## Friday, October 19, 2012

### A Simple Example of How Adverse Selection can Lead to Multiple Equilibria

This came up when I was writing homework problems on adverse selection for a money and banking class and without intending to, wrote one that had 2 equilibria.

Take the market for used cars  a la Akerlof. There are 10 potential buyers and 12 potential sellers, 4 each  with cars of Low, Medium and High quality. Buyers reservation prices  are 15, 10 and 5 thousand dollars for High, Medium and Low quality, respectively.  Low Quality sellers need at least 3,  Medium sellers 7, and High sellers 11 thousand dollars. Quality is known to sellers but not to buyers, who know only the distribution.

There is an equilibrium at a price of \$7500, in which Medium and Low quality cars sell,  but no High quality. The expected value of  a  car for buyers is is \$7500. Excess demand is 2, but at a price above 7500, there is excess supply as no buyers are interested, since it will be above the expected value of \$7500. At prices above 11, the expected value of a car will be  \$10,000, so no deals will be made at such prices either.

Think about what happens as we drop the price below 7500. 10 buyers are interested and 8 sellers until we hit 7000. At that point , only low quality sellers will be selling, so the buyer reservation price drops to 5000, and we have no buyers therefore until we hit 5000. This is the second equilibrium: there is excess demand of 6 below and at this price, but excess supply of 4 just above it. Only low quality cars are for sale. This second equilibrium is Pareto-dominated by the higher-price equilibrium.

Now imagine that the sellers are workers, with reservation prices representing opportunity costs, and buyers are employers whose reservation prices represent productivity.  And that productivity is private information for the workers. Then we can get an interesting rationalization for a Card-Krueger positive relationship between employment and the minimum wage. The market suppose is in the \$5000 wage equilibrium:  imposing  a \$7500 minimum wage would put the market in the better equilibrium with higher employment.

With a little hand-waving and mutatis mutandis, it seems one could get a rationalization of anti-usury laws. Here the bad equilibrium would be the high interest rate equilibrium, with only the lowest quality borrowers wanting loans. Then an anti-usury law can produce the low interest rate equilibrium, where the average quality of borrowers is higher.

This is probably old hat to most, and to the extent that I haven't made glaring mistakes, the idea has I'.m sure been developed  with orders of magnitude more sophistication by others. When I google scholared "adverse selection and multiple equilibria" I get lots of hits, including what looks like a seminal paper by Charles Wilson which I printed out and plan to read right now.  But  sometimes simple examples can be helpful at isolating the way a mechanism works, so I thought I would pass this one along.

#### 1 comment:

city said...

thanks for sharing.