Signaling and Lemons
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Today's Agenda
Part 1: Job Market Signaling
Part 2: The Market for "Lemons"
Big Idea
One agent has information about the game that the other agent lacks.
The central problem here is how to credibly signal information;
absent that ability, there can be an adverse selection problem.
Job Market Signaling
Job Market Signaling (Spence, 1973)
There are two types of workers: "high-ability" and "low-ability."
High-ability workers
are worth \(y_H\) to a firm
Low-ability workers
are worth \(y_L\) to a firm
Assume both firms and high-ability workers would be better off if firms could observe their ability.
Need some mechanism to create a separating equilibrium.
![](https://s3.amazonaws.com/media-p.slid.es/uploads/560495/images/4669374/photo-ann-dean-message-daca_1.jpg)
![](https://s3.amazonaws.com/media-p.slid.es/uploads/560495/images/6189270/FIG01.01_STRATEGY3_CH29.jpg)
Workers are of two types: 1/3 are high ability and 2/3 are low ability.
They can choose to get an education (E) or not (N)
The high type incurs a cost of education of 4; the low type incurs a cost of 7.
Firms observe the education -- but not the type of the worker
-- and choose to put them into a management job or a clerical job.
A high-ability worker in a management job is worth 10 to the firm;
a low-ability worker in a management job is worth 0 to the firm.
Either type is worth 4 in a clerical job.
The management job is worth 10 to either type of worker;
a clerical job is worth 4 to either type of worker.
Is there a separating equilibrium?
Is there a pooling equilibrium?
The Market for Lemons
The Market for Lemons (Akerlof, QJE 1970)
There are two types of used cars: "lemons" and "plums."
Assume there are equal numbers of each car.
"Plums" are worth
$2000 to a seller
and $2400 to a buyer.
"Lemons" are worth
$1000 to a seller
and $1200 to a buyer.
If the quality of a car is observable to a buyer, what will happen?
If the quality of a car is not observable to a buyer, and all cars are on the market, what is the expected value to a buyer from buying a random car?
If that is the most buyers are willing to spend, which cars will be offered for sale?
Both types will be sold.
$1800
Only lemons!
![](https://s3.amazonaws.com/media-p.slid.es/uploads/560495/images/4669386/1991miata.jpg)
![](https://s3.amazonaws.com/media-p.slid.es/uploads/560495/images/4669388/miata.jpg)
How can we solve this problem?
Convert to a separating equilibrium in which sellers
credibly reveal the type of car they're selling.
Suppose the seller could pay $100 to get their car quality certified.
Assume that if the car is certified, it's sold for $50 less than the buyer value: \(p_P = 2350, p_L = 1150\). If a car isn't certified, its price is \(p\).
(buyer pays $2350; seller gets $2250)
(buyer pays $p;
seller gets $p)
(buyer pays $1150; seller gets $1050)
(buyer pays $p;
seller gets $p)
Could \(p\) be high enough to get sellers of plums to not certify their cars?
No.
Is it ever worth it for sellers of lemons to certify their cars?
No.
![](https://s3.amazonaws.com/media-p.slid.es/uploads/560495/images/5837006/Screen_Shot_2019-02-28_at_10.34.53_AM.png)
The market for lemons: separating equilibria
Without certification possibility
With $100 certification
Sellers of plums don't put their cars on the market; sellers of lemons do.
Buyers believe any car for sale is a lemon
Price of any car is $1150;
only lemons sell.
Sellers of plums pay to get their car certified; sellers of lemons don't.
Buyers believe any car that isn't certified is a lemon.
Price of a certified-plum car is $2150, price of a lemon is $1150. All cars sell.
Copy of Econ 51 | 17 | Signaling and Lemons
By Chris Makler
Copy of Econ 51 | 17 | Signaling and Lemons
Signaling and Lemons
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