Search and Ripo¤ Externalities
Mark Armstrong
Oxford University
UCL: October 2014
Mark Armstrong ()
Search and Ripo¤ Externalities
UCL: October 2014
1 / 19
Introduction
Markets contain a mix of “savvy” and “non-savvy” consumers
Old intuition:
savvy consumers protect the rest
consumer protection policies only needed when there aren’t enough
savvy types present
Recent focus:
savvy consumers prey on the non-savvy
This talk explores:
when savvy consumers do protect the rest
when instead non-savvy consumers protect (or are exploited by) the
savvy
when consumers have aligned or divergent views on regulation
Mark Armstrong ()
Search and Ripo¤ Externalities
UCL: October 2014
2 / 19
Notions of “savviness”
A consumer might be well informed about prices available in the
market, and/or be able to discern product quality
savvy consumer knows quality of wine from the label
connoisseur can recognize “old master” painting in junk shop
savvy consumer knows range of prices for a new TV before buying (eg.,
she is online)
savvy consumer can interpret “small print” in contracts, food labels, etc
A consumer might be strategically sophisticated, and understand the
nature of the market game being played
even if she cannot directly observe a product’s quality, she understands
the relationship in equilibrium between price and quality
even if she doesn’t observe prices, she anticipates equilibrium prices
she foresees a …rm’s incentives to set future and “add-on” prices
she foresees her own future behaviour and temptations
Mark Armstrong ()
Search and Ripo¤ Externalities
UCL: October 2014
3 / 19
A framework
There are two kinds of consumer: savvy and non-savvy
proportion of savvy types is exogenous, σ 2 [0, 1]
the tastes of consumers do not di¤er across the two groups
Consumers in equilibrium:
VS (σ ) is surplus of an individual savvy consumer
VN (σ) is surplus of an individual non-savvy consumer
since savvy consumer can follow non-savvy strategy and tastes are the
same, expect VS
VN
V (σ ) = σVS (σ) + (1 σ )VN (σ ) is aggregate consumer surplus
possible for aggregate consumer surplus to rise even if VN and VS
decrease with σ
Mark Armstrong ()
Search and Ripo¤ Externalities
UCL: October 2014
4 / 19
A framework
Suppliers in equilibrium:
ΠS (σ ) is pro…t from a savvy consumer
ΠN (σ ) is pro…t from a non-savvy consumer
comparison between ΠS and ΠN depends on context, but “usually”
ΠN
ΠS
Π(σ) = σΠS (σ ) + (1 σ)ΠN (σ ) is industry pro…t
(pro…ts are zero in competitive markets)
W (σ) = V (σ) + Π(σ) is total welfare
Mark Armstrong ()
Search and Ripo¤ Externalities
UCL: October 2014
5 / 19
A taxonomy of markets
Search externalities: non-savvy are protected by the savvy
VN (σ) increases with σ
Ripo¤ externalities: savvy prey on the non-savvy
VS (σ ) decreases with σ
No externalities:
VN and VS do not depend on σ
We study two families of models:
an indivisible product with price dispersion
add-on pricing
Mark Armstrong ()
Search and Ripo¤ Externalities
UCL: October 2014
6 / 19
Price dispersion
Varian (1980):
Symmetric …rms supply homogeneous product to consumers
consumers have idiosyncratic valuation v for product
fraction σ of consumers observe all prices in the market and buy from
the cheapest supplier (if v p)
remaining 1 σ consumers visit single supplier and buy if v p
[they might be strategically naive, and think the “law of one price”
prevails, or not know of other suppliers]
equal shares of non-savvy consumers for each supplier
Mark Armstrong ()
Search and Ripo¤ Externalities
UCL: October 2014
7 / 19
Price dispersion
In a mixed market with 0 < σ < 1, …rms choose price with a mixed
strategy and there is price dispersion
savvy consumer obtains (weakly) lower price than any non-savvy
consumer, so VS > VN , ΠS < ΠN
Larger σ makes a …rm’s demand more elastic, and forces …rms to set
lower prices on average
VS and VN increase with σ, Π falls with σ
consumer policy which boosts σ welcomed by all consumers
classic instance of a search externality
Mark Armstrong ()
Search and Ripo¤ Externalities
UCL: October 2014
8 / 19
Variants of Varian: tacit collusion
Schultz (2005) studies tacit collusion in Varian’s model
all rivals observe deviation to a lower price
only σ consumers can react to the price cut
Increasing fraction of savvy types has two e¤ects
reduces one-shot (mixed strategy) punishment pro…ts
increases fraction who are able to respond to a price cut, and so boosts
deviation pro…ts
Two e¤ects cancel out
if δ is the discount factor, condition for collusion is
n
1
1
δ
which doesn’t depend on σ
so payo¤s VS and VN don’t depend on σ
Mark Armstrong ()
Search and Ripo¤ Externalities
UCL: October 2014
9 / 19
Variants of Varian: uncertain match quality
Symmetric …rms compete to sell a horizontally di¤erentiated product
all consumers see all prices
with probability α a consumer likes a given product, which is then
worth 1 to her
otherwise the product is useless, then worth 0
If all consumers can observe their match quality, model akin to Varian
consumers buy from cheapest …rm with a good match
mixed price strategy since some consumers are captive with only one
good match
Suppose fraction 1 σ of consumers are non-savvy and cannot
observe match quality ex ante
they are rational, anticipate expected match quality α from all …rms,
and buy from …rm with lowest price (if below α)
these non-savvy consumers act to intensify price competition
instance of “ripo¤ externality”
Mark Armstrong ()
Search and Ripo¤ Externalities
UCL: October 2014
10 / 19
Add-on pricing
Related insights apply to add-on prices, which are often less observed
or considered than the core product’s price
Many examples:
minibar prices in hotel room
toner cartridges after buying printer
after-care service for your new car
extended warranty for new TV
casual overdraft from your bank
carry your luggage in the hold if it’s slightly too large for the cabin
Mark Armstrong ()
Search and Ripo¤ Externalities
UCL: October 2014
11 / 19
Add-on pricing: rational but uninformed consumers
A monopolist supplies a core product, with cost C and price P and
which consumers value at X
if consumer has the core product, an optional “add-on” product is
available with unit cost c
if the add-on price is p, all consumers with core product will buy q (p )
units of the
R add-on
if s (p ) = p q is consumer surplus from the add-on priced at p,
consumer buys core product if
X + s (p )
P
…rm chooses add-on price p in advance
all consumers see P, but only σ see p as well
remaining 1 σ do not see p but foresee …rm’s incentives
Mark Armstrong ()
Search and Ripo¤ Externalities
UCL: October 2014
12 / 19
Add-on pricing: rational but uninformed consumers
Suppose …rm o¤ers same add-on terms to all consumers
so VS = VN and ΠS = ΠN
[when uninformed have “passive conjectures” about p] equilibrium
add-on price satis…es
(1
σ )q (p ) + (p
c )q 0 (p ) = 0
when σ = 1 add-on price is e¢ cient p = c
when σ = 0 add-on price is monopoly price p M that maximizes add-on
pro…t π (p ) (p c )q (p )
[With log-concave q] all consumers and the …rm are better o¤ with
higher σ
Hard to do competitive version of this model
easier, and often more natural, to study models with naive consumers
Mark Armstrong ()
Search and Ripo¤ Externalities
UCL: October 2014
13 / 19
Add-on pricing: naives do not foresee need for add-on
Consider variant of add-on pricing model where naive consumers
do not foresee they might need add-on service
can see add-on price p (but aren’t interested)
they purchase myopically and buy core product if X
P
as before, savvy types are forward-looking and buy if X + s (p )
Mark Armstrong ()
Search and Ripo¤ Externalities
UCL: October 2014
P
14 / 19
Add-on pricing: naives do not foresee need for add-on
Analysis is most transparent in competitive case (at least four …rms)
asymmetric pure strategy equilibrium has savvy types being o¤ered
cost-based tari¤ (P, p ) = (C , c )
naive types face “bargain then ripo¤” prices, with add-on price p M
that maximizes π (p ) (p c )q (p ), and core product price
P=C
π (p M )
which just ensures break-even
these contracts do not depend on σ
neither type wishes to take contract aimed at other type
policy to limit “ripo¤s” has no impact on savvy consumers
Naive surplus isn’t necessarily increased if ripo¤s are eliminated
subsidy funded by ripo¤s mitigates ine¢ ciency caused by myopic
consumers participating too rarely
Mark Armstrong ()
Search and Ripo¤ Externalities
UCL: October 2014
15 / 19
Add-on pricing: naives do not foresee need for add-on
Many other situations where competitive deals o¤ered to savvy and
naive consumers do not depend on σ
astrology (or similar), where savvy consumers know it doesn’t work and
will never buy it
over-optimism about gym attendance (DellaVigna & Malmendier, Eliaz
& Spiegler)
insurance (Sandroni & Squintani)
Mark Armstrong ()
Search and Ripo¤ Externalities
UCL: October 2014
16 / 19
Add-on pricing: bill shock
Adaptation of Gabaix & Laibson (2006)
Savvy types just pay headline price
Naive types can be tricked into paying more
they inadvertently buy add-ons they do not particularly want (eg.,
overdraft charges levied by bank, airport vs. online check-in, mobile
call charges beyond contract limit)
[similar outcomes if naive consumers can be persuaded to buy worthless
add-on (eg., extended warranty for a very reliable TV), or are o¤ered
highly-priced add-ons, while cheaper substitutes are available with
advance planning (eg., minibars)]
Examples:
Ryanair charges £ 70 to check in once at the airport, £ 50-70 to check
“over-sized” bag into the hold
in UK retail banking in 2006, 75% of customers paid no unarranged
overdraft fees, while 1.5 million customers paid more than £ 500
Mark Armstrong ()
Search and Ripo¤ Externalities
UCL: October 2014
17 / 19
Add-on pricing: bill shock
Product has price P and cost C
naive end up paying an (exogenous) extra amount R
X is idiosyncratic value for product, where fraction of consumers with
X
P is Q (P )
Both savvy and naive consumers have demand Q (P ) for product
savvy because they pay P
naive because they think they will pay P
Firms cannot distinguish savvy from naive in advance, so o¤er same
price to all
in competitive market the equilibrium price is
P=C
(1
σ )R
savvy types just pay this P, but naive types pay C + σR
payment increases with σ for all consumers
Mark Armstrong ()
Search and Ripo¤ Externalities
UCL: October 2014
18 / 19
Add-on pricing: bill shock
Surplus of savvy and naive consumers with price P is
VS = S ( P ) =
Z
P
Q ; VN = S ( P )
Q (P )R
some naives have negative surplus
VS decreases with σ
ambiguous impact on naive surplus, but if R not too large then VN
also decreases with σ
total welfare W rises with σ
Regulation might constrain rip-o¤ element R
improves welfare and naive surplus
but harms savvy types
this lack of consensus makes these policies controversial
in banking context, say, it may be poor people who are ripped o¤,
which adds distributional dimension
Mark Armstrong ()
Search and Ripo¤ Externalities
UCL: October 2014
19 / 19