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Recent developments in the economics of information Maarten C.W. Janssen University of Vienna
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 wland wh, with wh< vand 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 (iffw > 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) + (1- G(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