The Market for Lemons:The Good, the Bad and the Ugly

Questions to keep in mind: Does an informed player have a reason to signal her type to her opponent? Can the informed player do so credibly? Suppose the players are a buyer and a seller. The seller is one of two types: Either a cherry (good quality) or a lemon (bad quality). How are market price and availability affected by buyer uncertainty? Would buyers only be willing to pay for average quality? Would a willingness to pay only for average quality cause owners of higher quality goods to withhold their goods from the market? Will poor quality goods drive high quality goods from the market?

The Good and the Bad

Al Gleamer

Stu deBakerStu deBaker goes to Al Gleamer's used car lot in search of his first car. There are only two types of cars on the lot: cherries and lemons. Al knows which is which, but Stu cannot distinguish one from the other. If Stu buys a cherry then the cost of repairs and upkeep will be $200, but if he buys a lemon then the cost of repairs and upkeep will be $1700.

Stu values his first set of wheels at $3200 before accounting for repairs and upkeep. Thus his net valuation of a cherry is $3000 and his net valuation of the lemon is $1500. Al feels that a used car has an intrinsic value of $2700. A good car has a net value to Al of $2500 and a lemon has a net value to him of $1000. We can organize this information in Table 1.

Table 1

Valuation Repair CostNet

Valuation

Lemon

Buyer (Stu) 3200 1700 1500

Seller (Al) 2700 1700 1000

Cherry

Buyer 3200 200 3000

Seller 2700 200 2500

Irina

It would seem that there is room to trade. Suppose Irina bin Sandin is an accomplished auto body repair technician and mechanic. Since I. bin Sanden can affect repairs herself she is interested in buying a lemon for as much as $1500. If both she and Al can recognize a lemon for what it is then they will strike a deal between $1000 (his valuation) and $1500 (her valuation). Similarly, if Stu is only interested in a cherry and Al can present him with one truthfully, then they will strike a deal between $2500 (Al) and $3000 (Stu).

To see just where the opportunities for trade exist we will compute for the buyer and the seller the payoffs, G, from trade in lemons and cherries. First, organize the way in which the payoffs are to be computed in Table 2. The seller can offer a warranty on the car.

Table 2Buyer Seller

Lemon

Warranty

For p < 2700, G = 0 since the seller keeps the car when the price

is so low.

G = 3200-p for p 2700

For p < 2700, G = 1000 since the net value of holding onto the lemon is 1000

and no trade takes place.

G = p-repair for p 2700

No Warranty

G = 0 for p < 1000 since the seller keeps the car.

G = 3200-repair-p

G = 1000 for p<1000

G = price for p 1000

Cherry

Warranty

G = 0 for p<2700 since the seller keeps the car if he cannot get at

least 2700 for it.

G = 3200-p for p 2700

G = 2500 for p < 2700 since 2500 is the seller's net value from holding onto a

cherry.

G = p-repair for p 2700

No WarrantyG=0 for p<2500

G=3200-p-repair for p 2500

G = 2500 for p < 2600

G = p for p 2600

Now use the formulas to compute the actual payoffs and report the results in Table 3.

Table 3

Price

Lemon Cherry

Warranty No Warranty Warranty No Warranty

Buyer Seller Buyer Seller Buyer Seller Buyer Seller1000 0 1000 500 1000 0 2500 0 25001200 0 1000 300 1200 0 2500 0 25001400 0 1000 100 1400 0 2500 0 25001500 0 1000 0 1500 0 2500 0 25001600 0 1000 -100 1600 0 2500 0 25001800 0 1000 -300 1800 0 2500 0 25002000 0 1000 -500 2000 0 2500 0 25002200 0 1000 -700 2200 0 2500 0 25002400 0 1000 -900 2400 0 2500 0 25002500 0 1000 -1000 2500 0 2500 500 25002600 0 1000 -1100 2600 0 2500 400 26002700 500 1000 -1200 2700 500 2500 300 2700

2800 400 1100 -1300 2800 400 2600 200 28002900 300 1200 -1400 2900 300 2700 100 29003000 200 1300 -1500 3000 200 2800 0 30003100 100 1400 -1600 3100 100 2900 -100 31003200 0 1500 -1700 3200 0 3000 -200 3200

Consider the market for lemons with a warranty. If Stu offers to pay $2800 then the net value of the car to him is $400. The net value of the trade to Al is $1100. Indeed, there is non-negative net value to both of them at any price between $2700 and $3200. At a price below $2700 Al feels that he is better off hanging onto the car, so no trade takes place. When lemons are offered with no warranty there are opportunities for trade between a price of $1000 and 1500. Checking the table you can see that at a price of 1500 Stu is indifferent to the trade and Al values the trade at 1500, which is greater than his intrinsic value of the car.

Consider the market for Cherries with a warranty. Trades will take place between a price of $2700, where Al is indifferent to the trade, and 3200, where Stu is indifferent to the trade. When there is no warranty then trades will take place between $2500, when Al is indifferent, and $3000, where Stu is indifferent.

Let us now introduce the possibility that Stu cannot distinguish a lemon from a cherry. There are equal numbers of lemons and cherries on Al Gleamer's lot. The most Stu would knowingly pay for a lemon is his valuation of a lemon, $1500. And the most Stu would knowingly pay for a cherry is his valuation of a cherry, or $3000. If Stu picks a car

at random from Al's lot then 50% of the time he will get a lemon and 50% of the time he will get a

cherry. Therefore Stu will offer to pay for the randomly chosen car. But recall that Al can tell the difference between the cherry and the lemon. If Stu has picked out a lemon and offers $2250, Al will

accept the deal. But if Stu has picked out a cherry and offers $2250 then Al will decline the offer, since the cherry has a value of $2500 to him. By studying Table 3 Stu is able to discern this behavior and will never offer to pay

more than $1500 whenever lemons and cherries are in equal proportions on the lot. The lemons have driven the cherries out of the market when the buyer cannot distinguish the types of car.

Will this always be the case? Suppose that only 1/3 of the cars on Al's lot are lemons. Now the expected value to

Stu of a randomly chosen car is . If Stu happens to choose a lemon and offers $2500

then Al will accept the deal. When Stu happens to choose a cherry and offers $2500 then Al will be indifferent to

the deal. Indeed, whenever the proportion of lemons on the lot is less than 1/3 there will be some opportunity for

both cherries and lemons to be traded.

Now introduce warranties. Suppose that Al does not offer a warranty on a lemon, but he does sell the cherry with a

warranty. When Stu picks out a car and sees that it has no warranty he will offer $1000. If he picks out a car that

has a warranty with it then he will offer $2700. In both cases he is just offering the seller's reservation price.

Would Al ever offer a warranty on a lemon? If he warranted a lemon then he would receive $2700 for the car, since

Stu knows that this is the gross value to Al of a cherry. After paying for repair costs Al would net $1000 on the deal,

which is precisely what he would have gotten if he had sold the lemon without the warranty. Al has no incentive to

switch the signal on his lemons. He also would not remove the warranty from the cherry, since he would then have

to price the 'no warranty' cherry at $1000.

What has happened? We have a separating perfect Bayes equilibrium. By separating we mean that the prices

of the two types of car are different and the two prices depend on the signal. A pooling equilibrium would mean

that Al asks the same price for both types of car. The perfect Bayes part refers to the way in which Stu revises his

prior for the probability of selecting a lemon. Before seeing the warranty he believes that, say, 1/2 the cars lemons.

Once he sees the warranty affixed to the car he is able to revise his priors. The posterior probability is P(lemon|

warranty) = 0.

The Ugly Underbelly of the Market for Used Cars

Carr Ben-Daytonat work

To add some excitement to the game we will add elements of offer and counter offer. There is no warranty. Al will always sell a cherry for $2500. If the car is a lemon then he will offer to sell the car for $2500 with probability µ and

for $1000 with probability (1-µ). Half of Al's cars are lemons.

Stu has decided that he will reject any car with a price above $2500. He will accept a car priced at $2500 with probability q. He will always reject a car with $1500 < price < $2500. He will always accept a car priced at or

below $1500.

Stu believes that if a car is priced below $2500 then it is a lemon for sure. He also believes that cars priced at $2500 or more are lemons with probability ß and cherries with probability (1-ß).

What is the probability that a car is sold if it is a lemon?

1. We can use Al's pricing rule to express Stu's beliefs in terms of µ by using Bayes rule.

Stu says he believes P(lemon | price 2500) = ß. From Bayes rule we can write this as

P(lemon) = 1/2 since half the cars on the lot are lemons. Al's rule gives us the other part in the numerator. There are two ways that a car is sold for $2500 or more under Al's rule: All cherries are sold for $2500, and µ of the lemons are offered for $2500. So the denominator is P(lemon and price $2500) + P(cherry and price $2500) = P(price $2500|Lemon)P(Lemon)+1/2 = µ(1/2)+1/2. So

2. If Stu rejects a price of $2500 then his expected payoff is zero. If he accepts the price then his expected payoff is (3200-2500-200)(1-ß)+(3200-1700-2500)ß = 500-1500ß. Since Stu sometimes accepts and sometimes rejects an offer price of $2500, these two expected payoffs must be equal. Therefore 500-1500ß=0 and ß=1/3, which is the probability of a lemon given its price is $2500 or more.

3. We can use this result for ß to solve for µ, the probability that a car will be offered at a price of $2500 when it is a lemon.

4. If Al's car is a lemon and he offers it for $1000, then that is his expected payoff. If he offers the the car at a price

of $2500 then his expected payoff is 0(1-q)+2500q. Whenever Al has a lemon he offers it for $1000 sometimes and

for $2500 sometimes, so the two expected payoffs ought to be equal. 2500q = 1000, or q = 2/5.

5. This brings us back to the original question, what is the probability a car is sold if it is a lemon? A lemon will only

be sold if it has a price tag of $2500 on it. A car will be sold only if it has been offered by Al for a price of $2500

and only if Stu accepts it at a price of $2500. We can write the question as a probability statement.

Stu's accepting an offer is independent of Al's making an offer, therefore we can write

Making the necessary substitutions we find

or

By randomizing the prices of lemons, Al Gleamer is able to move 20% of them off the lot. Given the first part of this 'lecture' can you explain what has happened?

http://isc.temple.edu/economics/Econ_92/Game_Lectures/11th-Lemons/market_for_lemons.htm

In Brief

Imagine that owners of lemons are willing to sell for $1000 and owners of plums are willing to sell for $2000. Imagine that purchasers are willing to pay up to $1200 for a lemon and up to $2400 for a plum. Assume that sellers know what kind of car they have, but buyers can't tell. All buyers know is that half of all used cars are lemons. Therefore, based on the expected probability that a given car is a lemon, they will pay only up to $1800 for any car (1/2*1200 + 1/2*2400). But plum owners aren't willing to sell for only $1800, so only lemon owners will sell. The logical conclusion is that only the lemons will be sold, and the equilibrium price will be between $1000 and $1200. The mere presence of inferior goods destroys the market for quality goods (an externality problem) when information is imperfect. Plum owners need some way of signalling their car's quality.

Possible market solutions: warranties/guarantees (shared risk), iterated interaction (brand names, chains), certification (diplomas, JD Powers, credit reporting). Possible non-market solutions: government certification agencies (FDA), licensing.

To put this in terms of X and Y, asymmetric information (X) leads to adverse selection (Y).

Asymmetric information: The buyer and seller have unequal information about the vehicle's type. Adverse selection: The buyer risks buying a car that is not of the type he expects--e.g. buying a lemon when

he thinks he is buying a plum.

Basically, the "lemon principle" is that bad cars chase good ones out of the market. This is related to Gresham's law (bad money drives out good money through mechanism of exchange rates).

2008 was a year of sustained price deflation in the used car market. As our chart shows, the index of prices for second hand cars fell sharply and, in a

second illustration of the weakness of the market place, there was a huge fall in the proportion of original new car price retained. By December 2008 this

rate of depreciation had fallen to 33% for a car averaging 39 months and 42,100 miles - in other words, a new car lost two thirds of its original showroom

value within three and a half years.

Activity is strong in the motor auction halls as thousands of used cars come up for sale having been ditched by their owners. Some of these fire-sales are

the result of a slashing of spending on fleet cars by larger businesses including car rental companies. Others are attempts by motor finance companies to

claw back some of the bad debts that they have made with car buyers having reneged on their vehicle purchase loans. Negative equity in the car market

is becoming more frequent.

This article from the Telegraph explains the problem

“Buying a car is often a family’s biggest financial transaction apart from home purchase. Thousands of motorists try to spread the bill through a system

known as Personal Contract Purchase. This entails putting a deposit down and then paying monthly installments for two or three years, before having the

option to buy the car outright. The final payment – known as a balloon payment – is based on what the car is expected to be worth at the end of the

contract. But the collapse of the second hand market has meant that the amount demanded by finance companies is often far more than the car is

actually worth.”

A strong and active used car market is important for sellers of new vehicles because prospective buyers of a shiny new car want to know that the value of

their big-ticket purchase will not collapse like a deck of cards within a few months. But with wholesale and retail credit for financing car purchases much

harder and more expensive to maintain. And with unemployment on the rise and consumer confidence remaining exceptionally low, there is little chance

of a recovery in demand and prices for used cars during this year of recession.

http://www.tutor2u.net/blog/index.php/economics/comments/negative-equity-in-the-used-car-market

Washington DC March 23, 2009; The AIADA newsletter reported that economic uncertainty, tighter credit standards, and stronger warranties on nearly new vehicles are luring price-conscious, credit-squeezed consumers away from new cars and trucks to used ones.

According to the Detroit Free Press, last year, more than 13 percent of new car shoppers left dealerships with a certified used vehicle instead, up from 8.3 percent in 2003.

While new car sales are expected to decline to as low as 10.1 million this year, from dismal sales of 13.2 million in 2008, CNW Marketing Research is forecasting that used vehicle sales will grow through 2012. This year, the firm forecasts used car sales of 40 million, up 9.5 percent from 2008's weak volume of 36.5 million.

Already, 42 percent of dealers are reporting too little used vehicle inventory as a result of the trend, according to a March survey by Wachovia Securities analyst Rich Kwas. He added that was the highest level recorded in the past three years.

This is good news for dealers, who often will make a bigger profit on selling a 2- or 3-year-old car than on selling or leasing customers a new one.

http://www.theautochannel.com/fpmenu/usedcarbuyersguide.html