Monday, January 21, 2008

A Separating Equilibrium?

Frodo, a local auto dealership, wants to hire a salesperson. Automobiles are sold for $20,000 each. A good salesperson can sell 8 autos a month, and a bad salesperson can sell only 1. Salespeople at Frodo earn a base salary of $1000 each month plus a commission per auto sold. If we assume that good salespeople can earn $5000 a month at another job and bad salespeople can earn $2000 a month at another job, in what range must the commission percentage fall if Frodo wishes to hire only good salespeople and it can't tell good from bad salespeople during the initial interview? Show your work.

Congratulations to Tiffany McKee on being the first to submit a correct answer. Read Tiffany's answer in the comment below.

The notion of a separating equilibrium is part of a larger literature on the economics of signalling. Signalling becomes particularly important in economic situations involving asymmetric information (i.e., when one person has more information than another.) In the case above, Frodo is not quite sure which type of salesperson he's interviewing. However, by carefully setting the commission rate, Frodo is able to get the job candidates to "reveal" their true identity during the hiring process.

1 comment:

tikee06 said...

The good salespeople sell 8 cars per month and make $4,000.00 in commission ($5,000.00-$1,000.00). The bad salespeople sell 1 car per month and make $1,000.00 commission ($2,000.00-$1,000.00).
Divide the total made in commission by the number of cars sold to find commission made per car.
$4,000.00/8=$500.00
$1,000.00/1=$1000.00
Then divide amount made in commission per car by the total the cars sell for which is $20,000.00 to find the percentage of commission made.
$500.00/$20,000.00=0.025=2.5%
$1000.00/$20,000.00=0.05=5%
So the good salespeople make a commission of 2.5% and the bad salespeople make a commission of 5%. So, if Frodo wanted to hire only good salespeople the commission percentage would fall between 2.5% and 5%.

Tiffany McKee