Recent developments in the
economics of information
Maarten C.W. Janssen
University of Vienna
Course Outline
Adverse Selection
• There are (many) sellers with quality (reservation
value) θ between θl and θh. Distribution quality
given by some cdf F
• If buyers know quality, they are maximally willing
to pay vθ, with v > 1. (Gains from trade)
• Buyers do not know quality, form expectations of
qualities traded in the market
• Can there be a market price p such that all gains
from trade are realized? Only if θh < p < vE(θ)
• Generally, market inefficient and high qualities do
not sell.
Leasing - Hendel, Lizzeri (AER, JPE)
• Some well know issues that leasing solves
– Durable goods monopolist is its own future
competitor (leasing prevents demand going down)
– Capital market imperfections (poor people may
lease)
– Eliminates second hand market
• HL: leasing partially solves adverse selection
problem
What HL want to explain?
• Both leasing and selling are widely observed in car
market
• Buyers of new cars keep their cars much longer
than those who lease
• Ceteris paribus, used cars that were leased tend to
have higher quality than those used cars that were
initially bought
• Cars become more durable and leasing is more
recent phenomenon. Is there a relation?
• Leasing includes option to buy the car at end of
lease contract. Why is this price set such that
option to buy is used.
Main new feature HL
• Who is a seller, who is a buyer in second hand
market is not exogenous
• Seller is someone who bought new car before
and probably want to have new car again (high
valuation guy)
• The interaction with the primary market gives
new perspective on the opportunity costs (to
buying and selling) of the players
• To what extent reduces adverse selection
problem because of this interaction
Model HL
• Dynamic model, good last only two periods,
players discount future pay-off with δ
• Interaction between primary and secondary
markets
• In primary market, seller sells (exogenous)
quantity y. (Expected) Quality of new is v
• Buyers are heterogeneous in their valuation of
the quality, between θl and θh with cdf F
– Some consumers only buy second hand
– Some consumers get new and get rid of them
– Some consumers get new and keep them.
Model HL
• Consumers utility per period is θq-p, with q is
quality and p price
• In second period, quality of car depreciates and
is between wl and wh, with wh < v and G(.) the
distribution of second-hand quality.
• Leasing contract i specifies pL(i), pk(i), leasing
price and option price of keeping car
• Buying is special case where pk(i) = 0
• Important: in second hand market, if seller is
owner, there is asymmetric info, otherwise not
Additional notation
• wu(i) is buyers’ belief about quality of the car
after lease contract i. Note that wu(i) < Ew
– Note that consumers are expected to observe the
type of leasing in primary market
• pu(i) is market price of used car after leasing
contract i
• Θy is the consumer such that there is a
fraction y of consumers with higher valuation
Benchmark: no quality uncertainty
• If quality in second-hand car market is w < v, then
there is no uncertainty in 2nd hand market
• always buy second hand yields discounted sum of
Vu(i,θ) = (θw –Pu) / (1-δ)
• Buy each period new yields discounted sum of
pay-off VL(i,θ) = (θv – Pn + δPu) / (1-δ)
• Note that as w < v, if θ buys new, then all θ’ > θ
do. Thus, three segments: upper y consumers buy
new, middle y segment buys used cars, lower
segment does not buy at all.
• Prices?
Possible choices consumers
• In a stationary equilibrium, consumers have two
options:
• always buy second hand from leasing contract i,
yielding instantaneous pay-off θwu(i) -Pu(i),
discounted sum of Vu(i) = (θwu(i) -Pu(i) ) / (1-δ)
• Take lease contract i and then keep iff you have a
relatively good quality (iff w > x(i,θ), where x is
some cut-off level), yielding, discounted sum of
pay-off VL(i,θ) = θv - PL(i) + δ( G(x(i,θ))VL(i, θ) + (1G(x(i,θ))) E(w given w > x(i,θ)) - Pk(i) + δVL(i,θ) )
Cut off decision x(i,θ)
• x(i,θ) is increasing in θ
• Intuition: people with higher valuation for quality, are
willing to pay higher prices for quality (and therefore
are willing to give up what they have more quickly if
quality is not high enough).
• Proof. θx(θ) + δVL(θ) = Pu + VL(θ) …….
• Three intervals in θ: low interval does not buy car at all,
middle interval buys second hand, highest interval
leases, with
– Within middle interval, higher θ’s buy higher expected
quality
– Within upper interval, higher θ’s lease with higher option
price
Equilibrium properties
• For two leasing contracts with Pk(i) > Pk(j),
– wu(i) > wu(j)
– G(x(i,θ)) > G(x(j,θ’)) for all θ and θ’ that decide to lease a
new car with contract i and j, respectively.
– Thus, both average quality and volume of sales after
contract i higher than after contract j
• Implications for leasing (Pk(i) > 0) vs. buying (Pk(j) = 0):
– average quality (thus higher prices) of off-lease cars is
higher than average quality after buying;
– Number of people who decide not to keep car is larger
after leasing than after buying
• Compare observations
Intuition for these properties
• Higher turn over and higher average quality stem
from higher cut-off value
• Menu of contracts segments market
– High valuation consumers want to drive every period
in new car, don’t care about option value
– Low valuation consumers care about option as they
seriously consider it: they prefer low option price (i.e.,
they buy) and only get rid of car if quality is really low
• After leasing (with high option value), average
quality is higher than after buying