Leasing, Lemons, and Moral Hazard
Justin P. Johnson Cornell University
Michael Waldman Cornell University
Abstract
A number of recent papers have analyzed leasing in the new-car market as a
response to the adverse-selection problem in the used-car market originally
explored in the seminal 1970 paper by George Akerlof. In this paper we consider
a model characterized by both adverse selection, as in these earlier papers, and
moral hazard concerning the maintenance choices of new-car drivers. We show
that this approach provides explanations for a number of empirical findings
concerning real-world new- and used-car markets, including that leasing has
become more popular over time, very high income new-car drivers lease more,
and used cars that were leased when new sell for more than used cars that were
purchased when new. We also compare and contrast our approach to new-car
leasing with alternative approaches.
1. Introduction
In the last 30 years there has been a dramatic change in the way new cars are
marketed. In the early 1980s consumer leasing of new cars was almost unheard
of, while by the end of the first decade of the 2000s roughly one-fourth of new
cars marketed directly to consumers were leased. The obvious questions are,
what is the role of leasing in the new-car market, and why has new-car leasing
grown so dramatically? Recently, both Hendel and Lizzeri (2002) and Johnson
and Waldman (2003) have argued that leasing in the new-car market is a response
to the adverse-selection, or lemons, problem in the used-car market originally
explored in Akerlof (1970). This paper analyzes a model characterized by both
adverse selection, as in these earlier papers, and moral hazard concerning consumer maintenance, and the resulting analysis provides explanations for a number of empirical regularities concerning real-world new- and used-car markets.
As discussed in earlier papers such as Henderson and Ioannides (1983), Smith
and Wakeman (1985), and Mann (1992), there is an important cost associated
with leasing, which is that leasing is likely to be associated with moral hazard
concerning consumer maintenance. In particular, these authors argue that a
We would like to thank an anonymous referee and the editor, Sam Peltzman, for helpful suggestions.
We would also like to thank Ari Gerstle and Kameshwari Shankar for research assistance.
[Journal of Law and Economics, vol. 53 (May 2010)]
䉷 2010 by The University of Chicago. All rights reserved. 0022-2186/2010/5302-0012$10.00
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leased unit will be inadequately maintained because there is high probability that
the consumer will return the unit to the lessor at the end of the lease contract.
As we will show, given asymmetric information, moral hazard also applies to
units that are purchased when new because maintenance expenditures are not
reflected in the price for which used units sell on the secondhand market. The
other important point to note is that in the automobile market real-world lease
contracts typically contain a variety of provisions, such as those concerning
mandatory maintenance, that are included to reduce the moral hazard problem.
As a result, in the automobile market moral hazard can actually be more severe
for cars that were purchased rather than leased when new.
This paper’s model, which combines adverse selection and moral hazard, leaves
unchanged most of the major results of Johnson and Waldman (2003) such as
that used cars that were leased when new sell for more than similar cars that
were purchased when new, while at the same time a number of interesting new
findings emerge. First, our model provides a possible explanation for the dramatic
growth in new-car leasing over time. Specifically, we find that leasing can increase
when there is a significant increase in the degree to which new cars are reliable
or trouble free, and in fact new-car reliability has substantially increased over
time. Second, consistent with empirical findings in Aizcorbe and Starr-McCluer
(1997), we find that under plausible conditions high-income new-car drivers
have a higher frequency of leasing. Third, although this is not a direct implication
of the model, because in the model new cars do not vary in terms of their
reliability, our general approach predicts that the frequency of leasing should be
higher for car models that are more reliable or trouble free. This result is consistent with evidence reported in Desai and Purohit (1999) and Mannering,
Winston, and Starkey (2002), which both show in cross-sectional analyses that
leasing is positively related to new-car reliability.
One focus of this paper is investigating the extent to which a model of the
new- and used-car markets based on adverse selection and moral hazard can
explain evidence from the automobile market. Adverse selection and moral hazard are potentially important in other markets as well, but we have not yet done
any systematic study of the extent to which this paper’s results are consistent
with evidence from other markets. For example, Gilligan (2004) finds evidence
in favor of adverse selection in the market for used business aircraft, and it
would be interesting to know whether evidence concerning leasing in that industry is consistent with our theoretical results.1
1
There are a number of empirical studies that look for evidence of adverse selection in automobile
markets. Bond (1982, 1984) investigates the market for used pickup trucks and finds evidence of
adverse selection in the market for older trucks only, while Genesove (1993) finds some evidence
for adverse selection in dealer-auction markets for used cars. More recently, Porter and Sattler (1999)
and Schneider (2008) find evidence inconsistent with adverse selection in studies of the automobile
market, while Pierce (2007) and Emons and Sheldon (2009) find evidence in favor of adverse selection
in studies of the automobile market.
Leasing and Moral Hazard
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2. Model and Preliminary Analysis
In this section we construct a model of the new- and used-car markets characterized by adverse selection. We then analyze the model and show the role of
leasing in reducing the problem. In Section 3 we introduce moral hazard.
2.1. The Model
There are two main differences between this section’s model and the model
analyzed in propositions 1–3 in Johnson and Waldman (2003). First, here we
allow more than two consumer groups. When we extend the model in Section
3, this assumption allows us to develop results concerning how leasing should
vary with consumer income. Second, new cars now come in varying levels of
quality.
Consider an infinite-period model in which a perfectly competitive industry
produces cars. Cars last 2 periods, and a car 0 periods old is referred to as new,
while a 1-period-old car is referred to as used. There are M ⫺ 1 types of cars,
where a car of type m (m p 1, . . . , M ⫺ 1) is of quality q mN when new and
costs cm to manufacture. We further assume that q mN 1 q kN and cm 1 ck if m ! k.
Because of stochastic depreciation there is uncertainty concerning used-car quality. In particular, the quality of a used car of type m is a random draw from a
distribution described by a probability density function hm(q U) and cumulative
distribution function H m(q U), where hm(q U) 1 0 for all q L ! q U ! q mN and
hm(q U) p 0 for all q U outside of this interval. The expression E(q mU) denotes the
unconditional expected quality of a used car of type m.
There are M groups of infinitely lived consumers, where consumer group m
consists of a continuum of nonatomic consumers of mass x m and m p 1,
. . . , M. In each period an individual in group m drives either no car or one
car, and vm is the valuation per unit of quality that a group-m individual places
on driving a car in any period (v1 1 v2 1 . . . 1 vM). Also, firms and all consumers are risk neutral and have a discount factor d (0 ! d ! 1).
New cars can be purchased or leased for a single period, and a lease contract
contains both lease and buyback prices. The buyback price is the price at which
a consumer who leases a new car can buy the car at the end of the lease period.
If a consumer leases a new car in period t, then at the beginning of period
t ⫹ 1 the consumer either returns the car or purchases the car at the buyback
price. If the car is returned, then the firm sells the car on the secondhand market
in period t ⫹ 1.
The information assumptions follow. First, the quality of any specific used
car is known only by the individual who drove the car when it was new.2 Second,
as in Hendel and Lizzeri (2002) and Johnson and Waldman (2003), buyers on
2
However, we assume that the individual who drove the car when it was new cannot purchase
the car on the secondhand market (the consumer does have the option of purchasing a different
used car on the secondhand market). Without this assumption, leasing would not reduce adverse
selection because it would not suppress the private information of new-car drivers.
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the secondhand market can observe whether a used car was purchased or leased
when it was new, and they also know the car’s type.
The timing of moves in each period follows. First, each individual who drove
a new car in the previous period learns the quality of his or her used car. Second,
each consumer who leased a new car in the previous period decides whether to
return it. Third, each firm chooses which type of car to produce and announces
a purchase price for a new car. Further, when leasing is an option, the firm also
announces lease and buyback prices. Fourth, consumers make their purchasing
and leasing decisions. Fifth, a secondhand market opens up in which prices
equate supply and demand.3
Finally, to simplify the analysis we focus on equilibria in which contracting
and trading options are stationary. When only buying and selling of new and
used cars is allowed, we look for equilibria in which new- and used-car prices
are time invariant. When firms are also able to offer lease contracts, we focus
on equilibria in which each firm offers the same contract in each period and in
which market prices are invariant to time. Furthermore, to simplify the exposition, we do not consider equilibria in which firms offer terms that are not
accepted or equilibria characterized by trades among identical consumers.
2.2. Analysis
To simplify the analysis, we impose the following restrictions on the parameters. First, we assume that equation (1) is satisfied for all (m, k) pairs such that
m ! M and k ! M:
vM q mN ⫹ dvME(q mU) ! cm ! vm[q mN ⫺ E(q kU)].
(1)
This assumption ensures that group-M individuals never purchase or lease new
cars of any type m, while individuals in groups 1 through M ⫺ 1 never purchase
used cars. (At the end of the section we discuss how the analysis changes when
consumers in more than one group are potential buyers on the secondhand
M⫺1
market.) Second, we assume that x M 1 冘mp1 x m. This assumption ensures that
secondhand-market prices are positive. Third, for tractability reasons we impose
a restriction that ensures that individuals in each group m (m p 1, . . . , M ⫺
1) purchase or lease type-m new cars rather than type-k new cars, where k (
m (for details, see Johnson and Waldman 2008, app. A). Fourth, our earlier
assumption—that for each car of type m, used-car quality is bounded between
q L and q mN—ensures that there is necessarily an adverse-selection problem when
there is asymmetric information and firms sell new cars (see Johnson and Waldman 2008, app. A).
We begin with a second-best analysis in which firms only sell new cars. Suppose
3
In modeling the secondhand market we assume that trades are made anonymously. That is, a
used-car buyer does not know the identity of the individual who drove the car in the previous
period. This eliminates the possibility that a consumer who sells used cars will establish a reputation
concerning his or her behavior in the secondhand market.
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311
there is a social-welfare-maximizing social planner who only controls the frequency with which a new-car driver sells the car on the secondhand market in
the following period (as is standard, we define social surplus as the summation
of economic profits and consumer surplus). The equilibrium in this case is as
follows. First, for every m ! M, a group-m driver purchases a new car of type
m in any period in which he or she does not own a used car at the beginning
of the period. Second, for every m ! M there exists a value q˜ m such that consumer
i of type m who owns a used car at the beginning of period t keeps and drives
the car if its quality exceeds q̃m. Third, in the same situation the consumer sells
the car to a group-M consumer and purchases a new car of type m if the used
car’s quality is less than q̃m. Fourth, group-M consumers never purchase new
cars, but in each period some purchase used cars on the secondhand market.
In other words, new cars are driven by higher valuation consumers and, among
these consumers, there is a positive correlation between the new car an individual
buys and the valuation the individual places on quality. Further, owners of used
cars choose to keep higher quality used cars and sell lower quality used cars on
the secondhand market.
The next step is to consider what happens when firms only sell new cars and
there is no social planner determining the frequency of secondhand-market trade.
In most respects this case does not look very different than the social planner
case just discussed. That is, consumers in groups 1 through M ⫺ 1 buy new cars
in any period in which they do not own used cars at the beginning of the period.
Further, when such a consumer does own a used car at the beginning of a period,
he or she keeps the car if its quality is high and sells the car and purchases a
new car if its quality is low.
But there is an important difference. In the social planner case the frequency
with which used cars are traded on the secondhand market is socially efficient.
That is no longer true in the present case. As first explored by Akerlof (1970),
given asymmetric information concerning used-car quality, a car’s price on the
secondhand market reflects the average quality of similar used cars offered for
sale rather than the car’s actual quality. The result is that too few used cars are
traded on the secondhand market.
Proposition 1 formalizes what happens in this case. Below, q itU is the realization
for quality in period t of the used car that individual i purchased and drove in
period t ⫺ 1 when it was a new car, E(q mPU) denotes the expected quality of
secondhand-market used cars of type m, and pmPU is the secondhand-market price
for those cars (for proofs, see Johnson and Waldman 2008, app. B). Note that,
to simplify the statements of the propositions, we assume that a consumer who
is indifferent between selling his or her used car and driving the car will sell it
(similarly, a consumer who is indifferent between returning a leased car when
it becomes used and driving the car will return it).
Proposition 1.
Suppose that firms sell new cars. Then there are one or more
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equilibria each of which is characterized by a function q*m (q*m ! q˜ m for m p 1,
. . . , M ⫺ 1), such that propositions 1.i–1.iii describe the equilibrium.
i) In every period t, all group-m consumers (m p 1, . . . , M ⫺ 1) who do
not own a used car at the beginning of the period purchase a new car of type
m at price cm.
ii) In every period t, each consumer i in group m (m p 1, . . . , M ⫺ 1)
who owns a used car at the beginning of the period characterized by q itU 1 (≤)
q*m keeps the used car and drives it (purchases a new car and sells the used car).
iii) In every period t, some group-M consumers purchase a used car on the
secondhand market.
The main result in proposition 1 is that, as discussed above, because of adverse
selection there is less trade on the secondhand market than in the social planner
case. Another interesting aspect of the proposition is that there are potentially
multiple equilibria. The logic is that the return to selling a used car on the
secondhand market is positively related to the secondhand-market price, which
is itself positively related in equilibrium to the frequency with which a consumer
who owns a used car at the beginning of a period decides to sell the car. So,
for example, for a fixed parameterization there can be both an equilibrium with
low secondhand-market prices and low values for q*m and an equilibrium with
high secondhand-market prices and high values for q*m. See Wilson (1980) and
Kim (1985) for earlier analyses of secondhand-market models characterized by
adverse selection with this type of multiplicity.
We now consider what happens when firms can sell or lease new cars. Note
that below, pmL is the price for a new car leased to a group-m consumer, pmB is
the buyback price in the lease contract signed by group-m consumers, E(q mLU) is
the expected quality of type-m used cars leased when new and then sold on the
secondhand market, pmLU is the price for which these used cars sell, p ⫹ denotes
social surplus in this case, and p denotes the highest equilibrium value for social
surplus when firms only sell new cars.
Proposition 2. Suppose that firms can both sell and lease new cars. Then
there exists a unique equilibrium characterized by all new-car drivers leasing
rather than purchasing new cars, where propositions 2.i–2.iv describe the equilibrium. Also, p ⫹ 1 p .
i) In every period t, all group-m consumers (m p 1, . . . , M ⫺ 1) who did
not lease a new car in the previous period lease a new car of type m at a price
pmL and buyback price pmB.
ii) In every period t, each consumer i in group m who leased a new car in
the previous period characterized by q itU 1 (≤) q˜ m purchases the car at the buyback
price and drives it (returns the used car and leases a a new car).
iii) In every period t, some group-M consumers purchase a used car on the
secondhand market.
iv) Also, pmB 1 pmLU for all m (m p 1, . . . , M ⫺ 1).
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313
Proposition 2 has a number of interesting results. First, when a car is leased,
there is no adverse-selection problem in the following period when the car
becomes used. That is, the used car is sold on the secondhand market given
exactly the same set of realizations for used-car quality as in the earlier social
planner analysis. The logic is that leasing and optimally setting the buyback price
suppresses the private information of new-car drivers, with the result that adverse
selection is avoided. Second, all new cars are leased rather than sold. This result
is a direct ramification of the first result. Since leasing avoids adverse selection,
new-car drivers prefer to lease rather than purchase because it improves their
welfare.
A third interesting result concerns buyback prices. As we found in Johnson
and Waldman (2003), a lease contract’s buyback price is higher than the car’s
secondhand-market price if it is returned. That is, pmB 1 pmLU for all m (m p 1,
. . . , M ⫺ 1). The logic is that it is only efficient for consumers in any group
m to keep used cars with quality close to q mN, and in order to achieve this result
buyback prices are set higher than secondhand-market prices. As we discussed
in detail in Johnson and Waldman (2003), this finding matches well with evidence
we collected from advertisements that appeared in the Sunday New York Times
during 1998 (see also the recent empirical analysis in Pierce [2007]).
As a final point, without the parameter restriction vm [q mN ⫺ E (q Uk )] 1 cm for all
(m, k) pairs such that m ! M and k ! M, there would be the possibility of multiple
consumer groups purchasing used cars on the secondhand market. We have
analyzed this case and, given that an equilibrium exists, the results are quite
similar.4 The only significant difference is that the matching of used cars to usedcar buyers is potentially less efficient than in the analysis found above. In propositions 1 and 2, since only one group purchases used cars in equilibrium, the
matching of used cars sold and the purchasers of these cars is (trivially) efficient.
In contrast, when multiple consumer groups purchase used cars, there is potentially inefficient matching of used cars sold with the purchasers of these cars
on the secondhand market.
3. Adverse Selection and Moral Hazard
In the previous section we showed that, given asymmetric information, newcar leasing improves social welfare because it avoids adverse selection. In that
analysis, however, when firms had the option of leasing, the result was that all
new cars were leased, but the real-world automobile market clearly exhibits a
mix of selling and leasing. In this section we do two things. First, we derive an
equilibrium that exhibits a mix of selling and leasing. Second, we discuss how
this model provides explanations for various empirical regularities concerning
real-world new- and used-car markets.
4
In our analysis of this case we were unable to show that an equilibrium necessarily exists. This
is because of possible discontinuities in the secondhand-market prices of used cars that arise in this
case.
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3.1. The Model
In order to generate an equilibrium that exhibits a mix of selling and leasing,
we introduce costs associated with leasing. The first cost we introduce is, as in
Johnson and Waldman (2003), a cost to consumers of abiding by the standard
restrictions found in lease contracts such as those concerning maximum mileage.
The second is a cost due to moral hazard concerning consumer maintenance.5
The idea is that if a consumer leases a new car, then the consumer underinvests
in maintenance because if the consumer returns the car, he or she does not bear
the consequences of inadequate maintenance. We also incorporate the idea that
in real-world lease contracts some aspects of this problem are avoided through
provisions that stipulate mandatory maintenance activities.
We introduce the following changes. First, z it denotes the cost consumer i
incurs in period t if he or she drives a leased car in period t. In particular, each
z it is a random draw from the probability density function f(z) and cumulative
distribution function F(z), where f(z) 1 0 if 0 ! z ! Z and f(z) p 0 for all z
outside of this interval. We also assume that each z it is privately observed by
individual i at the end of period t ⫺ 1. Note that for tractability reasons we
assume that z it is a new draw from the probability density function f(z) each
period rather than being constant from period to period.
Second, consider consumer i, who purchases a new car in period t. During
period t the consumer privately observes the realization of a random variable
l it and also the realization of z it⫹1. The variable l it captures both the inherent
deterioration of the car as it ages and the car’s return to maintenance and is a
random draw from a distribution described by the probability density function
g(l) and cumulative distribution function G(l), where g(l) 1 0 for all 0 !
l ! 1 and g(l) p 0 for all l outside of this interval. On the basis of these
realizations, the consumer then chooses a maintenance level eit, where eit 苸
[0, ¯e], for which he or she bears the cost k(eit), where k(e) is a strictly increasing
and convex function with k(0) p k (0) p 0.
The quality of the used car owned by the consumer at the beginning of period
t ⫹ 1 is then given by the continuously differentiable function q mU(l it, E it), where
m is the car’s type, E it p eit ⫹ y, and y 苸 [0, Y ]. We assume for all m (m p 1,
. . . , M ⫺ 1) that q mU(l, E) is strictly increasing in l for any given E, strictly
increasing in E for any given l, and strictly concave in E. We also assume for
all m (m p 1, . . . , M ⫺ 1) that q mU(l, 0) p q L and q mU(l, E) ≤ q mN for all
(l, E) pairs. In words, independent of the realization of l, used-car quality equals
the minimum value if both y and the maintenance expenditure equal zero, and
used-car quality never exceeds new-car quality. Note that in this specification y
captures the potential importance of moral hazard. That is, the smaller y is, the
5
See Mann (1992) for an earlier formal analysis of leasing and moral hazard concerning consumer
maintenance. Other analyses that consider durable goods and consumer maintenance, but not in
terms of the leasing decision, include Schmalensee (1974), Kim (1985), Shapiro (1995), and Carlton
and Waldman (2010).
Leasing and Moral Hazard
315
larger the moral hazard problem, in the sense that not maintaining a used car
translates into worse outcomes for used-car quality.
Third, consider consumer i, who leases a new car in equilibrium. With probability 1 ⫺ a the consumer is free to choose any maintenance level as above.
However, with probability a a minimum maintenance level, emC(l), is specified
in the lease contract, where m refers to the car’s type. In words, with probability
a a problem with the car is identified during routine maintenance and the lease
contract specifies a minimum maintenance level, while with probability 1 ⫺ a
the consumer privately observes the problem, so the lease contract cannot specify
a minimum maintenance level.
One interesting aspect of this moral hazard problem is that it applies to both
newly leased and newly purchased cars. The logic is that because asymmetric
information means that the secondhand-market price an individual receives for
a used car is not directly a function of its quality, an individual who purchases
a new car and anticipates selling it in the subsequent period underinvests in
maintenance. A related point is that the moral hazard problem will sometimes
be more severe for new cars that are purchased than those that are leased. The
reason is that, as discussed above, when a new car is leased, part of the moral
hazard problem is avoided by requiring minimum maintenance levels for problems identified during routine maintenance, but this option is not available when
a new car is purchased.
The timing of moves in each period is now as follows. First, each consumer
i who drove a new car in the previous period finds out the realization of that
car’s current quality. Second, each consumer who leased a new car in the previous
period decides whether to return the car or purchase it at the buyback price.
Third, each firm chooses which type of car to produce and announces a newcar purchase price. Further, when leasing is an option, each firm announces a
lease price, a buyback price, and a minimum maintenance level for each l for
new-car problems identified during routine maintenance. Fourth, consumers
make their purchasing and leasing decisions. Fifth, a secondhand market opens
up in which prices equate supply and demand. Sixth, each consumer i who
purchased or leased a new car observes l it and z it⫹1 and then, subject to contractual provisions, chooses a new-car maintenance level.
3.2. Analysis
As in the previous section, we impose a number of parameter restrictions.
First, as before, we restrict the analysis to parameterizations such that group-M
individuals never purchase or lease new cars, while individuals in groups 1
through M ⫺ 1 never purchase used cars. To ensure this we assume that equation
(1) is still satisfied for all (m, k) pairs such that m ! M and k ! M, where
E(q mU) now refers to the expected quality of a type-m used car given a maintenance
expenditure equal to ē and E(q Uk ) is defined similarly. Second, we again impose
a restriction that ensures that individuals in each group m (m p 1, . . . , M ⫺
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1) purchase or lease type-m new cars rather than type-k new cars, where k (
m. Third, we restrict the analysis to parameterizations such that for each of
groups 1 through M ⫺ 1 some individuals purchase new cars in equilibrium,
which is ensured by assuming that Z is sufficiently large (an earlier assumption
ensures that there is some leasing in equilibrium). Fourth, we continue to assume
M⫺1
that x M 1 冘mp1 x m, which again ensures that secondhand-market prices are positive (see Johnson and Waldman 2008, app. A).
Similar to the analysis of the previous model, this analysis begins with a brief
discussion of what happens when firms only sell new cars and there is a social
planner who only controls the frequency with which a new-car driver sells the
car on the secondhand market in the following period. In particular, as in the
previous model, the social planner chooses a frequency for each new-car driver
to sell the car on the secondhand market in the following period, and then each
driver keeps the used car if it is high quality or sells it if it is low quality. In
this model this idea translates into a function l̃ m such that an individual in
group m (m p 1, . . . , M ⫺ 1) who owns a used car at the beginning of period
t ⫹ 1 keeps the used car and drives it (purchases a new car and sells the used
car to a group-M individual) if l it 1 (≤) l˜ m.
We now consider what happens without a social planner when firms only sell
new cars. Given our parameter restrictions, in this case individuals in groups 1
through M ⫺ 1 do not purchase used cars, while individuals in group M do not
purchase new cars. There are four additional conditions that characterize what
happens in this case. First, every individual in group m (m p 1, . . . , M ⫺ 1)
purchases a new car of type m in every period in which he or she does not own
a used car at the beginning of the period. Second, there is a function lKm (m p
1, . . . , M ⫺ 1) such that an individual in group m who owns a used car at
the beginning of period t ⫹ 1 keeps the used car and drives it (purchases a new
car and sells the used car to a group-M individual) if l it 1 (≤) lKm, where
lKm ! l˜ m for all m (m p 1, . . . , M ⫺ 1). Third, in every period in which an
individual in group m (m p 1, . . . , M ⫺ 1) drives a new car and anticipates
selling the car in the following period, the maintenance expenditure equals zero.
Fourth, for each group m (m p 1, . . . , M ⫺ 1) there is a single price that
applies to all type-m used cars sold on the secondhand market, where this price
equals vm multiplied by the average quality of the type-m secondhand-market
used cars (which itself depends on lKm).
The intuition behind these results is as follows. Because of asymmetric information, all used cars sold by a particular consumer group sell for the same
price, and this price reflects the average quality of all the used cars this consumer
group offers on the secondhand market. In turn, because of adverse selection,
just as in Akerlof’s (1970) analysis and the analysis of the previous section, fewer
cars are traded on the secondhand market than maximizes social welfare.
As discussed earlier, there is also moral hazard in this model even in the
absence of leasing. As just mentioned, with asymmetric information the secondhand-market price for a used car sold by a particular consumer in some group
Leasing and Moral Hazard
317
m reflects the average quality of type-m secondhand-market used cars. Hence,
moral hazard arises because when a consumer sells a used car, the price the
consumer receives is not a function of the previous maintenance expenditure.
As a result, because new-car drivers correctly anticipate when they will sell their
used cars in the following period, the previous period’s maintenance expenditures
for cars offered on the secondhand market equal zero.
We now allow leasing. Below, E(q mPU), E(q mLU), pmPU, pmLU, p ⫹, and p have the
same definitions as previously. Also, emC(l it) is the contractually specified minimum maintenance level for a type-m new car leased when new, given that a
new-car problem is identified during routine maintenance.
Proposition 3. Suppose that firms can both sell and lease new cars. Then
every equilibrium is characterized by functions z m⫹, lKm(z), l*m(z), pmL, pmB, and
emC(l), such that propositions 3.i–3.v describe the equilibrium.
i) In every period t, if z it ≥ z m⫹, then each consumer i in group m (m p 1,
. . . , M ⫺ 1) who drove a used car in the previous period purchases a new
car of type m at price cm and chooses a maintenance level eit p (1) 0 if l it ≤
(1) lKm(z it).
ii) In every period t, if z it ! z m⫹, then each consumer i in group m (m p 1,
. . . , M ⫺ 1) who drove a used car in the previous period leases a new car of
type m at price pmL, where the contract is characterized by the buyback price
pmB and maintenance function emC(l). For new-car problems identified during
routine maintenance, the maintenance level chosen is at least emC(l it), where
emC(l) 1 0 if l is sufficiently small. For other problems eit p (1) 0 if l it ≤ (1)
l*m(z).
iii) In every period t, each consumer i in group m (m p 1, . . . , M ⫺ 1)
who purchased a new car in the previous period keeps the car if l it⫺1 1
lKm(z it), sells the car and takes the actions described in proposition 3.i if
l it⫺1 ≤ lKm(z it) and z it ≥ z m⫹, or sells the car and takes the actions described in
proposition 3.ii if l it⫺1 ≤ lKm(z it) and z it ! z m⫹. Any used car sold is sold to a
group-M consumer for pmPU p vME(q mPU).
iv) Suppose that a new-car problem in period t ⫺ 1 was not identified during
routine maintenance. In every period t, each consumer i in group m (m p 1,
. . . , M ⫺ 1) who leased a new car in the previous period buys back the car
if l it⫺1 1 l*m(zit), returns the car and takes the actions described in proposition
3.i if l it⫺1 ≤ l*m(zit) and z it ≥ z m⫹, or returns the car and takes the actions described
in proposition 3.ii if l it⫺1 ≤ l*m(zit) and z it ! z m⫹. Any returned used car is sold
to a group-M consumer for pmLU p vME(q mLU).
v) Suppose that a new-car problem in period t ⫺ 1 was identified during
routine maintenance. In every period t, each consumer i in group m (m p 1,
. . . , M ⫺ 1) who leased a new car in the previous period either buys back
the car, returns the car and takes the actions described in proposition 3.i (this
requires that z it ≥ z m⫹), or returns the car and takes the actions described in
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proposition 3.ii (this requires that z it ! z m⫹). Any returned used car is sold to a
group-M consumer for pmLU p vME(q mLU).
Proposition 3 is characterized by a mix of selling and leasing. For each group
that drives new cars in equilibrium, those with low leasing costs lease new cars
and avoid adverse selection, while those with high leasing costs purchase new
cars and avoid the leasing cost. The equilibrium is also characterized by moral
hazard and specifically the idea that leasing allows a consumer to avoid moral
hazard when a new-car problem is identified during routine maintenance. That
is, propositions 3.i and 3.iii tell us that when a consumer purchases a new car
and anticipates selling the used car in the following period, the consumer spends
nothing on maintenance. Similarly, propositions 3.ii and 3.iv tell us that when
a consumer leases a new car, a new-car problem is not identified during routine
maintenance, and the consumer anticipates returning it to the manufacturer in
the following period, then nothing is spent on maintenance again. However, if
a consumer leases, a new-car problem is identified during routine maintenance,
and l is small so there is a large return to maintenance, then a positive amount
is spent on maintenance whether or not the consumer anticipates returning the
car.
Finally, there can be multiple equilibria here for the same reason that multiple
equilibria were possible in proposition 1, where each equilibrium has the properties described in proposition 3. That is, there can be an equilibrium in which
there are low secondhand-market prices for used cars that were purchased when
new and a small proportion of these cars are traded on the secondhand market
and an equilibrium in which these prices are high and a high proportion of
these cars are traded. Further, there is now an additional reason why multiple
equilibria can exist. That is, for each group m (m p 1, . . . , M ⫺ 1), there is
a possibility of multiple lease contracts in equilibrium (each of which is consistent
with propositions 3.i–3.v), where each group-m consumer is indifferent across
all these contracts.
3.3. Further Results
In this section we discuss five further results that follow from our approach
to modeling the new- and used-car markets and that serve as explanations for
various real-world empirical regularities.
Corollary 1 to Proposition 3. Holding all other parameters fixed, if y is
sufficiently small, then there exist values a L and a H (0 ! a L ! a H ! 1) such that
an increase from a value a ! a L to a value a 1 a H increases the percentage of
new cars leased.
The corollary states that, if y is sufficiently small—that is, the function that
translates new-car maintenance into used-car quality is such that the moral
hazard problem is potentially large—then increasing the proportion of new-car
problems identified during routine maintenance from a sufficiently low value to
Leasing and Moral Hazard
319
a sufficiently high value increases leasing. The logic is as follows. Since, when a
new-car problem is identified during routine maintenance, a minimum maintenance level is specified in the lease contract, as the proportion of problems
identified during routine maintenance rises, the advantage of using leasing to
address these problems also rises. The end result is that increasing this proportion
from a sufficiently low value to a sufficiently high value causes leasing to increase.6
This first result provides an explanation for the growth in leasing during the
last 30 years. The typical problem not identified during routine maintenance
occurs when a part in the car becomes defective or worn out unpredictably.
Hence, the above result suggests that if new cars become sufficiently more trouble
free or reliable, the proportion of problems not caught by routine maintenance
will decrease, which in turn should increase leasing. This is an explanation for
the growth in leasing during the last 30 years because new cars have, on average,
become substantially more trouble free or reliable during this time period. For
example, Consumer Reports (2003, 2005), on the basis of survey evidence, reports
a significant increase in new-car reliability over this time period.7,8
Note that an alternative approach to modeling increased reliability is to assume
that increased reliability increases built-in durability, and thus a car’s quality
when used relies less on the maintenance decisions of new-car drivers. That is,
increased reliability decreases the importance of the moral hazard problem. Although we do not show it formally, this alternative approach to modeling increased reliability provides a complementary avenue using our framework by
which increased reliability can increase the proportion of new cars that are leased.
To see this, suppose that, as in corollary 1, the starting value for a is low.
With a sufficiently small a the costs associated with moral hazard will be larger
for cars that are leased rather than purchased when new. This is because with
a small a, leasing’s advantage in addressing moral hazard through mandatory
6
Given that the logic is straightforward, one might ask why the result holds only given a sufficiently
small y and a large enough movement in a . Basically, the model is such that the return to purchasing
a new car can increase (but does not have to) as a increases, and this can stop the result from
holding generally. Assuming a sufficiently small y limits how much the return to purchasing can
increase as a increases, while the large change in a places a lower bound on how much the return
to leasing increases. Hence, these two conditions together are sufficient to ensure that the proportion
of cars leased rises.
7
To make our argument more precise, we note that in reality there are two types of maintenance—
one type is routine maintenance, such as oil changes, that can be made a function of vehicle age
and/or vehicle mileage, while the other is maintenance that is a response to vehicle problems that
arise over time. A lease contract can obligate the lessee to maintenance levels for all types of routine
maintenance and some proportion of problem-related maintenance. Given this, as the number of
problems has decreased over time (see, for example, Consumer Reports 2003, 2005) the proportion
of maintenance expenditures specified in lease contracts should have increased, which is basically
the same as increasing a in our model.
8
Recently, there has been a decline in new-car leasing from roughly 30 percent of total new-car
transactions to roughly 25 percent. One possible reason for this recent decline is that lease terms in
the late 1990s and early 2000s were overly generous because manufacturers systematically overestimated residual values, and lease terms have become less generous recently as manufacturers realized
their mistake and started to more accurately estimate residual values This argument is consistent
with a discussion in ADESA Analytical Services (2003).
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maintenance will be smaller than its disadvantage due to a higher probability
of used cars being sold on the secondhand market when they were previously
leased rather than purchased. This means that, ignoring any increase in a due
to increased reliability but assuming that the initial value for a is low, leasing
will be associated with higher moral hazard costs, but an increase in reliability
that reduces the moral hazard problem should reduce the magnitude of these
extra costs. In turn, since leasing rather than purchasing a new car reduces adverse
selection, an increase in reliability that reduces the extra moral hazard costs
associated with leasing should increase the proportion of new cars that are leased.
A second result is that in a cross-sectional analysis more reliable new cars
should have a higher frequency of leasing. This result is not a direct implication
of our analysis, since in our analysis all new cars have the same a. However, it
clearly follows from our basic approach in that new cars that are more reliable
should have fewer problems not identified during routine maintenance, which
in turn means a smaller moral hazard problem if they are leased and thus leads
to more leasing. This result is consistent with evidence reported in Desai and
Purohit (1999) and Mannering, Winston, and Starkey (2002). Desai and Purohit
conduct an empirical analysis of how leasing varies by car model. They develop
a measure of reliability using information reported in Consumer Reports and
show that more reliable car models are leased more. Mannering, Winston, and
Starkey report similar results in an empirical study of the probability that a
household leases rather than purchases a new car as a function of various consumer attributes.
The third result captured in proposition 3 is that individuals who have higher
costs of abiding by the standard restrictions found in lease contracts should
purchase new cars, while those with lower costs should lease.9 The only study
that we know of that addresses this issue is the Mannering, Winston, and Starkey
study just mentioned. One of their results is that the probability of leasing is
lower if the household has attributes that indicate that it expects to drive a high
number of miles. In other words, leasing is less popular among households for
whom, on average, the cost of abiding by maximum mileage restrictions is likely
to be higher.
Our fourth result concerns how leasing varies with consumer valuation of
quality or, similarly, consumer income. Below, rmL denotes the proportion of
group-m individuals who lease.
Corollary 2 to Proposition 3. Holding all other parameters fixed, if y is
sufficiently small and a is sufficiently large, then r1L 1 rmL (m p 2, . . . , M ⫺
1), given a sufficiently large v1.
Corollary 2 to proposition 3 states that if y is sufficiently small and a is
sufficiently large, the highest valuation group leases more than lower valuation
9
Although we failed to point out this result in Johnson and Waldman (2003), it is also an implication of one of the analyses in that paper.
Leasing and Moral Hazard
321
groups if the highest group’s valuation is sufficiently high. In other words, if we
interpret higher valuations for quality as higher incomes, then very high income
new-car drivers lease more than lower income groups.
The logic behind this result follows. A sufficiently small y and a sufficiently
large a mean that the potential moral hazard problem is large, and leasing avoids
a significant proportion of the moral hazard problem through mandatory maintenance. In turn, when the potential moral hazard problem is large and leasing
avoids much of it, the frequency of leasing is primarily determined by moral
hazard considerations. Given this, consider very high income new-car drivers
whose valuation for quality is so high that they drive new cars almost every
period. For these consumers the moral hazard problem is severe, because they
almost never keep their used cars and so their unconstrained incentive is to
almost always invest nothing in maintenance. The result is that, because leasing
eliminates moral hazard for problems identified during routine maintenance,
leasing is common among these consumers.
Corollary 2 is consistent with empirical findings in Aizcorbe and StarrMcCluer (1997). Aizcorbe and Starr-McCluer analyze data from the Federal
Reserve Board’s Survey of Consumer Finances and the Bureau of Labor Statistics’s Consumer Expenditure Survey and find a positive relationship between
leasing and consumer income.10 For example, using the Consumer Expenditure
Survey, they find that in 1992 1.0 percent of households with incomes below
$10,000 leased a car, 1.0 percent of households with incomes between $10,000
and $25,000 leased, 1.6 percent of households with incomes between $25,000
and $50,000 leased, 4.1 percent of households with incomes between $50,000
and $100,000 leased, and 11.4 percent of households with incomes above
$100,000 leased. One interesting aspect of their findings is that the proportion
of new cars leased is not everywhere increasing with income (this follows given
that for lower income groups the percentage of households acquiring new cars
rose with income). Rather, similar to the result of our theoretical analysis, leasing
is positively related to income in the sense that very high income households
lease more than lower income groups.11
10
Mannering, Winston, and Starkey (2002) also show that leasing is positively related to consumer
income, but they do not provide detailed evidence concerning how leasing varies with income class,
as Aizcorbe and Starr-McCluer (1997) do.
11
Another possibility for why high-income households lease more often is that high-income households are in possession of more new cars at any point in time (note that this would yield a positive
relationship between leasing and income because in 1992 used cars were almost never leased).
However, other evidence reported by Aizcorbe and Starr-McCluer (1997) suggests that although this
is a contributing factor to their finding that high-income households lease more, it is not the sole
factor, and thus high-income households also have a higher propensity to lease when they acquire
new cars. For example, using the Survey of Consumer Finances, Aizcorbe and Starr-McCluer find
that the top two income groups were in possession of the same average number of vehicles in 1992,
while the percentage of these vehicles acquired as new was 52.9 percent for the second highest income
group and 66.0 percent for the highest income group. This factor by itself can explain why the
highest income group has a higher percentage of households in possession of a leased vehicle, but
it does not easily explain why, as reported above, the highest income group’s percentage is more
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Another interesting aspect of our fourth result is that the standard argument
concerning moral hazard and leasing found, for example, in Smith and Wakeman
(1985), makes exactly the opposite prediction. That is, the standard argument
suggests that moral hazard is a larger problem for high-income individuals because they drive new cars basically every period, but since in that argument
moral hazard applies only to leased cars, the prediction is that leasing rates
should be lower, not higher, among high-income individuals. In other words,
the standard argument concerning moral hazard and leasing does not explain
the finding in the data that high-income consumers lease more, not less.
Our fifth result follows from the next corollary.
Corollary 3 to Proposition 3.
For all m (m p 1, . . . , M ⫺ 1), pmLU 1 pmPU.
The fifth result is that for used cars of type m (m p 1, . . . , M ⫺ 1) the
secondhand-market price is higher for cars leased rather than purchased when
new. This result, which is also found in Johnson and Waldman (2003), follows
from the idea that leasing reduces adverse selection. In other words, because
leasing reduces adverse selection, type-m used cars offered on the secondhand
market that were leased when new are of higher average quality and sell for
more than type-m used cars offered on the secondhand market that were purchased when new. One might argue that in cases in which moral hazard is worse
for leased cars, the prediction should be ambiguous since leasing both increases
quality by reducing adverse selection but also decreases quality by increasing
moral hazard. But, in fact, this logic is wrong, and the price of used cars leased
when new must be higher.
To see why, suppose the opposite were true. That is, suppose that the usedcar price for type-m cars that were purchased when new is higher than the usedcar price for type-m cars that were leased when new. Then no type-m new cars
would be leased, since a group-m consumer could do better by purchasing and
investing in maintenance as if the consumer had leased. Hence, since given our
parameter restrictions some consumers in group m must lease, for every type
m (m p 1, . . . , M ⫺ 1), the secondhand-market price for used cars that were
leased when new must be higher than the secondhand-market price for used
cars that were purchased when new.
Desai and Purohit (1998) provide evidence consistent with this result. They
obtained used-car prices from a large automobile auction house and investigated
the relationship between a used car’s price and whether the car was purchased
or leased when new. In their empirical analysis, Desai and Purohit look at the
auction prices for a popular 1993-model car during the time period 1994–96.
After controlling for the car’s age, mileage, and auction date, they find that usedthan double that of the second highest income group. It seems that the highest income group also
has a higher propensity to lease when acquiring new vehicles.
Leasing and Moral Hazard
323
car prices are indeed higher for used cars that were leased rather than purchased
when new.12,13
4. Alternative Explanations
There are a number of alternative explanations for why a durable-goods producer would lease, some of which specifically address leasing in the new-car
market. One explanation for leasing is time inconsistency. Building on the seminal
article of Coase (1972), an extensive literature explores the time-inconsistency
problem faced by a durable-goods monopolist and the role of leasing (renting)
in solving the problem (see, for example, Stokey 1981; Bulow 1982, 1986; Ausubel
and Deneckere 1989; Butz 1990; Waldman 1993; Karp and Perloff 1996). Coase’s
insight was that a durable-goods monopolist that sells its output will not internalize how its output decision in one period affects the value of units sold in
previous periods, with the result that output in later periods is so high that the
firm’s profitability is reduced. In turn, this leads to leasing, since with leasing
the firm retains ownership of units previously produced and, thus, eliminates
its incentive to sell too much in later periods.
There are a number of reasons why time inconsistency is not the correct
explanation for leasing in the new-car market. First, time inconsistency is substantially reduced in a market characterized by replacement sales (see Bond and
Samuelson 1984), and the automobile market has frequent replacement sales.
Second, because time inconsistency is a monopoly explanation and there has
been increased foreign competition over time, the time-inconsistency argument
counterfactually predicts that leasing rates should have shrunk rather than grown
over time. Third, if leasing is used to reduce time inconsistency, then new-car
output should have fallen as new-car leasing became a larger share of the market.
But the evidence is not consistent with this prediction. For example, between
1990 and 1999 the percentage of new cars leased grew from 7.3 percent of the
market to 30.2 percent of the market, while the size of the new-car market was
13.86 million in 1990 and 16.88 million in 1999.14,15
12
To be precise, Desai and Purohit (1998) consider how quickly used-car prices decline with vehicle
age. Given that they constrain the prices of 1-year-old cars to be independent of whether the cars
were purchased or leased when new, if used cars that were leased when new sell for more, then, as
they find, price declines should be smaller for these cars.
13
There is one result in Johnson and Waldman (2003) and in Section 2 that is not found here.
This is that buyback prices are above secondhand-market prices. In the current model the relationship
between these prices is ambiguous.
14
The source for these figures is U.S. Department of Transportation, Bureau of Transportation
Statistics, Table 1-17: New and Used Passenger Car Sales and Leases (http://www.bts.gov/publications/
national_transportation_statistics/html/table_01_17.html).
15
Another monopoly explanation for leasing is put forth in Waldman (1997) and Hendel and
Lizzeri (1999). In that argument, a durable-goods monopolist leases because leasing is an effective
way of allowing the firm to reduce the availability of used units, where reducing used-unit availability
allows the firm to charge a higher price for new units. There are two reasons why this argument is
not the correct one for the new-car market. First, as above, a monopoly explanation is inconsistent
with the substantial growth in new-car leasing over time. Second, a central component of this
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Another explanation is that there are tax advantages associated with leasing
(see, for example, Myers, Dill, and Bautista 1976; Franks and Hodges 1987).
Since the Tax Reform Act of 1986 (Pub. L. No. 99-514, 100 Stat. 2085) included
a number of changes that increased the attractiveness of leasing an automobile
(for discussions, see Crocetti 1988; Auster 1990), in contrast to the explanations
discussed above, this explanation is consistent with the growth in new-car leasing
over the last 30 years. Specific changes include the phaseout of both sales tax
and personal interest deductions. There is a problem with this explanation,
however, in that it predicts growth in leasing after 1986 but a leveling off of the
percentage of new cars leased after the new-car market achieves a new equilibrium. This is a problem because the growth in new-car leasing continued to be
substantial long after 1986.
Two other explanations follow. First, as argued, for example, by Wyman (1973)
and Copeland and Weston (1982), leasing can be used as a way of transferring
risk. That is, if there is substantial uncertainty concerning the residual value of
assets, then leasing may be used to shift risk from risk-averse consumers to less
risk averse manufacturers or distributors. Second, an explanation popular in the
business press is that leasing is used as a way of lowering monthly payments
(see, for example, Woodruff 1994). The logic here is that, because of either
consumer myopia or imperfect capital markets, consumers perceive leasing as a
way of making new cars more affordable. Notice that both of these explanations
predict that new-car leasing rates should fall with consumer income. That is,
(absolute) risk aversion is likely to be negatively correlated with income, and
high-income consumers are likely both to be less myopic and to have better
access to captial markets. The problem with these explanations, therefore, is that,
as discussed earlier, the evidence indicates that leasing is positively, not negatively,
related to consumer income (see Aizcorbe and Starr-McCluer 1997; Mannering,
Winston, and Starkey 2002).
In summary, there are a number of alternative explanations for why there is
substantial leasing in the new-car market, but none of the major alternatives fit
the evidence very well. The time-inconsistency explanation is inconsistent with the
overall growth in new-car leasing during the last 30 years, and the tax argument
is inconsistent with the details of the time-series evidence, while explanations based
on transferring risk and lowering monthly payments are inconsistent with the
positive relationship between leasing and consumer income. Our conclusion is
that our explanation for new-car leasing based on adverse selection and moral
hazard matches the evidence better than any of the alternatives.
5. Conclusion
In this paper we have argued that two important factors determining the
extent of new-car leasing are adverse selection and moral hazard. In particular,
argument is that the durable-goods producer scraps some or all of the used units returned to the
firm, but this is inconsistent with standard behavior in the automobile industry.
Leasing and Moral Hazard
325
an important return to leasing is that it avoids the adverse-selection problem in
the used-car market by suppressing the private information of new-car drivers,
while leasing as well as purchasing are associated with moral hazard concerning
consumer maintenance. We constructed and analyzed a model of the new- and
used-car markets that incorporates both factors and also incorporates costs associated with consumers abiding by the standard restrictions found in lease
contracts, and we showed that this approach provides explanations for a number
of empirical findings concerning real-world new- and used-car markets. For
example, the model provides explanations for why leasing has become more
popular over time, why very high income consumers have a higher propensity
to lease, and why used cars that were leased when new typically sell for more
than similar cars that were purchased when new. We also argued that this approach is consistent with buyback provisions in new-car lease contracts and with
the cross-sectional variation in leasing across new-car models.
Much of the focus of durable-goods theory over the last 30 years has been
on the issue of time inconsistency first identified in Coase (1972).16 But we
believe that an equally important contribution to durable-goods theory is Akerlof’s (1970) seminal analysis of the market for lemons. That paper has, of
course, had an enormous impact in general since it was one of the papers that
started the asymmetric-information revolution in economic theory. But in terms
of durable-goods theory, Akerlof’s paper was mostly ignored for almost 30 years.
The main analysis in that paper, however, was an analysis of a secondhand market,
and so clearly the paper has implications for understanding the operation of
durable-goods markets. Our papers and Hendel and Lizzeri (2002) extend the
theoretical analysis of that paper in terms of its implications for durable-goods
markets and, most important, show that those implications match the empirical
evidence of the automobile market quite well. Hence, as we state above, our
feeling is that Akerlof’s analysis should be thought of not only as a classic
contribution to the literature on asymmetric information but also as a classic
contribution to the literature on durable goods.
There are a number of ways in which the analysis in our paper could be
extended. First, although we feel that useful insights follow from modeling the
automobile market as a perfectly competitive industry, it is clear that firms in
that industry possess some market power. Hence, one extension of the analysis
would be to explore the implications of adverse selection and moral hazard in
an oligopoly or a monopolistically competitive framework. Second, we feel that
it might be useful to allow cars to potentially last more than 2 periods. We believe
that such an extension would allow us to explain why leasing is common for
16
Although the issue of time inconsistency in durable-goods markets was first identified by Coase
(1972), the focus of the theoretical literature on durable goods did not turn to the time-inconsistency
issue until the publication of Stokey (1981) and Bulow (1982). Prior to those papers, the focus of
the literature was the analysis of optimal durability that appeared in Swan (1970, 1971) and Sieper
and Swan (1973). See Waldman (2003) for a survey of durable-goods theory that discusses this
history.
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new cars but rare in the marketing of used cars. Third, we believe that a more
realistic model of the automobile market would also incorporate a transaction
cost and/or switching cost associated with upgrading from a used car to a higher
quality new car, where this cost could potentially vary with the manner in which
this upgrading is achieved.
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