Microeconomics 2: Adverse Selection, Signaling, and Screening
Microeconomics 2: Adverse Selection, Signaling, and Screening
Microeconomics 2: Adverse Selection, Signaling, and Screening
Microeconomics 2
44706 (1394-95 2nd term) - Group 2
Chapter 13:
Akerlof, “The Market for Lemons: Quality Uncertainty and the Market
Mechanism”, QJE (1970)
Accepts the contract if the wage offered is greater than or equal 𝑟(𝜃)
Aggregate surplus:
so 𝑤 ∗ = 𝐸𝑥𝑝[𝜃]
Not Pareto optimal: either too many workers are employed or too few
Suppose
𝑟(𝜃) ≤ 𝜃 ∀𝜃
𝑟 ′ (. ) > 0
Assume as before:
𝑟(𝜃) ≤ 𝜃 ∀𝜃 and 𝑟 ′ (. ) > 0
𝑓(𝜃) is the PDF associated with 𝜃 and 𝑓(𝜃) > 0 ∀𝜃
A second hand car dealer tries to send signals that the car is of good
quality;
In a market with low and high ability workers, workers might be able to
send signals regarding their ability;
In many countries, the potential tenants for rental houses; provide a
letter from the previous landlords;
Recommendation letters for getting admission
Each worker can obtain some education prior to entering the job market,
which has these properties:
Worker’s utility if she obtains the education level of 𝑒 and get wage of 𝑤:
𝑢(𝑤, 𝑒|𝜃 ) = 𝑤 − 𝑐 (𝑒, 𝜃)
2) Observing her type; the worker decides about her level of education
3) Observing the worker’s education, but not her type; (two) firms
simultaneously make wage offer
After observing e the firm assigns a probability µ(e) that the worker’s
type is 𝜃𝐻
𝜇(𝑒)𝜃𝐻 + �1 − 𝜇(𝑒)�𝜃𝐿
In any PBE, the simultaneous game of offering wages is very much like a
Bertrand competition setting; in which both firms offer a wage equal to
expected productivity.
Separating Eq.: Different types of the sender send different signals, then
are distinguishable by the receiver (eg. in our example low ability and high
ability workers acquire different levels of education)
Pooling Eq.: Different types of the sender send the same signal, then it is
impossible for the receiver to distinguish them from each other (eg. in our
example both types of workers acquire the same level of education)
In this case both types of workers get the same level of education, and
should receive the same wage:
𝑒 ∗ (𝜃𝐿 ) = 𝑒 ∗ (𝜃𝐻 ) = 𝑒̂
𝑤 ∗ (𝑒̂ ) = 𝜆𝜃𝐻 + (1 − 𝜆)𝜃𝐿
If the worker is indifferent between two offers chooses the one with the
lower t