The Market for “Lemons�: Quality Uncertainty & the Market Mechanism Akerlof (QJE 1970) Presented by: Jay Li Feb. 2007
The Idea • This paper relates quality and uncertainty. • Buyers have incentive to sell inferior goods when the quality of goods is difficult to identify. • When the buyer is less informed about the quality than the seller, adverse selection may result.
Adverse Selection • The buyers, wary of being cheated by lemons, have lower willingness to pay for the goods than if they have full information. Meanwhile, with a lower price acceptable by the buyers, sellers of high quality good opt to quit, with only lemons left on the market, further shrinking the trade.
Market for Used Cars • The owners of a used car usually has better knowledge about the quality of the car than the buyer. • Because the buyer cannot tell the difference, bad cars and good cars have to be sold at the same price. • Good car owners are locked in while lemons stay on the market.
Formalize • Group 1 of traders have N cars with quality Xi ~ Uniform(0,2), income Y1 (including the proceeds from selling cars) and utility function
• Group 2 of traders have no cars, income Y2, and utility function
• M is numeraire with price set to 1.
Formalize • Both groups of traders are von NeumannMorgenstern utility maximizers. • The market demand and supply consist of demands and supplies from both groups. • The quality can be thought of as the underlying value of the car. The expected quality of the cars traded is denoted by mu.
Formalize • Writing the utility in indirect form n
V1 ( p, Y1 ) Y1 np xi Y1 np nE ( xi ) Y1 np n i 1
3 n 3 3 V2 ( p, Y2 ) Y2 np xi Y2 np nE ( xi ) Y2 np n 2 i 1 2 2
• Utility maximization for group 1 gives
• Utility maximization for group 2 gives
Formalize • The total demand is thus
Formalize • Group 1 supplies
• Average quality
• Only the cars with quality no more than p will be supplied, which have expected quality p/2. The proportion of cars that have quality no more than p is p/2, resulting in a total supply of pN/2. • Group 2 supplies 0.
Formalize • With average quality being p/2, at no price will any trade take place (D(p,u)=0 is the only scenario possible). • Lemons drive trade out entirely.
Another Perspective • In competitive equilibrium, to have positive demand, P=E[3/2x | x<=p]. • Group one would like to sell only if x<=p. • Group one is willing to buy a positive amount if the price paid equals the expected utility gain conditioning on group one would like to sell.
Another Perspective • That is,
3 p E[ x | x p ] 2 3 p xf ( x | x p )dx 2 0 3 p 1 x dx 2 0 p 3 p 4
• Equilibrium is achieved only when p=0 and thus no trade takes price.
If Information is Symmetric â&#x20AC;¢ Both groups have the same valuation of the cars.
If Information is Symmetric D=(Y1+Y2)/p
S=N=Y2
S=N=2/3Y2 D=Y2/p
0
1
3/2
p
If Information is Symmetric • Note there is a maximum utility gain of N/2 if the equilibrium is competitive (scenario (3)). • With asymmetric information, no trade takes place, U1+U2=Y1+Y2. • With symmetric information and competitive equilibrium (p=1), U1+U2=Y1+Y2+N/2.
Real World â&#x20AC;˘ Insurance â&#x20AC;&#x201C; People more than 65 years old can hardly buy medical insurance even if they are willing to pay a high price. Insurance companies know that with a high price, only those that are more likely to take advantage of the insurance will buy the policy. So policies are rarely sold on this particular market.
Real World • Cost of dishonesty – The presence of people who sell inferior goods tends to drive out the legitimate business. It is not only are the consumers cheated but also moral and legal concerns rise. – Expertise to tell the true value of undistinguishable goods is easily directed to arbitrage rather than real production purpose because the former is more profitable in a world full of lemons.
Real World • Credit market in underdeveloped countries – Entrepreneurs have to turn to “managing agencies”, people and companies with reputation and communal influence, for financing a newly started firm. – Rural credit market is dominated by loans with extortionate rates from local moneylenders rather than those with official rates from formal banks since only the former have good access to borrower’s information. Anyone who try to arbitrage tends to lose.
Real World • Counteracting institutions – Warrantees for durable goods – Brand-name goods and chains – Licensing practices – All aim to reduce information asymmetry