Planned Obsolescence and the Provision of Unobservable Quality Roland Strausz ∗ Free University of Berlin February 6, 2006 Abstract This paper develops the idea that obsolescence acts as an incen- tive device to provide quality for experience goods. The argument is that obsolescence affects the frequency at which consumers repur- chase products and may punish producers for a lack of quality. A higher rate of obsolescence enables a firm to convince its consumers that it provides high quality. We identify a trade–off between quality and durability, implying that the two are substitutes. This leads to excessive obsolescence. The inefficiency is due to unobservability and not monopolistic distortions. The theory follows naturally from the theory of repeated games. Keywords: Obsolescence, unobservable quality, reputation, repeated games JEL Classification No.: L15, D21 ∗ Free University Berlin, Dept. of Economics, Boltzmannstr. 20, D-14195 Berlin (Ger- many); Email addresses: [email protected]. I thank Heski Bar–Isaac, Helmut Bester, Jay Pil Choi, Daniel Kr¨ ahmer, and Timofiy Mylovanov for helpful comments and suggestions. Financial support by the DFG (German Science Foundation) under SFB/TR 15 is gratefully acknowledged. 1
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Planned Obsolescence and the Provision of
Unobservable Quality
Roland Strausz∗
Free University of Berlin
February 6, 2006
Abstract
This paper develops the idea that obsolescence acts as an incen-
tive device to provide quality for experience goods. The argument
is that obsolescence affects the frequency at which consumers repur-
chase products and may punish producers for a lack of quality. A
higher rate of obsolescence enables a firm to convince its consumers
that it provides high quality. We identify a trade–off between quality
and durability, implying that the two are substitutes. This leads to
excessive obsolescence. The inefficiency is due to unobservability and
not monopolistic distortions. The theory follows naturally from the
theory of repeated games.
Keywords: Obsolescence, unobservable quality, reputation, repeated games
JEL Classification No.: L15, D21
∗Free University Berlin, Dept. of Economics, Boltzmannstr. 20, D-14195 Berlin (Ger-
many); Email addresses: [email protected]. I thank Heski Bar–Isaac, Helmut
Bester, Jay Pil Choi, Daniel Krahmer, and Timofiy Mylovanov for helpful comments and
suggestions. Financial support by the DFG (German Science Foundation) under SFB/TR
15 is gratefully acknowledged.
1
1 Introduction
”The iPod is an example of the kind of poor design and obsoles-
cence that’s occurring in the electronics industry” - Shelia Davis
of the Silicon Valley Toxics Coalition.1
In October, 2001, Apple introduced its most successful product ever, the
iPod, a highly portable digital audio player. Consumers praise the iPod for
its ease of operation and design. Yet, in one important dimension the iPod’s
quality has been lacking: durability. In 2003 Apple acknowledges that the
iPod’s battery has a limited life time of 18 months and is irreplaceable. After
a failure of the battery consumers need to buy a new device, or use Apple’s
out–of–warranty battery replacement program for $99 dollars.2 The com-
pany defends its high fee by explaining that the replacement service actually
involves a replacement of the whole device. Hence, by design it is cheaper
for Apple to exchange the physical device than to replace only the battery.
This raises the question why Apple, with its high concern for quality in other
dimensions, has chosen to limit the device’s life time with something as sim-
ple as an irreplaceable battery. And how come that Apple did not address
this design issue in its subsequent generations? Three product generations
later, the iPod still has irreplaceable batteries.3 Even more surprisingly, how
come that despite fierce competition Apple’s iPods are still the most coveted
audio players in the market? Why doesn’t competition drive the iPod from
the market or force Apple to pick a more efficient level of obsolescence?4
This paper provides an answer to these questions by developing a new the-
ory of planned obsolescence that establishes a trade–off between a product’s
1http://www.detnews.com/2005/technology/0503/09/A08-111726.htm.2Originally, the replacement cost 250 dollars (http://www.ipodsdirtysecret.com). In
August 2005, Apple reduced the price from $99 to $59 dollars.3For this reason, the distinguished German testing agency Stiftungwarentest degraded
the recent iPod shuffle to a “disposable product” in its issue 07/2005.4E.g., the most distinguishable feature in its advertisement of Creative’s ”No-
mad Jukebox Zen NX” audio player is its ”removeable, high–capacity Li-ion battery”
(http://www.nomadworld.com/products/jukebox zen nx/).
2
durability and its other quality features and is not based on monopolistic
behavior.
The explanation is as follows. Consider a producer who produces a good
with an endogenous quality level that becomes only observable to a buyer
after consumption. If the producer and buyer meet only once, the producer
does not have an incentive to deliver appropriate quality. Klein and Leffler
(1981) and Shapiro (1983), however, argue that when the producer produces
repeatedly, he may develop a reputation for high quality. Hence, repeated
interactions may lead to an appropriate provision of quality. The poten-
tial of reputation in providing quality depends on the frequency of these
interactions. Since obsolescence affects this frequency, the reputation motive
provides a theory of planned obsolescence. This paper confirms this idea
and demonstrates that it leads to a trade–off between durability and other
quality aspects.
The question of excessive obsolescence has been on the economists’ re-
search agenda for a long time (e.g. Wicksell 1923, Kleiman and Ophir 1966,
Swan 1970). Yet, existing theories have mainly focused on monopolists and
cannot explain how, under competition, inefficient levels of obsolescence may
persist.5 Schmalensee (1979) offers an extensive overview of different theo-
ries. The most prominent one is due to Bulow (1982, 1986) who argued that
the time–inconsistency problem of a durable monopolist identified in Coase
(1972) induces a monopolist to choose excessive obsolescence. Most subse-
quent work on the issue of excessive obsolescence uses this framework (e.g.
Waldman 1993, Choi 1994, Waldman 1996, Ellison and Fudenberg 2000, and
Nahm 2004).
This paper proposes a theory of planned obsolescence based on repeated
games rather than the time–inconsistency problem of Coase. It does not
require the presence of a monopoly, but may also explain planned obsoles-
cence under Bertrand–like competition. The crucial ingredient of the theory
5A recent exception is Grout and Park (2005).
3
is an unobservability of a quality characteristic different from durability. In
this respect, it is related to Choi (2001), where firms may use observable
durability as a signal for unobservable quality. A fundamental difference is,
however, that in Choi’s framework reduced durability is a signal rather than
an incentive device. Moreover, Choi’s signalling idea requires that durability
is observable, whereas we explicitly show that this is not needed in our frame-
work. Our explanation also markedly differs from Grout and Park (2005),
who argue how planned obsolescence may promote a good’s secondary mar-
ket and therefore arise even with competition. In Grout and Park there exist
no asymmetric information between producer and customer; asymmetric in-
formation only arises in the secondary market.
2 The Setup
We illustrate our theory in the classic framework of durability as introduced
by Kleiman and Ophir (1966). A firm produces a good that is characterized
by a quality level q and a durability level d with the interpretation that a
good (q, d) yields a consumer a utility stream of q for d time units. That is,
the consumer’s discounted utility of a good (q, d) is
v(q, d) ≡∫ d
0qe−rtdt =
(1 − e−dr)q
r, (1)
where r is the common interest rate. Hence, we extend the durability frame-
work of Kleiman and Ophir by introducing an additional quality attribute q
that is different from durability. In our theory, this second attribute will not
be directly observable. An example of an unobservable quality in the case
of Apple would be the iPod’s ease of operation, which consumers only learn
during the day–to–day use of the device. Yet, even the iPod’s design may
be seen as an unobservable quality attribute. Only over time consumers will
find out that the design is a “classic” and does not become boring or runs
out of fashion.
4
There is a single consumer who requires at most one functioning unit of
the product. This simplifying assumption enables us to demonstrate clearly
the role of unobservable quality on the choice of durability. In particular, it
eliminates the effect identified by Bulow (1982,1986) that a producer may use
planned obsolescence to mitigate the Coasian time–inconsistency problem of
a durable monopolist.
We make the following standard assumptions about the producer’s cost
function c(q, d). It is twice differentiable, weakly increasing in both q and d,
and convex in (q, d). Hence, c′q, c′
d, c′′
qq, c′′
dd ≥ 0. In order to strengthen our
results, we assume that, from a productive perspective, quality and durability
are complements, c′′qd ≤ 0. Moreover, a quality level of zero is costless to
provide and the marginal cost of quality at q = 0 is zero: c(0, d) = 0 and
c′q(0, d) = 0 for all d ≥ 0. Consequently, there are no fixed costs and the
average cost of quality is smaller than its marginal cost, c(q)/q < c′q(q, d). We
further assume that the marginal cost of quality becomes infinite at an infinite
level of quality: c′q(∞, d) = ∞ for all d ≥ 0. Finally, at a quality of zero and
a durability of zero the marginal cost of durability is zero: c′d(0, 0) = 0.
Given the consumer’s preferences and the firm’s production technology,
the social surplus from a good with quality q and durability d is
s(q, d) ≡ v(q, d) − c(q, d) =(1 − e−dr)q
r− c(q, d).
Since a product of durability d breaks down after a time interval d, the
consumer has to repurchase the product every d periods. This implies that
the overall discounted surplus of a stream of goods (q, d) is
S(q, d) ≡∞∑
i=0
(
e−rd)i
s(q, d) =q
r− 1
e−dr − 1c(q, d).
The first order condition
c′q(q∗(d), d) =
1 − e−dr
r. (2)
5
yields the socially efficient quality level q∗(d) for some fixed level of durabil-
ity d. Since the right–handside increases with d, it follows from the firm’s
production technology that the optimal quality q∗(d) is increasing in d.6
As a consequence, higher durability makes quality more socially desirable.
Hence, from both a social and a productive perspective quality and durabil-
ity are complements. We want to stress this fact, because the next section
argues that when quality becomes an experience good, this basic economic
relationship is overturned; under unobservability quality and durability are
substitutes.
Our assumptions on c(q, d) allow us to consider the extreme case that
durability is costless to provide. Since this assumption enables us to present
most clearly the paper’s main arguments, Section 3 will first focus on this
extreme. In Section 3 we, therefore, express the cost function simply as c(q).
Section 4 explicitly shows that qualitative results remain unchanged under
the more natural assumption that costs depend on durability.
If durability is costless to provide, the social surplus S(q, d) is maximized
for a product of indefinite durability (d∗ = ∞). Consequently, the first best
quality is q∗ = limd→∞ q∗(d). Or, alternatively, satisfies
c′(q∗) =1
r.
3 Unobservable Quality
Now suppose that the buyer cannot observe the producer’s quality q before
purchase, but observes it only after buying and consuming the good. In the
terminology of Nelson (1970), the producer offers an experience good. As
the consumer cannot observe the quality directly, he will form some beliefs
qe about it at the time of purchase. Since the consumer observes the price p
6By the implicit function theorem we may differentiate (2) with respect to d and find
∂q∗/∂d = (e−dr − c′′qd)/c′′qq > 0.
6
and durability d, his beliefs qe may, in general, depend on it. Formally, the
belief qe(d, p) is a function qe : IR2+ → IR+.
Now suppose that the firm offers a good of indefinite durability (d = ∞)
so that the consumer needs to purchase the good at most once. For goods
with indefinite durability, there exists no equilibrium in which the producer
chooses a positive quality level and the consumer buys the product. Indeed, if
such an equilibrium existed, it would mean that the producer chooses some
quality q > 0, sold it at some price p, and the consumer’s belief qe(∞, p)
was such that v(∞, qe(p,∞)) ≥ p. This cannot be an equilibrium, because,
given the consumer’s beliefs and behavior, the producer could have gained
by producing the good (0,∞) and charging the price p.
If the firm produces a good with a finite durability, d < ∞, the con-
sumer must renew his purchase every d periods. The good’s limited life–time
thereby changes the game into an infinitely repeated game. From the theory
of infinitely repeated games it is well known that, depending on the discount
factor, positive levels of quality may be sustainable. By using appropriate
trigger strategies the consumer induces the firm to provide adequate levels
of quality. This section investigates this idea and studies to what extent the
possibility of repeated purchases may sustain positive levels of quality.
Formally, we consider a repeated game that is preceded by an initial stage,
where the seller chooses some observable, fixed durability d.7 After durability
becomes fixed the seller and buyer play an infinitely repeated version of the
following stage game:
The seller sets the price p and chooses quality q. Upon observing the
price p the buyer decides whether to buy the product. Thus, in each stage
game the seller chooses as her strategy an unobservable quality q ≥ 0 and
a price p ≥ 0, and the buyer’s strategy, b ∈ {0, 1}, is to buy (b = 1) or not
7For expositional reasons we first assume that durability is observable and chosen once–
and–for–all at the beginning of the game. Section 4 demonstrates that these two assump-
tions are inconsequential.
7
to buy (b = 0) the product. Then, for a given durability d, we have a stage
game Γ(d) with payoffs
us(q, p, b) =
p − c(q) if b = 1;
0 if b = 0;and ub(q, p, b) =
v(q, d) − p if b = 1;
0 if b = 0.
We may now construct the supergame Γs(d) where the seller and the buyer
play the stage game Γ(d) every d periods. Since each stage lasts for d periods,
the effective discount factor in the supergame Γs(d) is δ = e−rd.
Within this framework we identify the combinations (d, q) such that the
supergame Γs(d) has an equilibrium outcome for which in each round the
seller chooses q, and some price p ≥ 0, and the buyers always buys. Apply-
ing the arguments of Abreu (1986), we may identify the set of sustainable
combinations (d, q) by considering the following trigger strategies:
Strategy σs: As long as the seller and the buyer have chosen (q, p, b) =
(q, p, 1) in all previous stages, the seller chooses the quality q = q and a price
p = p. Otherwise, he chooses p = q = 0.
Strategy σb: As long as the seller and the buyer have chosen (q, p, b) =
(q, p, 1) in all previous stages and the seller choose p = p in the current
period, the buyer buys, i.e., chooses b = 1. Otherwise, he chooses b = 0.
The strategies σs and σb pin down behavior for any possible history in
the game. They imply two modes of play: a cooperative mode during which
the players choose (q, p, b) = (q, p, 1) and a punishment mode with (q, p, b) =
(0, 0, 0).
The strategies (σb, σs) yield the outcome q = q, p = p, and b = 1 with
payoffs
Ub(q, d, p) ≡∞∑
i=0
δi (v(q, d) − p) =v(q, d) − p
1 − δ; (3)
for the buyer and
Us(q, d, p) ≡∞∑
i=0
δi (p − c(q)) =p − c(q)
1 − δ; (4)
8
for the seller.
We now check the conditions under which the strategy combination (σb, σs)
constitutes a subgame perfect equilibrium of the supergame Γs(d). By the
single deviation principle it is sufficient to consider only single deviations.
That is, one must verify that players may not gain from a single deviation
in the cooperative or in the punishment phase. Since (q, p, b) = (0, 0, 0) is a
subgame perfect equilibrium of Γs(d), players have no incentive to deviate in
the punishment mode.
If the buyer deviates in the cooperative mode by playing b = 0, it yields
the buyer a payoff of zero. Hence, the buyer has no incentive to deviate