# 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.

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!

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)

seller gets \$p)

(buyer pays \$1150; seller gets \$1050)

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.

### 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.

By Chris Makler

# Copy of Econ 51 | 17 | Signaling and Lemons

Signaling and Lemons

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