits by raising
to cost), lowering
its
its
its overall
systems price
the manufacturer could eliminate some or
by
all
offering a lower total cost of ownership,
eliminated deadweight
manufacturer
[base-good] prices above market levels
aftermarket prices below market levels
informing buyers that
A
is
at or
(i.e.,
(i.e.,
closer
closer to cost),
below market.
and
In this fashion,
of the deadweight loss, attract consumers
and
still
capture as profits some of the
In other words, and unhke traditional monopoly power,
loss.
the manufacturers have a direct incentive to eliminate even the small inefficiency caused
'it
is
easy to see that
if
a
-I-
A(l
—
a)
<
a'
and there
is
a small cost of unshrouding, then the Shrouded Prices
When A is large enough another equilibrium exists.
Shrouded Prices and Unshrouded Prices Equilibria both exist.
''"For empirical appUcations,we reexpress Proposition 1 in the case where the marginal costs c and c < e are not
zero. In this case, if q < a' p = c — (1 — a) (p — c) + h, and ifa > a, p = c + c— e + p.. The value of p does not
Equilibrium
Specifically,
is
the unique symmetric sequential equilibrium.
when a < a^ < a + A(l —
a), the
,
change.
"See the literature review in the present paper and in Ellison [2005].
^'In many seemingly competitive markets the price of the base good is
printer, hotel, car rental, financial services), while the price of the
cartridge, hotel
phone
call,
gas charge,
minimum
balance
fee).
13
add-on
below its marginal cost (e.g.,
above its marginal cost (printer
typically set
is
set well
by poor consumer information [Shapiro 1995,
p. 495].
In the Shrouded Prices Equihbrium, Shapiro's intuition about inefficiency appUes, but his anticipated unshrouding effects are overturned by other forces.
In general, high markups in the
aftermarket do not go away as a result of competition or advertising.
Why
doesn't Shapiro's rmshrouding effect arise?
by advertising low add-on
Shapiro conjectures that firms will compete
prices, thereby attracting
consumers by highlighting the benefits of
efficiently priced add-ons.
However, Proposition
Specifically,
1
shows that
this competitive effect
is
overturned by a "curse of debiasing."
educated consumers would prefer to fiequent firms with high add-on prices that they
can avoid rather than defecting to firms with marginal cost pricing of both the base good and the
add-on.
Again consider the
illustrative case of perfect competition,
/i
=
0.
If
a sophisticated consumer
gives her business to a firm with shrouded market prices, the sophisticated consumer's surplus will
be:
sophisticated surplus
By
contrast,
if
— —p —
e
=
(1
— a)p —
e
>
{1
- a)p -
{1
=
0.
- a)p
the sophisticated consumer gives her business to a firm with zero markups on both
the base good and the add-on, the sophisticate's surplus will be exactly
cated/educated consumer
is
strictly better off at the firm
0."''^
So the
sophisti-
with shrouded prices (and high add-on
markups), than deviating to the firm with marginal cost pricing.
This preference
for
the firms with high mark-ups refiects the fact that the sophisticated con-
sumers are subsidized by pricing
policies designed for
uninformed myopic consumers. Educating
rminformed myopes enables them to get more value out of
firms.
their relationships
with high markup
After education, myopes anticipate the high add-on prices, and hence substitute away from
add-ons while
still
enjoying loss leader prices on the base good.
^^The particular value
the surplus
will
of a
surplus depends on the choice of normahzation.
be V.
14
The newly educated consumers
If
we
shift all utilities
by a factor V,
and avoid the high
benefit from the "free gifts"
This generates the curse of debiasing.
consumers. Newly educated consumers
ically,
A
(i.e.,
firm does not benefit by debiasing uninformed
myopic
sophisticates) are not profitable to any firm.
Specif-
— and
sophisticates prefer to patronize
fees.'^'*
in particular, exploit
— firms that
offer loss-leader
prices on base-goods.
This intuitive analysis explores pricing deviations in which a firm
myopes from other firms (using low markups
sophisticates.
Naturally, both deviations
educate and attract
Naturally, equilibrium analysis
as the lure).
which a firm with high markups
also analyze deviations in
tries to
must be considered
tries to drive
must
away (money-losing)
in the proofs of Proposition
1.
In summary, the presence of uninformed myopic consumers incentivizes firms to adopt pricing
Making more myopes
schedules that have the unintended consequence of subsidizing sophisticates.
sophisticated will not help any firm.
Because of
when education
to educate myopes, even
this curse of debiasing,
no firm has an incentive
is costless.
Welfare
II.D.
We now
provide a welfare analysis of the Shrouded Price Equilibrium and highlight the
ineffi-
ciency of this equilibrium.^^
Proposition 2 In the Shrouded Prices Equilibrium, the
consumers are p — e units better
there
is
no
inefficiency
and
Proof of Proposition
2.
all
off
marginal
exert effort
e,
social welfare loss
In the
proportional (with factor
is
p,
is
sophisticates are
Proposition
produced
1,
at
ae. Sophisticated
is
Shrouded Prices Equilibrium,
p—
>
the fraction of
all
of the sophisticated agents
ae. Also, as sophisticates pay e to avoid buying the add-on,
e better off
marginal
indeed, one needs A
e) to
Recall that the firms can produce
than myopes.
Unshrouded Prices Equilibrium, no consumers exert costly
add-on, which
^""in
cost. In the
so the deadweight loss
and myopes pay
A=
well-off.
agents that exerts costly effort e to avoid consuming the add-on.
the add-on at
is
than myopic consumers. In the Unshrouded Prices Equilibrium,
consumers are equally
The
social welfare loss
0,
cost.
There
is
but otherwise the
no
effort,
and
all
purchase the
efficiency loss.D
specific value of
A does not matter. The reEison
clear from the proof. Sophisticates are less profitable than myopes, so after unshrouding an increase in the
of sophisticates, caused by A
''"As often in welfare
>
0,
reduces total
is
number
profits.
economics, the pricing distortion
is
efficiency losses.
15
hkely to have greater redistributional effects than net
Since the add-on can be produced at zero social
consumed.
a consumer substitutes away from the add-on (at
If
In the case with inefficiency {a
socially inefficient.
<
In this section
myopes
add-on.
learn to
we
we
sophisticates.
then an equilibrium
is
consume the (high-priced) add-on.
Extensions
discuss several extensions of the model.
become
Finally,
effort cost e),
a^), the welfare losses increase as the fraction
of sophisticates increases; in this case sophisticates do not
III.
the add-on to be
cost,'^^ it is socially efficient for
Second,
we analyze the
First,
we
discuss the case in which
case of continuous
demand
for the
discuss a series of additional considerations that influence the persistence of
shrouding.
III. A.
Learning
In some markets, myopes eventually learn the high price of the add-on, thereby becoming
We
sophisticates.
present an extension that reflects this learning process and demonstrate
how
learning affects equilibrivmi pricing.
We
adopt the same timing as before, but now we assume that the decision about add-on
consumption
is
repeated.
Specifically, after
choosing a firm from which to buy the beise-good,
sophisticates face the add-on purchase decision
whether to pay avoidance cost
and make sophisticated choices
Tms =
0.^^
We
Tms
Our
times. ^^
assume that firms choose
For each decision, sophisticates decide
times.
buy the add-on
Uninformed myopes buy the add-on
sophisticates.
and
e or
T5
for price p.
Tmm
times. ^^
original
Informed myopes act just
They then become
model corresponds to Ts
their shrouding policies
and
like
sophisticates
=
prices once
Ti\jn/
and
=
1
for all
and do not change them during the game.
The
following Proposition shows that there
sophisticates
a
is
This assumption
is
a Shrouded Prices Equilibrium
if
the fraction of
low.
is
made without
''In practice, the propensity to
loss of generahty.
become sophisticated should
would lead to an interesting extension of the framework.
^'in some cases is may be natural to assume Ts = Tmm
Shrouded Prices Equlibrium does not depend on it.
39c
See Miao [2005] for another analysis.
16
+
increase with the cost of behaving myopically. This
Tms, but we do not make
this
assumption here, the
Proposition 3 Let
tt _
=1-3^ ™^ (^5: Tmm + Tms)
a"
,^,
1
(7)
If
Q < a^\ then there
Call this the
exists a
symmetric equihbrium in which firms shroud the add-on pricing.
Shrouded Prices Equihbrium:
(8)
In this equilibrium the
cation
is
p
= -
p
=
(1
- a)pTMM + M
p.
myopes purchase the add-on
until they
socially inefficient since sophisticates substitute
sophisticated consumers and educated
The myopia model
myopes are p
=p
become
sophisticates.
away from the add-on. The
for the
The
banks decline with customer tenure.
allo-
beliefs of
add-on price at firms that shroud.
predicts that consumers will eventually learn to avoid add-on fees.
[2005] empirically evaluate these
et al.
.
Agarwal
dynamics, confirming the prediction that add-on fees in
This learning pattern
is
inconsistent with the predictions of
a classical price discrimination model of add-on pricing.
Our
consumers learn to avoid add-on
fees,
does shrouding eventually vanish along with high add-on prices? Several countervailing forces
may
analysis raises the question of long-run dynamics.
sustain shrouding in the long-rim.
Second, sophistication
is
First,
falls.
and priced above marginal
is
a
When
the add-on
is
new
it
tends
Over time, shrouding decreases and the add-on
cost.
Using our notation, the fraction a of sophisticates increases over time and shrouding
eventually disappears. "^"^
We
new shrouding techniques
and Sinkey 1999]
believe that fees for specific add-ons have a lifecycle.
to be shrouded
price
Third, and most importantly,
For example, the emphasis on fee-based revenue in the banking sector
recent development [Rogers
We
generations of myopic consumers enter the market.
sometimes overturned by forgetting or distraction, particularly when the
absolute costs of the add-on are small.
endogenously evolve.
new
If
thank Douglas Bernheim
for
suggesting these lifecycle dynamics.
17
Continuous add-on demand
III.B.
we
In this section,
We
generalize the
model
show that equilibrium shrouding survives only when
The
substitutes for the add-on.
details of the original
game except
Total consumer utility
cost of purchasing
firm
is
game
in this section mirrors the
the extensions enumerated below.
decomposed into two
parts: the value of
owning the base good and the
— or substituting away from — the add-on.
Let Uai represent agent a's value of
—
PiQai represent the costs associated
base good, overlooking the add-on.
i's
for the add-on.
sophisticates have relatively inexpensive
structure and timing of the
for
demand
to the case of continuous
Let u(eai,qai)
with the add-on, reflecting both the add-on quantity
qai
away from the add-on. The leading case
/dcaidqai
is d'^u{ea,i,qai)
and any costly
<
0.
efforts Cai to substitute
The net
value of buying the
base good can be written
Uai
+
-Pi
U
base good utility
In period
1,
2,
=
sophisticates pick
corresponding indirect
-
Uai
qa-,
like sophisticates,
We
We
since informed
\
call
u^
=
(pi)
=
u{eai, qai) the
Epi}'^
myopes observe the add-on
i
to
maximize
pi.
Uai
2,
a price p.
rminformed myopes pick
q^i to
(p) represent
Let
q^ (p)
the equilibrium add-on
demand
represent the equihbriimi add-on
of a sophisticate
=
e^ which
maximize
demand
who knows
u{eai,%r)
=
u{e^i{Epi),qai{eai{Epi),pi))
= 2(e„i(pi), 5a.{eai(pi),Pi))18
she
of an uninformed myopic
^'For example Uai could represent the value of the base good assuming a zero price for the add-on.
{pi)
In
— Pi-
level of substitution effort in period 1
In period
i.
the the marginal cost of the base good and c the marginal cost of manufacturing
the add-on. Let q^
^-S®
maximize
-Mai-
call c
will face
Piqai-
effort Cai to
myopes do not take account of the add-on when they pick a firm
not responsive to shrouded variation in
u{e^i,qai)
utility
expectations case in which pi
Uninformed myopes passively choose a default
is
Piqai
and substitution
maximize u{eai,qai) —
uninformed myopes pick a firm
1,
i
"
1.
In contrast, uninformed
period
to
qai)
+ max E < max [u {cai, qai) - Piqai]
utility for the rational
Informed myopes behave just
information in period
Pi
,
add-on
sophisticated consumer a picks a firm
Uai
In period
{eai
who
initially
monopoly
overlooks add-on prices because they are shrouded.
price in the add-on market, given
p™ =
(9)
arg
max {p -
We
assume that there
is
a unique
by
c)
[af {p) +
-
{1
a) q^" (p)]
.
V
Now we
characterize symmetric sequential equilibria.
Proposition 4 Suppose that unshrouding makes
all
consumers sophisticated (A
=
The
1).
price
vector
-
(10)
V
=
(11)
P
= P™
supports a Shrouded Prices Equilibrium
-
and only
c)^ (p)
if i?
loss of social surplus (for sophisticate
>
+
fj.
1,
where Bis the debiasing
ratio:
myopes
demand) due
to add-on
mark-up
(l-a)(p--g)(g^^(p-)-g^(p-))
[u^ {c)-cqS (c)] - [uS (p^) - cqS (p^)]
(13)
The
if
ip
cross-subsidy to sophisticates from
B =
(12)
c
beliefs of sophisticated
consumers and educated myopes are p
=
p"^ for the
add-on price at
firms that shroud.
The proof is
in
Appendix
2.
This no-advertising result contains a boundary condition that determines when advertising will
B >
appear:
than the
social welfare distortions
of this theory
high
B
To
Advertising does not arise
1."*^
would calculate
values tend to be
the cross-subsidies to sophisticates are larger
due to price deviations from marginal
ratios in different markets,
loss of
^
'
empirical test
is
easier to directly interpret:
market
consimier surplus (for sophisticate demand) due to add-on mark-up
(p--c)[ag^(r') + (l-cv)y^(p--)]
- 2g5 (2)] - [uS (p^) - p^qS (pm)]
[uS (?)
With the
Condition
An
more shrouded.
loss-leader subsidy in base- good
,
cost.
and determine whether markets with
heuristically derive the result, consider another ratio that
,
^
B
when
demand model of section 2, the subsidy is (1 — a) p, the distortion
q < q reproducing the result of Proposition 1.
discrete
B>
1 is
,
19
is e,
so
B=
S'
=
(1
—
a) p/e.
,
A sophisticate at
a shrouded firm wih not defect to a marginal cost pricing firm
if
the loss-leader
subsidy in the base-good market exceeds the consumer welfare gain from switching to marginal cost
pricing in the add-on market
(i.e.,
B'
>
Since aftermarket profit generates loss-leader competi-
1).
—
tion in the base-good market, the loss-leader base-good subsidy
is
which
The denominator
is
the average profit per customer in the add-on market.
ticates' welfare loss
(p"'
c)
\aq^ {p^)
+
of B'
u^
(c)
—
cq^
(c)
,
Putting these results together, we get the expression of B' in equation
tion 13) by subtracting {p^
iS B'
>
c)
variant
is
we
discuss
some
tractable variants of our
15.
— p^q^
the
We can recover B
(p^)
(equa-
Hence
into account the add-on prices of
fraction A of them),
all
all
firms.
not change.
If
a firm "unshrouds,"
The
educates the myopes (or a
it
price.
The
price charged in the
The reason
is
that,
The
results of this
results of Proposition 1
results of Proposition 4
model - do not change, except that the add-on
between marginal cost and the monopoly
if
- the
- the continuous demand
Shrouded Equihbrium
falls
a firm lowers the price of the
more sophisticated consumers.
In another variant, myopic consumers simply underestimate their use of the add-on.
is
all
In contrast, sophisticates costlessly observe and take
and makes them aware of the existence of the add-on.
demand model - do
gets
relevant.
consmners. Myopes, however, just do not consider
variant are very close to the results of the present framework.
it
model that are empirically
that of "observable prices but limited awareness.'"''' In this version, the prices of
(or even think of) the price of the add-on.
variant
c),
q^ (p™) from both the numerator and denominator of B'.
firms are always observable, at no cost, by
add-on,
=
1.
In this subsection,
discrete
the sophis-
Additional models of shrouded equilibria
III.C.
One
—
a) q^^ {p^)]
but in the shrouded prices equilibrium
the sophisticate pays add-on price p"* and realizes a lower add-on utility of u^ {p"^)
1
is
—
from high mark-ups in the add-on market. At marginal cost pricing (p
sophisticate would realize add-on utility of
B>
(1
relevant
when consumers
or lines of credit [Landier
^
This
are overoptimistic about the use of credit cards [Ausubel 1991]
and Thesmar 2005] Such a microfoundation would not change the
.
results
of the present paper.
The model
also
makes predictions about which attributes
will
be shrouded,
for a given
Indeed, one can generalize the model to a good with several shrouded attributes, which
"•^This vajiant is developed in the
May
2004 version of the present paper, which
"^Section 7.3 of our 2004 working paper.
20
is
available
upon
good.
may have
request.
different values for a, e
and
p.
Shrouded Prices Equilibrium
will
be shrouded
if its
Our Proposition
for
an attribute
debiasing ratio
B=
{1
if
also applies to
1
a <
1
- e/p
— a)p/e
is
each attributes. There will be a
for that attribute.
greater than
1.
Other influences on shrouding
III.D.
To simplify exposition, we have ignored
encourage shrouding. First, we have so
assumed that
several additional factors that influence the prevalence
we quickly
In this subsection,
of shrouding.
discuss these factors, starting with the factors that
overlooked the consumer entry decision, since
far
consumers must buy a base good.
all
may buy
these myopic consumers
When some
when they should avoid the market
the base good
lifetime operating costs are at least ten times higher.''^
add-on prices
will drive
some
we have
so far
possible that unshrouding
at that single firm.
Third,
if
is
a fixed cost
{l
C
iff
Fourth,
e.
1,
1977].
costly add-ons at all firms.
However,
it is
instead
=
1
1 is
if
/i
would impede unshrouding.
then unshrouding
B
where
=
will
again be impeded.
Then Proposition 4
is
is
Specifically,
adjusted so that a Shrouded
defined as before except the numerator of
and k equals the munber of firms
if
^
is
This implies that shrouding
new add-ons and new
is
more pervasive when the market
is less
learning will accelerate unshrouding.
B
very
adjusted so that a Shrouded Prices Equilibrium exists
we have already mentioned that
vation will create
Some
is costly,
B >
Analogously Proposition
— a)p+kC >
effect
of unshrouding.
incremented by kC, where k
large.*^
Hence,
by one firm leads consumers only to think about the unshrouded add-on
This narrow framing
Prices Equilibrium exists
realizing that the
assumed that once a consumer becomes informed about the costly add-on
education/advertising
suppose there
altogether
of these myopic consumers out of the base-good market.
consumer takes account of the
at one firm, that
costs,
Firms that compete by unshrouding high
consumer entry decisions are adversely affected by unshrouding [Spence
Second,
we have
consumers overlook add-on
Think of a consumer who buys a $50 deskjet printer without
[Elhson 2005].
is
Hence an attribute
iff
competitive.
However, irmo-
opportunities for shrouding.
forces besides learning, however, will favor unshrouding. For instance,
heterogeneous tastes and firms have heterogeneous add-ons, firms
if
consumers have
will advertise to
enable con-
*
At the moment, black and white text costs between 2 cents and 15 cents per page, depending on the inkjet
Color text costs more than black and white text. A photographic image costs an order of magnitude more.
Printing 10 pages per day at only 10 cents a page costs $1460 over four years.
printer.
'
The proof
is
a simple modification of the proofs of Propositions
large.
21
1
and
4,
with a Taylor expansion when
fi is
very
sumers to find the base-good with the right add-on.
This informative advertising will accelerate
unshrouding.
Also, third party
consumer education
finance magazines tend to
IV.
we
may be
incentives to give
active portfolio
underfinanced.
bad advice.
—
will ac-
Moreover,
for-
For example, personal
management, thereby
Consumers may not know which advisor to
discuss the
— or
existence of shrouding.
We
and
Consumer Reports
like
justifying ongoing
trust.
Measuring and regulating shrouding
problem of a regulator
benefits
may have
recommend
for these magazines.
In this section
magazines
Non-profit educational organizations
profit educational organizations
demand
e.g.,
However, various impediments prevent such educational mechanisms from
celerate unshrouding.
working perfectly.
—
measurement and regulation of shrouding.
an economic researcher
— who
We
first
consider the
wishes to empirically identify the
then consider potential regulatory remedies, emphasizing both the
pitfalls of these policies.
Measuring shrouding: diagnostics
rV.A.
Five different empirical strategies can be used to identify the existence of shrouding.
researchers
may
First,
conduct consumer surveys. Such surveys would determine whether consumers
at
the point of purchase are aware of the add-on costs that they will later face. This corresponds to
measuring a, an index of average "consumer I.Q." For example, Hall [2003] finds that only
consumers who buy desk-jet printers know the associated ink costs
printer.'**
Of
course, such ignorance
from exogenously high search
may
costs).
or
may
at the
not imply shrouding
Consumer surveys might
3%
of
time they purchase the
(e.g.
ignorance
also test for incorrect
may
result
consumer
expectations. For example, at the point of purchase consumers could be asked to estimate their ink
costs.
In shrouded equiUbria, a large fraction of consumers should underestimate such costs (and
relatively few
consumers should overestimate those
costs).
Naturally, whenever possible, surveys
should use incentive compatible designs. For example, respondents could be told to estimate the
ink costs of a consumer
cartridges.
With such
'Office of Fair
Trading
who
prints a specific
number
of pages per
month and
a set-up, accurate behefs could be financially rewarded.
[2002] provides related evidence.
22
uses non-generic
The
Second, researchers could test comparative statics assumed or predicted by the model.
model assumes that consumers show a greater response to up-front
More
model assumes that consumers show a
generally, the
contingent, camouflaged, distant, or disaggregated costs.
consumers are
[1982] find that
far
more responsive
relatively
Hausman
costs than to delayed costs.
muted response
[1979]
to complex,
and Hausman and Joskow
to the store prices of appliances (e.g.
erators) than to the net present value of the energy costs of operating the appliances.
Odean and Zheng
[forthcoming]
loads than to ongoing
show that mutual fund
management
more responsive
for
shrouded attributes. Researchers could
A
that
costs.
MBA
and more generally
to direct costs than to shipping charges,
also study
find field evidence
comparative statics by conducting controlled
see the standard marketing material as well as
Choi
et al.
[2005]
conduct a
field
A
treat-
an unshrouded statement of the
experiment with the structure above. They find
students avoid investing in mutual funds with high
fees are exphcitly
sensitive to front-end
control group might receive standard (shrouded) marketing materials.
ment group would
add-on
more
Barber,
Hossain and Morgan [2005, 2006] find that consumers
fees.
are
experiments.
investors are
refrig-
management
fees only
when those
unshrouded with an exogenous intervention.
Third, researchers could also determine whether firms gratuitously increase the search cost for
add-on
prices.
For instance, firms
may make add-on
prices
much harder
to find than other less
important information.
Fourth, researchers
at loss-leader prices
may conduct product
and
if
audits,
which determine
add-ons are being sold at high mark-ups.
goods and high markups on add-ons are only necessary conditions
if
base goods are being sold
Of
course, loss-leader base
for the existence of a
shrouded
equilibrium.
Fifth, regulators could look for learning effects implied
shrouded and consumers encounter these
consumers
fees as
by shrouded equihbria.
they gain more experience with a product, then
will slowly learn to avoid these fees (see section III. A).
imphes that learning
effects
may
The consumer who just "bought"
to the
fee
and the other consumer did
the add-on will have a lower future add-on
consumer who did not buy the add-on
(since the latter
being unaware of the add-on trap). Such dynamic
of add-on
Indeed, the logic of shrouding
generate reduced form preference reversals. For example, consider
two bank accoimt holders: one consumer just triggered an add-on
not.
If fees are initially
demand
demand compared
consumer has a higher chance of
reversals contradict standard theories
demand, which feature consumer heterogeneity and price discrimination. Agarwal
[2005] find learning effects in the retail
still
et
al.
banking market. Other authors have argued that consumers
23
with a better general education get better prices in the marketplace.
more educated consumers pay
field
less in
[2003] finds that
the mortgage market controlling for default
experiments can be designed to identify the
IV. B.
Woodward
effect of
risk.
Controlled
unshrouding.
Regulatory interventions
Shrouded
available. It
economic
equilibria generate
is difficult
inefficiencies.
However regulatory remedies may not be
to outlaw ignorance or misleading (but accurate) marketing.
If
regulators
find evidence for inefficient shrouding, they have four types of (imperfect) regulatory remedies that
they might consider employing. Of course, the usual costs of regulation could easily outweight
its
possible benefit.
First, regulators
may compel
disclosure.
For example, regulators could compel printer manu-
facturers to report the cost of ink of printed page in a prominent place
regulators have occassionally adopted such unshrouding policies
usage labelhng, and financial product labelhng).
(e.g.
on the product.
nutrtitional labelling, energy
However, disclosure laws
for credit cards
mortgages have met with only mixed success [Ausubel 1991, Woodward 2003]. Indeed,
markets
to design
it is difficult
and enforce a
successful disclosure regulation.
would one compel banks to make financial service
fees sahent?
thousands of complementary financial services with associated
overdraft fees, bounced check fees, etc). There
simunarizes bank
fees.
of the fine print.
whether that
is
is
no summary
Regulations will probably not succeed
Nobody
desirable
yet
knows how
A
in
and
most
For example,
how
bank account provides access to
fees (e.g., out-of-network
statistic like ink cost per
if
Indeed,
ATM fees,
page that
they simply change the font size
And
to compel transparency.
it
remains to be seen
— or possible — in practice.
Second, regulators could simply warn consumers to pay attention to shrouded costs. For example, required "warning labels" could be placed prominently on marketing materials,
cigarette warning labels. For example,
like
mutual fund marketing materials could be required to con-
tain the following warning label: "Investors are urged to check loads,
charges before investing in any mutual frmd.
do not forget to ask about
much
If
management
fees,
and other
these fees are not reported in marketing materials,
them.'"*^
Third, regulators could
make add-on markets more
competitive.
For example, regulators
could require that printer manufacturers allow competitive entry in the printer cartridge market.
""The U.K. Treasury
shank 2000].
is
in the
midst of a broad expansion of transparency regulation in the banking sector [Cruick-
24
Right now, most printer manufacturers prevent such entry by designing cartridges with integrated
patented printer heads (instead of incorporating the printer head into the printer
contains an analysis of this anti-competitive practice.
The famous Kodak
itself).
Hall [2003]
copier case [Klein 1993]
presents another example of an add-on market in which competition was effectively eliminated,
resulting in a
supreme cotut decision against the aftermarket monopoly. However, we tend to be
skeptical of regulations that prevent companies
regulations
may
have the unintended negative consequence of discoiir aging technological innovation.
Finally, regulators
regulates the
from exerting market power. Such pro-competitive
may impose markup
mark-up the hotel charge
exist for regulating
shrouded
fees,
for
caps on shrouded attributes.. For example, Singapore
phone. ^^ However, even
V.
We
myopia that explains such shrouding.
We
even when unshrouding
A
identify conditions
Firms
will
when they
items.
present a model of consumer
under which shrouding survives in
not induce firms to reveal information
is free.
no firm can capture or even
Debiasing a consumer improves consumer
partially share these benefits.
interact with debiased consumers.
Firms receive lower profits
Debiased consumers know how to avoid high-priced
Moreover, firms can't drive away such debiased consumers without losing (profitable)
myopic consiuners as
well.
Debiased consumers can pretend to be myopes, enabling the debiased
consumers to take advantage of the traps that firms
The economics
of shrouding suggest
Finally,
we would
like to
set for
myopes.
some new research
the scope of firms' efforts to shroud information.
myopia.
will
we
com-
not educate the public about the add-on market,
"curse of debiasing" suppresses unshrouding.
welfare, but
may produce
their products, particularly high prices for
show that competition
that would improve market efficiency.
arguments
Conclusion
Following a suggestion by Elhson [2005],
competitive equilibrium.
theoretical
are often counterproductive.
Firms often shroud the negative attributes of
plementary add-ons.
good
such regulations put us on a slippery slope that
Mark-up regulations
great unintended harm.
if
know how
quickly the fog returns as firms introduce
questions.
We would like
to
We
would
like to
measure the degree of consumer
quickly learning unshrouds information
new products and
Singapore requires that hotels price their international phone
Singaporean cents (which is about 20 U.S. cents).
25
measure
and how
"better" marketing techniques.
calls at
marginal cost, plus a
maximum
of 30
Appendix
We define D (x)
demand
as the
The Demand Function D
1:
of a firm that offers an average perceived surplus x units greater
than the average perceived surplus provided by
D{x) using random utihty theory
for
We
lent review).
where
Sai
is
i.i.d.
density f
=
F'.
Fadden
Di
1981].
assume that good
across firms
We
We
i
(see
develop the microfoundations
gives agent a decision utihty equal to Uai
normahze the mass
maxj^i
Vj
— pj +
consumers to
of
Saj).
We
aU firms have the same
S =
same
D{x) =
Plx + ei> max
Ej
^j
1
V
j=2...n
for firm
quality v*
S*
=
Di
for firm 1 is
=
F
and
v*
thus:
is
i
where a
and price p* and
,
—
p*
,
introducing
= D {S — S*),
where
/
/
/
(o)
F"-'
{x
on the difference S — S* between the surplus S
competitors.
Lemma
1
The foUowing Proposition
Suppose that In /
and values
v,
is
The demand depends only
Lemma
Nalebuff [1991],
the
first
and
so
1.
Theorem
order condition
p —
c
=
The
^.
is
2
by the
and the surplus S*
firms,
characterizes the symmetric equihbrium.
c
=
^ :=
p
is
D (0) JD' (0).
(p
—
c)
D {p* — p).
=maxxD(-x +
and Proposition
- p)-{p -
Then
there
is
a rniique
Also,
/-i)-
X
existence of the symmetric equihbrium
D (p*
by
offered
concave, and that firms compete in prices, and have identical costs
^D(O)
(17)
Proof of
offered
so that the profit of a firm charging
symmetric equihbrium with p —
+ e) de.
7_,
See Perloff and Salop [1985] or Anderson, de Palma and Thisse [1992].
c
+ Sai,
pi
define
(16)
its
—
Vi
for syrmnetric equilibria
— p and
v
Then the demand
short-hand for the net average surpluses.
=
consumer preference [Mc-
The demand
1.
be looking
will
In those cases, one can set
a.
an excel-
for
with cumulative distribution function
a,
firm posts quality v and prices p, while the other firms post the
we
We
Anderson, de Palma and Thisse [1992]
and agents
i
competitors.
its
interpret Sia as a tremble or an idiosyncratic
= P {vi — pi + Sai >
{x)
7. If
c)
D'
marginal costs are
(p*
-
p)
=
0.
26
guaranteed by Caphn and
and profits are
{p
—
c)
D {p*
In the symmetric equihbrium,
Finally, equation 17 just reflects that a price
c=0.
c
is
p
=
p*
=
/x is
p
- p),
= p*
an equilibrium
if
A
few cases have compact closed forms.
exp(-e~^), the demand
D (x) =
logistic:
is
distributed with density e~'le>o, the
demand
If
the noise
1/
[1
=
Dix) = x +
=
-x")/n
if
X e
and D(x)
[0,1],
Appendix
Proof of Proposition
We
equilibrium of the game.
We call p*and p*
and we
call
If
1 for
a;
e^
<
x >
Gumbel
1) e~^].
[l
- lx>o
-1,
distributed,
If
the noise
(1
-
D (x) =
is
e~^)"] /n.
(l
F (c) =
i.e.
exponentially
If
the noise
+ x)"/nforx
is
£ [-1,0],
1.
Longer Derivations
2:
timeline
is
detailed in section
We
II.
specify the sequential
use the terminology from Fudenberg and Tirole [1991, pp. 337-341].
the equilibrium prices at other firms for the base good and the add-on respectively,
p and p the
prices at firm
We
about add-on prices.
actions.
The
1.
for
-
(n
D (x) =
is
uniformly distributed in [-1/2, 1/2), then I? (x)
{l
+
is
We
i.
call
p and p* the
beliefs of the sophisticated
consumers
need to check sequential rationality and consistency of the behefs and
a firm unshrouds
then the sophisticated consumers know
p,
p,
which pins down their
behef. If a firm shrouds p, then sophisticated consumers rationally believe that the firm will charge
the monopoly price in period
Given the beUef p
the
eff'ort
=
2:
p
= p,
as this
Hence sequential equilibrium very simply characterizes the
e.
beliefs of the
who
myopes do not matter,
check that firm
Case
a <
1:
Firm
who behave
consumers
is
to exert
beliefs of sophisticated
exactly like sophisticated consumers.
as they just pick with equal probability a firm
The
amongst the
charge the lowest base good prices.
We now
•
the profit maximizing price for the firm that shrouds.
p, the sequentially rational action for the sophisticated
consiuners and the newly educated myopes,
firms
is
i
i
does not want to deviate from the aimounced strategies.
a^ and the Shrouded Prices Equilibrium.
can shroud and pick p and
77
as the behefs are
only on p*
— p.
p
= p* =p
This profit
=
p. Its profit is equal to
(p -h (1
-
a) plp<p) D{p*
and the demand
is
clearly
TT
=
for the
base good of
maximized when p
(p
-I-
(1
-
27
- p),
a)p) D{p*
=p
all
so that
- p).
the consumers depends
The base good
=
p)
•
for
= p*
p
Firm
i
some
of the
price
is
p that
p
solves the first order condition
= p* =
—(1 — a)p
can unshroud and pick p and
myopes and the
+
p.
-
+
(p
(1
—
a.)p)
D'{p* -~p) + D{p*
-
ji.
By unshrouding
its
becomes
fraction of sophisticates
add-on
a'
price, firm
i
educates
= a + A(l — a). The
myopes
keep ignoring the price of the add-on when deciding to buy the add-on while the sophisticates
incorporate
-
If
p <
it
and
will
it iff
p <
e.
e
7r
which
buy
is
=a
+ p) D{—p - p + p*
{p
=
maximized when p
e.
-I-
e)
-
(1
-I-
Otherwise firm
i
a') {p
+ p) D{p*
can increase p by a small positive
increment, decrease p by the same increment, and not change the
consumers while increasing
strictly the
demand
-p),
demand of sophisticated
of naive consumers.
Hence, the profit
can be reexpressed:
TT
As a <
a'
,
this profit
is
=
(p-h e) Dip*
smaller than (p
4- (1
—
-
p).
a)p) D{p*
If
p
>
p), the profit firm
i
could
= p.
achieve by choosing to shroud and price at p and p
-
—
e,
7r=(p+(l-a')%<p)^(p'-p),
which
is
strictly smaller
than (p
-|-
(1
—
choosing to siuoud and price at p and
- We
—
Case
•
{1
2: a^
Firm
i
< a and
p*
the profit firm
i
could achieve by
p=p.
conclude that the best response of firm
— a)p + p and p =
— p),
a)p) D{p*
i
is
to shroud
and price
at p
=
p*
=
—p.
the Unshrouded Prices Equilibrium.
can unshroud and pick p and
p.
-lip<e,
K
which
is
=
a' [p
+ p) D{-p - p + p* +
maximized when p
tive increment, decrease
=
e.
e)
+
[l
-a'){p+p)D{p* -p),
Otherwise firm
i
can increase p by a small posi-
p by the same increment, and not change the demand of
28
so-
phisticated consumers while increasing strictly the
=
+
e)
D{p* —
condition,
—
(p
TT
—
(p
p >
If
+
—
p)
+ D{p* — p) =
This implies that p
0.
Hence
of naive consumers.
In equilibrium, the base good price p solves the
p).
D'{p*
e)
demand
=
p*
first
order
= ~e + fi.
only myopes buy the add-on, and
e,
7r=(p + (l-Q')%<p)^(P*-p)-
This profit
which
is
Firm
maximized when p
strictly smaller
to unshroud
•
clearly
is
and price
than
at
(p
= p. The profit
+ e) D{p* — p),
p and p
=
=
the profit firm
i
(p
+
(1
—
a')p)
D{p* — p),
could achieve by choosing
e.
can shroud and pick p and p and get a
i
is tt
profit equal to
7r=(p+(l-a')plp<p)-D(p*-p),
as the beliefs are
p
= p. One needs a'
rather than
a
above expression, because the other
in the
firms tmshroud, so they educate a fraction A of the myopes. This profit
when p
—
p.
The
the profit firm
•
We
i
is it
=
(p
+
(1
—
= p* =
consumers
p),
which
is
i
is
to unshroud
and
clearly
price at
p
=
p*
= —e +
/i
e.
be either
3.
We
e or p.
after unshrouding.
follow closely the proof of Proposition
Recall that a'
If
= a
-\-
the firm unshrouds,
A(l
—
1.
The
firm's optimal value
a) represents the fraction of informed
its profit
depends on whether p
n(p=e) = m&-x{p+[a'Ts+{l-a'){TMM+TMs)\e)D{p* -p),
(19)
n(p =
(20)
than
p= e.
(18)
If it
maximized
also strictly smaller
could achieve by choosing to unshroud and price at p and
Proof of Proposition
still
D{p* —
Q:')p)
conclude that the best response of firm
and p
p must
profit
is
p)
does not unshroud,
= m^[p+{l-a')pTMM)D{p* -p).
its profit is
n = max(p+(l-a)rMMP)D(p*-p),
p
29
=
e or
p
= p:
To compare the
profits,
observe that
[a'Ts+{l-a)iTMM + TMs)]e < max{Ts,TMM + TMs)e
a <
as
a^^. This implies
not profitable. Also,
n(p =
11 (p
= p) <
high price p for the add-on
We
is
<
e)
U. Unshrouding and posting a low price e for the add-on
by equation
11
19,
>
20 and q'
a.
is
Unshrouding and posting a
also not profitable.
conclude that whatever price the firm chooses to charge for the add-on, unshrouding
is
not
profitable.
Proof of Proposition
We
4.
define the average
^{p)
(21)
we
In this proof,
call
p*and p*
= p™
demand
in the add-on
market
= afip) + {l-a)q^ip),
the equilibrium prices described in the Proposition.
We
check
We
check
that the shrouded prices in the Proposition constitute an equilibrium.
First,
it is
clear that
if
a firm shrouds, the add-on price
that the optimal base good price
we take
c
=
is
is
the monopoly price p™.
the one announced in equation 10. Without loss of generality,
to simplify exposition.^ ^
The
profits are
TI=(p+{^-c)^{D)d{-p + p*).
If
p
is
which
an equilibrium, dll/dp
is
=
at
p
=
p*.
This implies
p+{p^ -
c)^{p^)
= D (0) /D' (0) =
jj.,
new
p,
equation 10.
We now
calculate the profit of a firm that deviates, unshrouds, and sets
prices
p and
while the other firms keep shrouding and using the prices p*and p* given in equations 10-11.
sophisticate facing price
p
in the aftermarket gets the net utility
V (p)
(22)
Call q{p) (or q^ (p)
v{p)
'
+pq{p) the
To go back
if
A
there
is
gross utility.
= max u (e, g) — pq.
an ambiguity) the associated choice of add-on demand, and u{p)
The
utihty provided by the other firms
to the general case, replace
p by p —
c.
30
is:
u^*
=
-p*
+ v{p*).
=
.
The
firm's profit
n=
where x
=
+
(p
p
+
(i?
{p
is
-
—
,
? (?))
^)
c)
is
q{p)
d
{-p
+ v{p)-
This implies p
efficiently.
^
—
c
[(p
=
-
0.
c)
+ V (p)] =
q{p)
When
{p-c) q{p) + v{p)- u^*)
=
g (p)
-
p and noting
—q{p), we get
q{p)
+ ip-c)q
So the highest profit the firm can get after deviating
(p)
=
(j}-c)q
it
(p)
.
prices of the
add-on
is
= maxxD{-x + x*),
Il
X
=
with X*
v (c)
—
u^*
As the pre-deviation
want
profit is n, the firm does not
to deviate
iff
n<Mi?(o),
(24)
as fiD (0)
is
—
jjL
=
v{c)
z,
(24)
—u
—
is
fi
equivalent to x*
=
v{c)
—
V (p*)
<
^i.
To
+ p* —
find the sign of x*
firm does not
want to deviate
+^
iff
x*
(P*)
-
—^ <
0,
n,
we
calculate
by(10)and(22)
= «(c)-u5(^)+^^(^)_(J^_2)[^^(^) +
= u{c)-cf{d)-u' (P*)
—
jj.
= ^(2)-w^(p*)+P*g^(p*)-(p*-S)?(p*)
As the
max^ xD (— a;
the pre-deviation profit. Given equation 17, equation 23, and the fact that
non-decreasing in
X*
+
a firm faces only sophisticated consumers,
(23)
is
{-x
the total profit per customer. Maximizing 11 {x,p) over
that (22) and the envelope theorem imply gsv{p)
=
= xd
u^*)
(1
-
a) (p*
(l_^)§^/(^)] by
-
c) {q^' (p*)
the Proposition
is
-
(21)
^ (p*))
by (22).
proven.
Massachusetts Institute of Technology and National Bureau of Economic Research
Harvard University and National Bureau of Economic Research
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