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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
1
1
,
RoomE52-251
50 Memorial Drive
Cambridge,
MA 021 42
This paper can be downloaded without charge from the
Social Science Research Network Paper Collection at
http://ssrn.com/abstract=728545
informational shrouding flourishes even in highly competitive markets, even in markets with
costless advertising,
and even when the shrouding
JEL
DOO, D60, D80, LOO.
classification:
Keywords: behavioral economics, bounded
geirerates allocational inefficiencies.
rationality,
tion suppression, myopia, shrouded attributes.
consumer protection, informa-
Introduction
1
If
some consumers
are imperfectly rational, firms might try to exploit their biases. In
competitive pressure
may
solve the problem.
scheme to biased consumers and gain
in
A
some markets,
competitor firm could explain the exploitation
their patronage.
which firms have an incentive to debias consumers.
we
In this paper,
We
identify environments
also identify conditions
under which a
"curse of debiasing" occurs, whereby no firm chooses to compete with a debiasing strategy.
We
specifically
study markets
in
which firms choose to hide information from consumers.
For
example, banks prominently advertise the virtues of their accounts, but the marketing materials
do not highlight the costs
minimum
them.
balance
Indeed,
fees, etc.
of such
an account which include
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
fees in the
UK
banking
common
fees for
to supply
sector.
UK Treasury survey that
investigates the origins of high
Half of the respondents report having no information about the
financial services at their
own
bank.^
banking services to personal customers
[...]
The
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.
of their Inkjet printers, but do not
cartridges that cost ten times
reports that only
3%
compete on the principal
more than the
of printer
Printer manufacturers advertise the low price
cost of ownership
printer itself over the
life
—
i.e.,
patented ink
of the product.
Elall
(2003)
owners claim to know the printing cost at the time they buy their
printers.
At
first
glance, shrouding costs seems like a natural marketing strategy.
However, ecjuilibrium
theory implies that shrouded fees actually hurt the bank or printer manufacturer.
that
is
hidden
in the fine print
to be favorable to consumers.
be high
prices.
Any
— or excluded from marketing materials altogether —
Rational consumers
will anticipate that
Such reasoning creates an incentive
for
information
is
not likely
hidden prices are
likely to
information revelation and unravelling of
Respondents were asked "How accurately do you feel you know the charge for services on your account?" Response
About half of respondents choose
"E.xactly," "Roughly," "Not at all," and "Did not apply."
"Not at all."
'
categories included:
shrouding. Indeed,
We
future
all
firms choose to unshroud their prices in equihbria with rational consumers.
show that shrouding behavior
game
Some economists
tree.
will arise
if
"myopic" consumers incompletely analyze the
believe that such shrouding can not 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 consumers creates equilibrium shrouding that
We
Avith high
to such competitive pressure.
We
show that debiased consumers prefer
to give their business to firms
shrouded prices because these sophisticated consumers end up with a cross-subsidy from
myopic customers
To develop
(e.g.,
immune
that the existence of
derive conditions under which competitive price cutting and educational advertising will
not occur in equilibrium.
When
is
we show
efficient
(cf
DellaVigna and Malmendier 2003, 2004)."
intuition for our results, consider a hotel
a myopic guest checks
in,
the hotel will then rent the
room
costs the hotel $100 to supply.
the guest purchases add-ons that cost the hotel $10 to supply
parking, meals, minibar, phone,
markup, so the hotel charges $30
room that
gift
for the
shop items).
Suppose that those add-ons have a 200%
add-ons and makes a $20
for $80; in
profit.
In a competitive market,
competitive equilibrium, total costs ($100-|-$10) equal
total revenues ($80-F$30).
Now
consider a nearly identical "educated" customer,
add-ons and therefore avoids buying them
cell
phone instead
of relying
(e.g.,
on the hotel phone,
who
anticipates
all
of the
marked up
she eats before arriving at the hotel, she brings a
etc.).
The educated consumer
from the add-ons while reaping the benefits of the loss-leader room charge.
substitutes
Our paper
away
identifies
conditions under which educated consumers will not want to leave the firm with high markups,
even when competitors are offering marginal-cost pricing.
room and
It's
often better to pay $80 for a hotel
skip a few overpriced add-ons, than to pay $100 for the
same
hotel
room and
get add-ons
priced at marginal cost.
In essence,
we show that there
myopic consumers.
In equilibrium,
are
two kinds of exploitation.
Sophisticated firms exploit
In turn, sophisticated consumers take advantage of these exploitative firms.
nobody has an incentive
to deviate except the
myopic consumers.
But the nwopes
DellaVigna and Malmendier (2003, 2004) study cross-subsidies that arise from self-control problems.
Naive
consumers who don't recognize their self-control problems cross-subsidize sophisticated consumers who do.
Of course, the hotel would like to screen out such .sophisticated consumers, but this may not be possible.
do not know any better and often nobody has an incentive to show them the error of their ways.
Educating a myopic consumer turns liim into a
(less profitable)
An
This mechanism applies to a wide range of markets.
benefit of a $50 gift for opening an account
An
interest charges
and avoids paying
payment
late
An
fees.
for frequent cartridge
color, printing in draft
consumers prefer to
and avoids paying some
of the fees that snare
float,
myopic
and miles and avoids paying
educated home printer buyer gets a loss-leader price
replacements (by printing in black and white instead of
mode, or printing fewer large jobs
stick
prefers
educated banking customer gets the
educated credit card holder gets convenience,
and
who
good pricing and high-priced (but avoidable) add-ons.
to go to firms with loss-leader base
consumers.
sophisticated consumer
In such markets educated
at home).'^
with the firms that feature high add-on prices, since these firms have
loss-leader base-good prices,
and the educated consumer can
away from the
partially substitute
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
imply that firms have an incentive to disseminate information about their products and choose not
to do so only
We
if
such dissemination
identify conditions
is
costly (e.g.. Butters 1977, Salop
under which firms
lowering add-on prices, even
when
will
advertising
costless marginal information dissemination
with only rational consumers, firms
In our model, with
costlessly.
The
rest of this
will
choose
is free.
still
?iot
and Stightz 1977, Stahl 1989).^
to advertise
why
This explains
shroud their add-on
choose to disclose
all
and hence not compete by
industries with nearly
prices.*^
In a search
of their information
enough myopic consumers, shrouding
is
if
model
they can do so
the more profitable strategy.
paper formalizes our claims. Section 2 defines a shrouded attribute and presents
an equilibrium analysis of a market with discrete demand
sions, including the general case
for add-ons.
Section 3 discusses exten-
with continuous demand for add-ons. Section 4 concludes.
All
proofs are presented in appendices.
A
sophisticated consumer could also purchase the add-on from a third party, at
why base-good
^This can be viewed as the key difference
Stiglitz 1977)
approach,
if
some transaction cost. This is
and Hall (2003) for examples.
between modelling bounded rationality as search costs (e.g., Salop and
firms often hinder such third party transactions. See Salop (1993)
and modelling
it
directly as failure to anticipate an attribute as in our model.
In the search cost
firms can costlessly educate the consumers, they will do so because consumers are Bayesian.
way
If
a firm
consumers will rationally infer that it has something
to hide. So, if advertising costs are low, all firms reveal information to consumers.
Try finding the operating cost of a personal Inkjet printer on the web site of a printer manufacturer.
goes out of
its
to sustain high search costs, Salop
and
Stiglitz
A
Review
Literature
1.1
recent literature argues that consumers' psychological biases explain a variety of puzzling market
outcomes. DellaVigna and Malmendier (2003), Oster and Morton (2004), and Shui and Ausubel
(2004) apply quasi-hyperbolic discounting to respectively study
tions,
and
credit card accounts.
loss aversion to
gym
contracts,
Heidhues and Koszegi (2004) and Koszegi and Rabin (2004) apply
study bait and switch marketing. Gabaix, Laibson and Li (2004),
(2003) and Spiegler (2004) apply boundedly rational heuristics to study
exploit noise in
marketing hterature
consumer
(e.g.,
Bertrand
et
choice,
one would
al.
how market
Several lines of research
Hausman
affect
consumer demand.
loads than to ongoing
(2005)
Hausman and Joskow
show that mutual fund
management
fees.
prevalent on the Internet. Hossain and
Ellison
Morgan
tion to direct costs than to shipping charges,
place.
For example.
(1982) report that consumers put
investors are
and Ellison (2004)
more
life
of the product.
sensitive to front-end
find that price obfuscation
(2004, 2005) find that consumers pay
and more generaUy
more
more
find field evidence for
(2003) finds that less educated consumers pay
more
atten-
shrouded
in the
in
is
market-
the mortgage
for default risk.
long intellectual tradition argues that competition will prevent biases from affecting the
market equihbrium.
will drive out
will
Woodward
behavioral
to up-front costs than to
Other authors have argued that smarter consumers get better prices
market controlling
A
When
firms' customers.
show that consumers pay more attention
(1979) and
Odean and Zheng
attributes.
equilibria
firms have an incentive to recruit
weight on the store price of an appliance than on the electricity cost during the
Barber,
Leslie
2004, Morwitz, Greenleaf and .Johnson 1998,
know whether
like to
new customers by educating and debiasing other
delayed costs.
and
Mullainathan and Shleifer (2004) study market incentives to slant news.
Wertenbroch 1998) shows how frame manipulations
biases affect
.Jin
consumer product evaluations. Glaeser (2005) studies the supply of ideology by
political entrepreneurs.
Finally, the
magazine subscrip-
For instance, Becker (1957) works out conditions under which competition
employment discrimination by
firms.'
Our paper
asks whether competitive pressure
prevent shrouding and high mark-ups in the market for add-ons.
Many
'Cf.
authors have developed rational actor models that explain
Laibson and Yariv (2004).
why add-ons have
relatively
why
high markups, though none of these models explain
Ellison (2005) provides an excellent review of this literature. Here
markets."'*
Three types of explanations
findings.
firms gratuitously shroud those add-on
exogenous search
costs, inability to
for
we review the main
high mark-ups figure prominently in the literature: high
commit, and price discrimination.
We
highlight the difference
between these models and our model of consumer myopia.
Search-cost models impty that firms choose high add-on prices because
for
it is
exogenously costly
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 such search models, an inexpensive
communication technology eliminates equilibrium market power and markups.
However,
in our
model, the existence of free advertising does not diminish market power since firms individually
Our model generates voluntary information
prefer to shroud information about the add-on market.
suppression.
In the
modern economy, information dissemination
gratuitous shrouding
is
needed to explain why many
costs are sometimes quite low, implying that
firnrs
their add-ons. For example, the printing cost of personal
on the Hewlett-Packard web
site.
From each
of links to uncover the cost of printing,
itself.
Such shrouding does not
about printing costs
is
reflect
printer's
which
is
make
HP
it
difficult to
deskjet printers
is
observe the prices of
not easily accessible
homepage, one must follow a large number
ten times greater than the cost of the printer
exogenous information
diff'usion costs.
The information
away from the printer homepage^" than any other information about
further
the printer.
The
literature
on commitment shows that firms
will
not commit to add-on prices at the time the base good
choose high add-on prices
is
sold.
if
firms can-
This theory was introduced
in
Klemperer's (1987) work on switching costs (see the survey by Farrell and Klemperer, 2005) and
extended by Borenstein
et
(1995).
al.
When
firms cannot
add-on prices above marginal cost (and rational consumers
'"Ayres
will anticipate this).
Difficulties of
and Nalebuff (2003) propose that high add-on prices are partialh' due to suboptimal choices on the part
would make more profits if they had low add-on prices and consequently developed a
good corporate reputation.
'if firms can costlessly unshroud
A
rational
shrouding.
measure distance using the
and consumers are Bayesian, then firms will be forced to eliminate
consumer would expect the worst of a firm that engages in gratuitous
their attributes
gratuitous search costs in equilibrium.
We
to add-on prices, firms set
In their view, firms
of firms.
'
commit
click metric.
commitment may be
some
cases, such as the
we consider the polar case
analysis however,
in
relevant in
Kodak
antitrust case (Klein 1993). In our
which firms can commit to an add-on price
in
(e.g.,
our setting, printer manufacturers can freely and credibly preannounce the price of their printer
cartridges)
demand
Price-discrimination models imply that add-on pricing enables firms to charge high
consumers relatively more than low demand consumers (Ellison 2005). In Ellison's model, exogenous search costs make
profits
it
costly for
consumers to observe add-on
because add-on pricing generates a technology
that add-on pricing will not raise profits
exogenously small, see Stole
(200-5)).
when
Add-on
prices.
for price discrimination.
advertising
is
inexpensive
Ellison's analysis motivated our
(i.e.,
own
if
consumers are boundedly
Finally,
We
rational.
when
search costs are
if
advertising
is
costly
develop a model with the latter microfoundation.
we emphasize that our model explains both high add-on
mation shrouding.
Ellison points out
study, particularly his
concluding conjecture that the persistence of shrouding might be explained
or
pricing raises
prices
and gratuitous
Pre-existing models can explain high add-on prices, but none of
them
infor-
predict
voluntary shrouding.
2
We
Shrouded Attributes: Definitions and a Model
analyze a market in which firms can shroud attributes of their products.
attributes are not taken into consideration
by some potential customers.
might suppress information about minimum balance
consumers
will neglect to consider
such
minimum
purposes of our model, a shrouded attribute
is
fees in the
the deskjet price per page on their
web
site is
when
is
The Hewlett-Packard
two mutually exclusive categories: (avoidable) add-ons and (unavoidable)
generally,
communication costs need
to
even
decision to omit
fees, penalties, accessories, options, or
hidden feature of the ongoing relationship between a consumer and a firm.
More
firm,
an example of such information suppression.
Shrouded attributes may include surcharges,
with rational consumers.
hidden by a
Some
For the
picking a bank.
a product attribute that
-^^
For example, a bank
bank's marketing materials.
balance fees
though the attribute could be nearly costlessly revealed.
These shrouded
We
any other
divide this
list
into
sui^charges.
be low enough so that unshrouding would occur
in
an equilibrium
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
can avoid paying
hotel
room
for
room
service meals
complement a hotel
service
they instead use
if
by finding
cell
phones.
local restaurants.
For example, hotel
Likewise, hotel guests
Both
hotel
phone use and
Such complementary (voluntary) goods are referred
stay.
to as add-ons.
In our modeling,
we
distinguish between a "base good" and the shrouded attribute.
preceding example, the base good
We
a hotel
room and
the shrouded attributes are hotel services.
assume that myopic consumers pick a base good without considering shrouded
attributes. ^^
Timeline and overview of (discrete demand) shrouding game
2.1
We now
i.e.,
is
In the
discuss a
continuous
model with discrete demand
demand
— to section
discrete
demand game. We
Period
0:
•
3.2.
We
for the add-on.
start
We
postpone the general case
by providing an overview of the timing
discuss the details of the
game
Unshrouding a price
is
This
Firms pick
Period
prices for a base
good
(/j)
and an add-on
is
a
To make un-
equivalent to advertising that price.
shrouding/advertising maximally attractive to the firm, we assume that unshrouding
•
of the
after the timeline.
Firms decide to make information about the add-on shrouded or unshrouded.
binary choice.
—
is free.-*^
(p).
1:
• Sophisticated
consumers (fraction a of the population) always take the add-on and
into consideration.
If
information about the add-on
is
its
price
shrouded, sophisticates forni Bayesian
posteriors about the unobserved add-on.
•
Myopic consumers
(fraction 1
—a
observe the add-on information.
A
of the population) only consider the add-on
When
the add-on
is
observing the hotels' add-on pricing schedules.
they directly
shrouded, myopes do not observe the
consumer can compare prices of closely located four star hotels on a web travel
See Ayres and Nalebuff (2003).
13
We revisit this assumption in subsection 3.3.
'
if
site (e.g., Orbitz),
without
When
add-on information.
the add-on
unshrouded, fraction A E
is
(0, 1]
of
myopes observes
the add-on information.
•
Consumers choose a
•
Consumers can
firm.
initiate costly
behavior
(effort cost e)
that enables
them
to substitute
away
from future use of the add-on.
Period
2:
Consumers observe the add-on
•
price
portunity to purchase the add-on.
(if
they haven't observed
it
already) and are given an op-
Consumers who previously engaged
in costly substitution
behavior have a lower incentive to purchase the add-on.
Details of the shrouding
2.2
To motivate the model, we
in
which firms
offer
game
will discuss the
example of a bank, but the naodel applies to any setting
add-ons to their customers.
Period
2.2.1
In period
which
in
0,
banks
set
our example
and potentially shroud
is
prices.
Let p represent the price of a base good,
the price of opening a bank account.
add-on. In our example, violating the
p and p are chosen by each bank
minimum
in period 0.
balance
Without
is
Let p represent the price of an
an add-on service with price p}'^
loss of generality,
Both
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
p,
minimum
the
hidden
published in an obscure location.
a gratuitous search cost that
^*In
us
banks, a
check
fee,
minimum balance
fee.
If
the bank chooses to shroud
balance fee will not be seen by potential consumers.
in fine print or
some minimum that
its
tj-pical
is
is
large
minimum
strictly greater
or an insufficient funds fee.
don't have in their accounts.
One can
For example, p
may be
think of this action as creating
enough so that few consumers bother to see the add-on
price.
SIO and applies in months when an account balance falls below
balance fee is distinct from an overdraft fee, a bouncedThose fees apply to cases in which customers would like to use funds that they
balance fee
than
zero.
is
A minimum
Naturally, the model discussed here applies to those fees as well.
10
Without
loss of generality,
we assume
that shrouding implies that no consumer observes the add-on
price.
The bank may
alternatively costlessly advertise p, thereby revealing
consumers and to A fraction
assume that A
myopes
may
is
We
fixed.
— who may not
of
< A <
myopic consumers, with
it
Without
1.
to
sophisticated
all
loss of generality
we
allow A to be weakly less than unity to reflect the possibility that
the value of information about the add-on market
initially recognize
overlook that information even
when
it is
made
available.
We
define m.formed
myopes
—
as the
myopes that have seen (and noted) unshrouded information about the add-on. Informed myopes
behave exactly hke sophisticated consumers.
Analogously,
we
define uninformed
myopes
myopes that have not seen information about the add-on. Hence, when information
by one or more
firms, a fraction A of m5'opes
— and a fraction
1
—
A of myopes
is
— and
informed
is
Period
Consumers
become sophisticated
all
firms.
^'^
1
pick a firm from which to
buy the base good.
Sophisticates always take the existence
of the add-on into consideration, forming Bayesian posteriors about the add-on
shrouded. Myopes only consider the add-on
if it is
can consider add-on pricing when choosing a
high add-on prices can exert costly
For example, a consumer
effort e
who
Second, a consumer
firm.
>
in
period
faces a high
is
assume that add-on
forced to pay a high
fee,
fee
p
is
effectively
1
its
price
is
is
who
First,
a consumer
anticipates or observes
and thereby substitute away from the
minimum
into the account or cut back withdrawals so that the fee
We
when
revealed to them.
For a consumer, taking account of the add-on generates two sources of value.
add-on.
unshrouded
Hence unshrouding by am' firm increases the
uninformed.
sophistication of the pool of potential customers shared by
2.2.2
therefore
is
as those
balance fee could transfer balances
less likely to
bounded above by p >
e.
be invoked.
For example,
if
a customer
the customer might terminate her relationship with the bank or lodge
a complaint. Legal and regulatory constraints also limit the penalties/fees that banks can charge.
Finally,
p could represent the cost of a
last
minute consumer intervention that enables the consumer
to avoid purchasing the add-on.
"
Assuming that the impact
of advertising
is
more
local
would not change our
11
results.
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 Xj represent the anticipated net surplus from opening an account at bank
i
the antic-
less
ipated net surplus from opening an account at the best alternative bank (ignoring idiosyncratic
Throughout the paper we use starred variables to represent the (symmetric)
taste differences).
prices set
by other
We
firms.
analyze symmetric equilibria in this paper.
For sophisticated consumers,
^i
=
[-Pi
- min {Ep, e}] -
[-p*
When
where Ep and Ep* are rational expectations.
- min [Ep"
When
of
myopes becomes informed.
A myope
p.
firms.
When
into two classes.
i
uninformed.
When
add-on information
is
shrouded,
is
all
with
like sophisticates
1
Ep =
behavior vis-a-vis
in his
unshrouded, a fraction
shrouded,
is
unshrouded, expec-
add-on prices are unshrouded, a fraction A
becomes sophisticated
However, even when add-on information
is
Ep mid Ep*
These informed myopes behave just
that was educated by firm
,
the add-on information
sophisticated consumers solve the Bayesian equilibrium to calculate
fall
e}]
the add-on information
tations are eciual to the true value of the add-on price.
Myopic consumers
,
—
all
A of myopes remains
n^opes are uninformed.
For uninformed myopes,
Xi
= -p^+p*.
Uninformed myopes neglect the add-on when deciding where
to
open
uninformed myopic consumers do not consider exerting substitution
their
bank account. Likewise,
effort e in
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
^We assume
demand
local risk neutrality
zero,
i.
i
L
Recall that
less
throughout the paper.
12
the average
The demand
function
A
presents
and bounded above by one. Appendix
function.
x,-
Period 2
2.2.3
Consumers observe the add-on
price
All other
they haven't observed
it
Consumers who have engaged
tunity to purchase the add-on.
purchase the add-on.
(if
consumers purchase the add-on
already')
and are given an oppor-
in substitution in
period
1
do not
at price p.^^
Symmetric equilibrium
2.3
We now
characterize the synrmetric Bayesian equilibrium in this game. Let
The
of sophisticated consumers in the marketplace.
choose high markups in the add-on market.
a
represent the share
following proposition shows that firms will
In the Shrouded Prices Equilibrium, firms will choose
markups that
are so high that the sophisticated consumers substitute out of the add-on market.
Proposition
1
Let
a^
=
1
- e/p
(1)
and
~
^L
If
a <
a', there exists a
this equilibrium, only
substitute
If
a >
'
i.e.,
a'
,
away from
The prices of
the base good
and
the
price.
Call this
add-on are respectively:
p
= -{l-a)p-hl.t
(3)
p
=
(4)
myopes purchase
p.
the add-on.
The allocation
is ineffi.cient
since sophisticates
the add-on.
there exists a symmetric equilibrium in which firms do not shroud, the add-on price.
we could assume that uninformed myopes buy the add-on in period 2 without observing the
myopes believe that the unobserved add-on price is low enough to justify the purchase.
Alternatively,
the
(2)
symmetric equilibrium in which firms shroud the add-on
the Shrouded Prices Equilibrium.
In
= D{0)/D'{0).
13
Call
price:
this the
In
Unshrouded Prices Equilibrium. The prices of the base good and the add-on are
this equilibrium all
p
=
-e +
p
=
e.
(5)
fj.
(6)
consumers purchase the add-on, so
In each of these equilibria, the
beliefs of
respectively:
the equilibrium is efficient.
consumers are p
=
p for
the add-on price at firms that
shroud.
Appendix B.
Proof:
Proposition
1
characterizes a Shrouded Prices Equilibrium^® in which firms choose inefficiently
high markups in the add-on market and choose to shroud those add-on
Prices Equilibrium, firms set p*
ecjuilibrium
p^
though the marginal cost
pay
inefficient since the sophisticates
is
consumption
=
the well-known
10
(i.e.,
the
demand curve
competitive market with small
^—
— a)p <
{1
and the base good
Our model
literature.
vertising
effort cost e to substitute
result that high
low or negative markups on the base good.-'^ This
p*
producing the add-on
Shrouded
is 0.
This
away from add-on
(see subsection 2.4 below).
Our model reproduces
competitive
of
In the
prices."''^
oi p* PS
will
/i,
—e <
be the
is
easiest to see
highly elastic, and hence
the base good
0.
is
markups
The model
is
for the
add-on are
when the market
/.i
is
is
close to zero).
offset
by
approximately
In a relatively
always a loss leader with a negative markup:
implies that the add-on will be the "'profit-center"
"loss leader."""'
also predicts equilibrium shrouding,
which
is
not predicted in the pre-existing 10
Indeed, previous authors have conjectured that the availability of inexpensi-v-e ad-
would drive down after-market prices and eliminate shrouding.
For example. Shapiro
^"^Proposition 1 characterizes some but not all of the symmetric equilibria.
When A is large enough another
equihbrium exists. Specifically, when q < a'^ < ol-\-X{1 — a), the Shrouded Prices and Unshrouded Prices Equilibria
both exist. 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 Equilibrium is the unique symmetric equilibrium.
^^For empirical applications, we reexpress Proposition 1 in the case where the marginal costs c and c < e are not
zero. In this case, if q < q
The value of p does not
p = c — (1 — o) (p — c) -f /i, and \ia>Q.\p = c-'rc— e +
/.i.
,
change.
See the literature review
^In
many seemingly
in
the present paper and in Ellison 2005.
competitive markets the price of the base good
printer, hotel, car rental, financial services), while the price of the
cartridge, hotel
phone
call,
gas charge,
minimum
balance
fee).
14-
is
add-on
typically set below its marginal cost (e.g.,
is
set well
above
its
marginal cost (printer
(1995) describes the inefficiency caused by high
markups
aftermarket and then observes that
in the
competition and advertising should drive them away.
Furthermore, manufacturers in a competitive equipment market have incentives to
A
avoid even this inefficiency by providing information to consumers.
could capture profits by raising
to cost), lowering
its
[base-good] prices above market levels
its
aftermarket prices below market levels
informing buyers that
its
overall systems price
the manufacturer could eliminate some or
by offering a lower
all
total cost of ownership,
eliminated deadweight
loss.
manufacturer
at or
is
of the
and
(i.e.,
still
and
closer to cost),
below market.
deadweight
closer
(i.e.,
In this fashion,
loss, attract
consumers
capture as profits some of the
In other words, and unlike traditional
monopoly power,
the manufacturers have a direct incentive to eliminate even the small inefficiency caused
by poor consumer information (Shapiro 1995,
p.
495).
In the Shrouded Prices Equilibrium, Shapiro's intuition
in the aftermarket
do not go away as a
Why doesn't Shapiro's
prices,
In general, high
markups
result of competition or advertising.
advertising argument apply?
by advertising low add-on
to apply.
fails
Shapiro conjectures that firms will compete
thereby attracting consumers by highlighting the benefits of
efficiently priced add-ons.
However, Proposition
1
shows that
this competitive effect
overturned by a "pooling"
is
Educated consumers would rather pool with uninformed myopes
at firms
effect.
with high add-on prices
than defect to firms with marginal cost pricing of both the base good and the add-on.
Again consider the
illustrative case in
which the firm has no market power, so
/j.
=
0.
If
a
sophisticated consumer gives her business to a firm with shrouded market prices, the sophisticated
consumer's surplus
will be:
sophisticated surplus
,
.
"
.
=
—p —
=
{1
>
(l-a')p-(l-a)p
=0.
15
e
— a)p —
e
By
contrast,
if
the sophisticated consumer gives her business to a firm with zero
the base good and the add-on, the sophisticate's surplus will be exactly 0."
cated/educated consumer
is
strictly better off pooling at the firm
markups on both
So the
sophisti-
with shrouded prices (and high
add-on markups), than deviating to the firm with marginal cost pricing.
This preference
for
pooling reflects the fact that the sophisticated consumers are cross-subsidized
by the uninformed myopic consumers. Educating uninformed myopes enables them to get more
value out of their relationships with high
markup
firms.
After education, myopes anticipate the
high add-on prices, and hence substitute away from add-ons while
on the base good.
The newly educated consumers
benefit
from the
still
enjoying loss leader prices
"free gifts"
and avoid the high
fees.
This generates the curse of debiasing.
consumers. Informed consumers
sophisticates prefer to patronize
(i.e.,
A
firm does not
want to debias uninformed myopic
sophisticates) are not profitable to any firm.
— and
in particular, exploit
— firms that
Specifically,
offer loss-leader prices
on base-goods.
In summary, the presence of uninformed myopic consumers incentivizes firms to adopt pricing
schedules that have the unintended consequence of cross-subsidizing sophisticates.
myopes sophisticated
will
not help any firm.
incentive to educate myopes, even
2.4
Making more
Because of this curse of debiasing, no firm has an
when education
is
costless.
Welfare
We now
provide a welfare analysis of the Shrouded Price Equilibrium and highlight the inefficiencj^
of this equilibrium.
Proposition 2 hi
consumers are
there
is
Proof.
p— e
tlie
Shrouded Prices Equilibriwn, the social welfare
units better off than
no inefficiency and
The
all
social welfare loss
costly effort e to avoid
consumers are equally
is
the
A=
ae. Sophisticated
Unshrouded Prices Equilibrium,
well-off.
proportional (with factor
consuming the add-on.
""The particular value of a
the surplus will be
myopic consumers. In
loss is
e) to
the fraction of agents that exerts
Recall that the firms can produce the add-on at
surplus depends on the choice of normalization.
V
16
If
we
shift all utilities
by a factor
V
marginal cost. In the Shrouded Prices Equilibrium,
so the deadweight loss
pay
p-
e better off
Unshrouded Prices
In the
add-on, which
produced
is
of the sophisticated agents exert effort
ae. Also, as sophisticates pay e to avoid buying the add-on,
is
p, sophisticates are
all
marginal cost. There
is
no
Since the add-on can be produced at zero social cost,"^
consumed.
If
In the case with inefficiency {a
<
of sophisticates increases; in this case sophisticates
and
all
purchase the
efficiency loss.
it is
socially efficient for the
a consumer substitutes away from the add-on (at effort cost
socially inefficient.
and myopes
than myopes.
Eciuilibrium, no consumers exert costly effort,
at
e,
e),
add-on to be
then an equilibrium
is
a^), the welfare losses increase as the fraction
do not consume the (high-priced) add-on.
Extensions
3
In this section
myopes learn
add-on.
we
to
discuss several extensions of the model.
become
Finally,
we
sophisticates.
First,
we
discuss the case in which
Second, we analyze the case of continuous
demand
for the
discuss a series of additional considerations that influence the persistence of
shrouding.
Learning
3.1
In
some markets, myopes eventually learn the high
ticates.
We
price of the add-on, thereby
becoming sophis-
present an extension that reflects this learning process and demonstrate
affects ecjuilibrium pricing.
how
learning
.
,
.
^
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 base-good,
sophisticates face the add-on purchase decision
whether to pay avoidance cost
sophisticates.
e or
Ts
This assumption
is
made without
T]\.js
buy the add-on
times. "*
Our
For each decision, sophisticates decide
times.
Uninformed myopes buy the add-on
and make sophisticated choices
for price p.
Ti\,jm times.
original
Informed myopes act just
They then become
model corresponds to Ts
like
sophisticates
= Tmm =
1
loss of generahty.
some cases is may be natural to assume Ts
Shrouded Prices Equhbrium does not depend on it.
"""in
,
= Tmm + Tms,
17
but we do not make this assumption here, the
and T\is
=
We
0.~^
assume that firms choose
their shrouding poHcies
and
prices once
and
for all
and do not change them during the game.
The
following Proposition shows that there
sophisticates
a
is
is
a Shrouded Prices Equilibrium
if
the fraction of
low.
Proposition 3 Let
II =
a"
If
a <
a^^, then there exists a
—
1
e
max {Ts.Tm
— M + Tms)
P
Tmm
.
symmetric equilihrium. in which finns shroud the add-on pricing.
Call this the Shrouded Prices Equilibrium:
P
=
-Ci-
p
=
p.
- a)pTMM +
IJ-
In this equilibrium, the myopes purchase the add-on until they become sophisticates.
is
socially inefficient since sophisticates substitute
are
p
=p
the add-on.
The
beliefs of
consumers
for the add-on price at firms that shroud.
The myopia model
et al.
away from
The allocation
predicts that consumers will eventually learn to avoid add-on fees.
Agarwal
(2005) empirically evaluate these dynamics, confirming the prediction that add-on fees in
banks decline with customer tenure.
This learning pattern
is
inconsistent with the predictions of
a classical price discrimination model of add-on pricing.
Our
analysis raises the question of long-run dynamics.
If
consumers learn to avoid add-on
does shrouding eventually vanish along with high add-on prices?
sustain shrouding in the long-run.
Second, sophistication
is
First,
may
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
Several countervailing forces
fees,
new shrouding techniques
Third, and most importantly,
For example, the emphasis on fee-based revenue
in the
banking sector
is
a
recent development (Rogers and Sinkey, 1999)
We
believe that fees for specific add-ons have a lifecycle.
to be shrouded
and priced above marginal
cost..
^See Miao (2005) for another analysis.
18
When
the add-on
is
new
it
tends
Over time, shrouding decreases and the add-on
price
Using our notation, the fraction a of sophisticates increases over time and shrouding
falls.
^^
eventually disappears.
Continuous add-on demand
3.2
In this section,
we generahze the model
to the case of continuous
when
that equilibrium shrouding survives only
The
for the add-on.
original
game except
Total consumer utility
cost of purchasing
firm
i's
is
for the
add-on.
We
show
sophisticates have relatively inexpensive substitutes
structure and timing of the
for the extensions
demand
game
in this section mirrors the details of the
enumerated below.
decomposed
into
two parts: the value of owning the base good and the
— or substituting away from — the add-on.
Let Uat represent agent a's value of
—
PiQai represent the costs associated
base good, o^'erlooking the add-on."'
Let u{eai,qai)
with the add-on, reflecting both the add-on quantity
away from the add-on. The leading case
is
qat
and any costly
efforts eat to substitute
<
net value of buying the
d'^u {eai, Qai) /deatdqai
The
0.
base good can be written
+
Uai-Pi
U{ea,,qai) -Piqai
base good utility
Li period
1,
sophisticated consumer a picks a firm
Uai
.
In period
2,
maximize u
utility for the rational
Informed myopes behave just
information in period
i
utility
and substitution
effort Cai to
(cai, qai)
— Piqm- We
call
u^
expectations case in which pi
like sophisticates,
since informed
=
[pi)
—
uieai-,
Ep^r^
myopes observe the add-on
thank Douglas Bernheim
myopes do not take account
for
of the add-on
when they
pick a firm
suggesting these hfecycle dynamics.
'For example Uai could represent the value of the base good assuming a zero price for the add-on.
(p.)
=
S:(ea,,ga,)
=
qm) the
1.
In contrast, uninformed
^*S^
maximize
= max E iuar- Pt + max [u (e^,, qai) - Piqa
sophisticates pick 5aj to
corresponding indirect
We
add-on
u(ea,(£p,),ga,(Ca,(£p,).p.))
=
U(eai(p.)=?ai(ea,(p,),p,))-
19
?'.
In
period
1,
uninformed myopes pick a firm
i
maximize
to
E {uai — Pi + Constant}
Uninformed myopes passively choose a default
not responsive to shrouded variation in
2(e^^5ai)
We
2,
uninformed myopes pick
qai to
which
is
maximize
-mai-
call c
the the marginal cost of the base good and c the marginal cost of manufacturing the
add-on. Let q
(p) represent
face a price p.
Let
initially
level of substitution effort in period 1
?^f
In period
pi.
.
q^
(p)
demand
the equilibrium add-on
represent the equilibrium add-on
of a sophisticate
demand
overlooks add-on prices because they are shrouded.
We
who knows
of an uninformed
she will
myopic who
demand
define the average
in the
add-on market
^{p)
and we assume that there
is
a unique
=
+ {l-a)q'Hp),
monopoly
p^ =
Now we
aqS{p)
(7)
price in the add-on market, given
-
arg max ((p
c)
f (p) j
by
(8)
.
characterize symmetric equilibria.
Proposition 4 Suppose
that unshrouding
makes
all
consumers sophisticated
(\
=
1).
The price
vector
P
= c- ip-c)q{p) + n
p
= P^
supports a Shrouded Prices Equilibrium
if
(10)
and only
if
B >
1,
where
cross-subsidy to sophisticates from,
_
loss of social surplus (for sophisticate
(1
-
[u^ (c)
q) (p'"
-
cqS
-
(9)
B is
myopes
demand) due
- q^ {p"'))
-^qS (j?n)]
(j?") -
the debiasing ratio:
to
add-on mark-up
c) {q^'^ (p^")
(?)]
-
[u^
20
(12)
The
beliefs of
The proof
consumers are p
is
=
p"" for the
add-on price
firms that shroud.
at
Appendix B.
in
This no- advertising result contains a boundary condition that determines
B >
appear:
when
Advertising does not arise
l?'-^
high
B
To
would calculate
values tend to be
B
loss-leader subsidy in base-good
"
consumer surplus
at a
empirical test
more shrouded.
,
A sophisticate
An
cost.
and determine whether markets with
ratios in different markets,
heuristically derive the result, consider another ratio that
loss of
advertising will
the cross-subsidies to sophisticates are larger
than the social welfare distortions due to price deviations from marginal
of this theory
when
shrouded firm
market
demand) due
(for sophisticate
will not defect to
easier to directly interpret:
is
to
add-on mark-up
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
B'
(i.e.,
>
Since aftermarket profit generates loss-leader competi-
1).
—
tion in the base-good market, the loss-leader base-good subsidy
is {p"^
which
The denominator
is
the average profit per customer in the add-on market.
ticates' welfare loss
sophisticate
would
from high mark-ups
realize
add-on
in the
utility of
(c)
— cq^
(c)
but
,
[aq^
(p'")
-I-
of B'
(1
—
a)
q^'^
(p^)]
the sophis-
is
At marginal cost pricing
add-on market.
u^
c)
(p
=
c),
the
shrouded prices equilibrium
in the
the sophisticate pays add-on price p"' and realizes a lower add-on utility of
li^ (p'")
— p^q^ (p"')
Putting these results together, we have,
- ?) [aq^ (7?") +
(c) - cq^ (c)] - [li^
(p^
B'
[u^
We
can recover
denominator of B'
B
.
B~
(equation 12)by subtracting
Hence
Note that the numerator of
"With
liS B' >
B
is
-
a)
(p'")
-
(1
1 is
(p™)
-
(p"^
—
c)
q-^^ (p"^)]
p'"^^
(p"^)]
q^ (p™) from both the numerator and
q^'^ (p*")]
p'"g^
-
{p"')]
(p^
-
-
(p"^
?)
-
q^ (p^)
c)
q^
{fP")
the (net) cross-subsidy to sophisticates resulting from high add-on
demand model of section 2, the subsidy is
Q < a^, reproducing the result of Proposition
the discrete
B>
g)
I.
- ?) [aq^ (p^) +
(c) - cq^ (c)] - [u^
(p"^
[u'^
Condition
B>
-
(1
21
(1
1.
— a) p, the
distortion
is e,
so
B =
(1
—
Q:)p/e.
prices,
(p'"
-
c)
[af (p- +
)
^
-
1
(
-
«) ^^^ (p-)]
(p™
loss-leader subsidy in base-good
-
c)
g^
(p-^)
'
'
^
market
'
funding from sophisticates
Simplifying this expression yields the numerator of B:
[i^ ^)ijr -c){t'
This cross-subsidy
represent
(p^
all
— c>
will
be positive
iff
the following three conditions hold:
<
1),
the monopoly price of the add-on exceeds
of the population {a
0),
and myopes buy more of the add-on than sophisticates
The denominator
of
B
surplus
utility of
u^
{c)
— cq^
only u^ (j?")
is
Hence, the
—
At marginal cost pricing
(c)
,
p"^q^
but
in the
loss of
(?)
(p^)
—
marginal cost
its
q^ (p^)
>
0).
- ?q^
-
—
c),
the sophisticate would realize
However, the firm realizes a surplus of
(f"')-
(?)]
{p
shrouded prices equilibrium the sophisticate's consumer
loss of social surplus (for sophisticate
[u^
{q^'^
sophisticates do not
represents the social welfare distortion (in the sophisticate case) resulting
from the high price of the add-on.
add-on
{D -f iT^n)
[k^
iPn -
consumer surplus due
to
demand) due
rf
to add-on
-
ip"")]
ip"'
add-on mark-up
(p"^
mark-ups
—
c)
q^ (p^)
given by,
is
-c)f (p"')
transfer to firm
Simplifying this expression yields the denominator for B:
[uS{?)-df{d)]-[u^ip"')-dfip'^)].
To
further interpret this proposition, consider the case
For this case a transparent "proof
costs are
0.
Now
is
available.
^t
=
0,
market power.
so firms have no
For simpUcity, also assume c
=c=
0,
so marginal
consider the equilibrium payoff of a sopliisticated consumer in the shrouded
ecjuilibrium:
Compare
this to the equilibrium payoff of a sophisticated
a firm with unshrouded marginal cost pricing: vr
9.9
(0).
consumer
if
The shrouded
the consumer has access to
equilibrium
is
robust
if
the
payoff with marginal cost pricing
less
is
than the payoff
in the
shrouded equilibrium:
Substituting equation (9) implies that this inequality can be reexpressed
Recalling that q {p^)
= aq^ {p^) +
which
is
a) q^^
(p"'),
and rearranging
yields
2^(0)-S5(p'")<(l-a)p'"(g^^(p'")-g^(p'")),
'
.
_,
—
(1
equivalent to the condition in Proposition 4
when
jj,
=
c
=
c
=
(14)
0.
Firms choose to unshroud when the cross-subsidies to sophisticates (the right hand side
inequahty (14)) are smaller than the
cost (the
left
hand
inequality (14)
Firms
will
from pricing that deviates from marginal
be able to educate and poach their
rivals
customers when
not satisfied.
Other influences on shrouding
3.3
To
is
side).
distor^tions arising
of
simplify exposition,
mine shrouding.
First,
we have ignored
In this subsection,
we have
we quickly
so far overlooked the
consumers must buy a base good.
several additional factors that either encourage or under-
discuss these factors.
consumer entry
When some
decision, since
we have assumed
consumers overlook add-on
costs, these
consumers may buy the base good when they should avoid the market altogether.
consumer who buys a $50 deskjet printer without
least ten times higher.'^
of these
that
all
myopic
Think
of a
realizing that the lifetime operating costs are at
Firms that compete by unshrouding high add-on prices
myopic consumers out of the base-good market.
will drive
some
Hence, consumer entry decisions are
adversely affected by unshrouding (Spence 1977, Ellison 2005).
"'At the moment, black and white text co.sts between 2 cents and 15 cents per page, depending on the inkjet
Color text costs a bit more than black and white text. A photographic image costs an order of magnitude
more. Printing 10 pages per day at 10 cents a page costs S1460 over four years.
printer.
23
Second,
consumers have heterogeneous tastes and firms have heterogeneous add-ons, firms
if
enable consumers to find the base-good with the right add-on.
will advertise to
This informative
advertising will accelerate unshrouding.
Third,
we have
so far
assumed that once a consumer becomes informed about the costly add-on
consumer takes account of the costly add-ons
at one firm, that
possible that unshrouding
at that single firm.
Fourth,
if
is
a fixed cost
incremented by
{l
fcC,
C
iff
— a)p+kC >
Fifth,
e.
is
B >
=
where k
1
1
=
if /i
is
instead
4
is
Specifically,
adjusted so that a Shrouded
defined as before except the numerator of
and k
ecjuals the
number
of firms
if
j.l
is
is
more pervasive when the market
that learning will accelerate unshrouding.
is
B
very
adjusted so that a Shrouded Prices Equilibrium exists
This implies that shrouding
new add-ons and new
is
again be impeded.
will
Then Proposition
B
where
1,
we have already mentioned
tion will create
then unshrouding
costly,
of unshrouding.
Analogously Proposition
large.'^^
it is
This narrow framing effect would impede unshrouding.
Prices Equilibrium exists
is
However,
by one firm leads consumers only to think about the unshrouded add-on
education/advertising
suppose there
at all firms.
iff
less competitive.
However, innova-
opportunities for shrouding.
Sixth, educational advertising might inform
consumers about the general problem of shrouded
add-on prices without enabling consumers to avoid the add-ons. For example, an ad might promise,
"We
offer
marginal cost pricing and no hidden
fees,
unlike our competition." If such advertising
contained enough information to be credible but not enough information so myopes could substitute
away from add-ons, then myopes would be attracted by such
ads, thereby breaking the
Shrouded
Prices Ecjuilibrium.
Finally, third party
celerate unshrouding.
working perfectly.
consumer education
^The proof
is
magazines
like
may be
Non-profit educational organizations
finance magazines tend to
for these
e.g.,
Consumer Reports
—
\v\\\
ac-
However, various impediments prevent such educational mechanisms from
profit educational organizations
demand
—
may have
recommend
incentives to give bad advice.
active portfolio
magazines. Consumers
underfinanced.
may
not
know which
a simple modification of the proofs of Propositions
large.
24
management,
1
and
Moreover,
for-
For example, personal
thereb)^ justifying ongoing
advisor to trust.
4,
with a Taylor expansion
when
/i is
very
Conclusion
4
Firms often shroud the negative attributes of their products, particularly high prices
mentary add-ons.
importantly,
We
we
We
Firms
under which shrouding survives
identify conditions
will
comple-
present a model of consumer myopia that explains this shrouding.
show that competition
efficiency.
for
will not
in
Most
competitive equilibrium.
induce firms to reveal information that would improve market
not educate the public about the add-on market, even
when unshrouding
is
free.
In equilibrium, sophisticated consumers
buy the
loss-leader base
good and substitute away from
For example, sophisticated credit card users take advantage of the "free
add-on consun:iption.
miles" and avoid interest rate charges and late
payment
from myopic consumers who pay those
Advertising low markups and educating consumers
about the add-on market
will
fees.
not attract customers.
fees.
Sophisticates receive a cross-subsidy
Sophisticated consumers would rather pool
with myopic consumers (and receive cross-subsidies) than defect to firms with marginal cost pricing.
A
firm that unshrouds
We
its
add-on prices
lower
its profits,
implying a "curse of debiasing."
do not develop here the policy implications of myopia and persistent shrouding, but we
can anticipate the tools required
and economists. The analysis
for
in this
such
measure
q, the degree of
I.Q." of sorts)
elasticities,
payment
of
analysis."^"
Regulatory agencies currentlj- employ lawyers
paper suggests that regulators should also consider employing
social scientists trained in experimental
Hah
will
and survey
techniciues.
consumer sophistication. This measure
Survey researchers could try to
of marketplace literacy (a "shopper
might complement traditional predictors of market distortion, such as Herfindahls,
and mark-ups. Survey research could determine whether new customers underpredict
banking
fees or the
scope of credit card borrowing or spending on ink cartridges
(cf
2003).
When
awareness a
is
low, one should not be confident that competitive forces will debias con-
sumers. Compulsory unshrouding might then be desirable.
'^'^
Regulators have already informally
"Spence (1977) investigates a situation in which consumers misperceive the rehability of a product. He studies
regulatory interventions, such as a mandatory warranty. He also investigates a solution via a signaling equilibrium.
"
He does
not consider the case where firms can directly debias consumers.
Jovanovic (1982) analyses a setting with Bayesian consumers. He concludes that there
too little, costly disclosure in equilibrium (firms overinvest in signalling).
25-
is
too much, rather than
engaged
We
in
such unshrouding policies
hope that ongoing research
compulsory unshrouding.
We
knows how
possible
—
to
food, energy usage, or financial product labelling) .^"^
will clarify the appropriate
also
ulations will probably not succeed
yet
(e.g.,
need to learn how to
if
and inappropriate domains
effectively regulate unshrouding.
they simply change the font
compel transparency.
And
it
for
size of the fine print.
remains to be seen whether that
is
such
Reg-
Nobody
desirable
— or
in practice.
''The UK Treasury
shank 2000).
is
in the
midst of a broad expansion of transparency regulation
26
in tlie
banking sector (Cruick-
Appendix A: The Demand Function
5
We
D (x)
define
demand
as the
of a firm that offers an average perceived surplus x units greater
than the average perceived surplus provided by
for
D{x) using random
that good
i
i
competitors.
its
theory (see Anderson
utility
a,
be looking
will
firms post the
set
1.
S =
for
for firm
thus: D,
is
i
for
F
and price
cjuality v*
S*
for firm 1 is
=
—
v*
Di =
and
p*,
p*, introducing
D (5 —
D{x) =
P
5*),
an excellent review).
and density /
1981).
= P {vi —
+ Sai >
Pi
+
(x
all
firms have the
et
(1992).
al.
f
F"'^
(s)
following Proposition characterizes the symmetric ecjuilibrium.
Proposition 5 Suppose
v,
S
offered by the firms,
that In
/
is
.
so p
—
c
Two
=
/i.
is
normalize the mass of
max^^i
D (p* — p)
Finally, Eq.
cases have
7.
—
—
c
a.
=
fiD{0)
firm-
i-i
charging p
= maxxD{-x +
is
If
marginal costs are
[p
—
D'
c)
[p*
—
logistic:
—
pj
+
eaj)-
We
while the other
p,
those cases, one can
Then the
{x
+ e)
de.
(15)
the difference
its
competitors.
D (x) =
[p
=
p)
If
and
c
0.
27
[I
+
c)
D {p*
—
Then
p).
there
is
a
Also,
(16)
fi).
profits are {p
—
c)
D (p*
— p),
In the symmetric equilibrium,
p
=
=
p*
the noise
1/
—
guaranteed by Caplin and Nalebuff (1991),
16 just reflects that a price p
is
is
D (0) /D' (0).
:=
compact closed forms.
exp( — e~'), the demand
a. In
Vj
and the surplus S* offered by
Proof. The existence of the symmetric equilibrium
and Proposition
interpret £,a as
concave, and thai firms compete in prices, and have identical
so that the profit of
unique symmetric equilibrium with p
order condition
We
.
The demand depends only on
The
2
F'
short-hand for the net average surpluses.
> max eA = f
£1
same
S* between the surplus
Theorem
=
assume
6ai is i.i.d. across firms
We
(McFadden
S~
and values
where
We
where we define
See Perloff and Salop (1985) or Anderson
costs c
develop the microfoundations
symmetric equilibria where a firm posts quality v and prices
same
— p and
V
demand
The demand
We
= Vi~ Pi + San
with cumulative distribution function
a tremble or an idiosyncratic consumer preference
consumers to
1992
et al.
gives agent a decision utility equal to Uai
and agents
D {x)
{n
—
is
=
p
is
an ecj;uilibrium
Gumbel
I) e~^].
If
if
c
the
=
p*
first
and
0.
F (o) =
distributed,
i.e.
the noise
exponentially
is
demand
distributed with density e ^l£>o, the
D (x) =
is
e^
—
[l
l3:>o (1
-
e
^)"] /n.
Appendix B: Longer Derivations
6
Proof of Proposition
6.1
We call p*and p*
and we
announced
Case
•
prices at firm i.We check that firm
a <
i
can shroud and pick p and
as the beliefs are
— p.
only on p*
=
p
p*
=p
This profit
The base good
—
iov
p
Firm
i
some
of the
=
price
p that
p*
p
is
p. Its profit is
[p+il-a)
and the demand
is
=
(jD
solves the
= p* =
+
(1
first
—{1 — a)p
can unshroud and pick p and
myopes and the
equal to
for the
p),
base good of
a)p) D{p*
=
all
the consumers depends
p so that
— p).
order condition
+
p.
—
-
plp<p) D{p*
maximized when p
clearly
TT
•
does not want to deviate from the
a^ and the Shrouded Prices Equilibrium.
TT=
p)
i
strategies.
1:
Firm
the equilibrium prices at other firms for the base good and the add-on respectively,
p and p the
call
1
—
+
(p
(1
—
a)p) D'{p* —p)
+ D{p* —
p..
By unshrouding
fraction of sophisticates
add-on
its
becomes
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
buy
it iff
p <
e.
e
TT
which
will
is
=
a.'
{p+p)D{~p-p + p* + e) + {l-a){p + p)D{p* - p),
maximized when p
=
e.
Otherwise firm
i
can increase p by a small positive
increment, decrease p by the same increment, and not change the
28
demand
of sophisticated
consumers while increasing
demand
strictly the
of naive consumers.
Hence, the profit
can be reexpressed:
=
TT
As a < a^
this profit
,
smaller than
is
+
(p
(p+
- Ifp >
—
(1
which
is
strictly smaller
=
+
(p
than (p
+
(1
(1
-
—
a)p
2: a^
Firm
-
i
If
11
and p
< a and
—
is
=
a' (p
=
e)
D{p* —
condition,
—
(p
p >
the profit firm
i
could achieve by
p-
is
i
to shroud
and price
p
at
=
p*
= — (1 —
=
p
e.
+ p* +
e)
+
(1
{p
e,
+
e)
Otherwise firm
a') (p
i
+ p) L'(p* — p),
can increase p by a sniall posi-
demand
of naive consumers.
In equilibrium, the base good price p solves the
p).
D'{p*
—
p)
+
D(p* — p)
=
0.
This implies that p
=
p*
first
= —e
of so-
Hence
order
-i- /z.
only myopes buy the add-on, and
This profit
is
-
p by the same increment, and not change the demand
TT
which
- p),
p.
+ p) D(-p -
maximized when p
+
If
p-
— p),
phisticated consumers while increasing strictly the
=
could
e,
tive increment, decrease
TT
i
the Unshrouded Prices Equilibrium.
TT
which
p), the profit firm
= p* = p.
can unshroud and pick p and
P <
=
p
a')plp<p) D{p*
conclude that the best response of firm
+
—
a)p) D{p*
a)p) D{p*
choosing to shroud and price at p and p
— We
p).
e,
TT
•
D{p* —
achieve by choosing to shroud and price at p and
"
Case
e)
is
clearly
= {p+{l -
maximized when p
strictly smaller
than
(p
-|-
e)
a-')plp<p)
=
p-
The
D{p* — p), the
29
D{p* -
profit
p).
is tt
=
profit firm
i
(p
-I-
(1
—
a')p)
D{p* — p),
could achieve by choosing
to unshroud and price at p and p
Firm
•
i
=
e.
can shroud and pick p and p and get a profit equal to
=
TT
as the behefs are
(p
= p- One needs
p
+
(1
-
plp<p) D{p*
a')
a' rather
than a
in the
-
p),
above expression, because the other
firms unshroud, so they educate a fraction A of the myopes. This profit
when p =
p-
The
the profit firm
We
•
If
is tt
=
(p
+
(1
—
a')p)
= p* =
firm
shrouds
i
is
D{p*
—
p),
which
is
i
is
to
maximized
also strictly smaller than
could achieve by choosing to unshroud and price at p and p
conclude that the best response of firm
and p
that this
i
profit
clearly
is
unshroud and price
at
—
p =
e.
p*
= —e + p
e.
its
add-on
the optimal price
price,
if
firm
consumers rationally believe
i
pi
=
p, as
the above proof shows
shrouds. Hence using sequential rationality, the announced
beliefs are consistent.
6.2
We
Proof of Proposition 3
follow closely the proof of Proposition
Recall that a'
= a+
the firm unshrouds,
If it
A(l
—
The
firm's optimal value
p must
still
be either
e or p.
a) represents the fraction of informed consumers after unshrouding.
its profit
depends on whether p
n (p =
e)
= max
(p
+
n(p =
p)
= max
(p
+(1-
does not unshroud,
1.
[a'Ts
+
(l
-
=
a')
e
or
p
=
p:
{Tmm + Tms)]
a') pTwi^/) I?
If
(p*-p).
e)
D (p*
-
p)
,
(17)
(18)
its profit is
n = max (p+(l-cv)TMMp)i:)(p*-p).
p
30
(19)
To compare
the profits, observe that
[a'Ts
as
a <
a^^
.
This imphes
p
We
add-on
for the
(l
is
- a)
n(p=
n(p =
not profitable. Also,
price
+
e)
<
p)
[Tmj^j
<
+
Tms)]
<
max (T^, Tmm + Tms)
<
(1
and
18, 19
>
a'
e
- a)pTMM
Unshrouding and posting a low price
IT.
by Eq.
11
e
a.
e for the
add-on
is
Unshrouding and posting a high
also not profitable.
conclude that whatever price the firm chooses to charge for the add-on, unshrouding
not
is
profitable.
Proof of Proposition 4
6.3
we
In this proof,
call
p*and p*
=
j?" 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
take c
=
the one announced in Ecp
is
to simplify exposition.'^-'
the
is
The
9.
monopoly
Without
price p"\
loss of generality,
we
profits are
ii=[p + {pr-d)^{p'^))Di-p + p*).
If
p
is
which
an equihbrium,
is
Eq.
We now
dU/dp =
at
p^p*.
This implies p
+
(?7"
- ?) f (p'") =
D (0) /D' (0) =
9.
calculate the profit of a firm that deviates, unshrouds,
and
sets
new
while the other firms keep shrouding and using the prices p*and p* given in Eq. 9-10.
facing price
/i,
p
prices
p and
p,
A sophisticate
in the afterniarket gets the net utility
V {p)
= max u
(e",
q)
—
pq.
(20)
g,e
Call q(p) (or q^ (p)
if
there
is
an ambiguity) the associated choice of add-on demand, and u{p)
'To go back to the general case, replace p by p
—
c.
31
=
v{p) +pq{p) the gross
The
firm's profit
n=
where x
+
(p
= p+
(p
(p
utihty provided by the other firms
c)
c)
q{p))
is
q{p)
This implies p
efficiently.
d
^
—
[(p
=
c
=
—p*
+
v{p*).
D {-p + v{p)- u^*) = xD {-X + {p-c} q{p) + v{p)- u^*)
the total profit per customer. Maximizing
=
that (20) and the envelope theorem imply gzv{p)
dp
=
u^*
is:
is
-
—
The
utility.
-
c)
When
0.
So the highest
+
q{p)
=
v{p)]
-
q{p)
{x,p) over
11
+ {p-c)q
q{p)
can get after deviating
= mSiXxD{-x +
Il
p and noting
—q{p), we get
(p)
=
{p
a firm faces only sophisticated consumers,
profit the firm
-
it
d) q (p)
.
prices of the add-on
is
x*),
(21)
X
with x*
=
v
(c)
-
u^*.
As the pre-deviation
profit
is /i,
the firm doesn't want to deviate
iff
n</.D(0),
as fiD (0)
is
X*
—
yU
(22)
the pre-deviation profit. Given Eq. 16, Eq. 21, and the fact that
non-decreasing in
=
,
z,
V [c)
(22)
~u
is
*
~
ecjuivalent to x*
jX
=
V {c)
—
V
<
{p*')
p.
To
find the sign of x*
—
maxj
we
ji,
xD {—x + z)
calculate
+ p* — p
= ?(c)-u^(ir)+p*g^(p*)-(p*-?)?(p*) by(9)and(20)
= v{c)-
u^
ip*)
+ p'f
= u{d)-?f (c) As the firm doesn't want
u^
(jT)
(p*)
-
(p*
-
?)
+ 3^ (p*) _
to deviate iS x*
—p<
0,
32
[aq^ (F)
(1
-
+
a) {p*
(1
-
-
a) q'' (p*)] by (7)
c) {q'' (p*)
the Proposition
is
-
proven.
f (p*))
by
(20).
is
7
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