Adverse Selection The table below shows the minimum wages that 3 types of worker

Question

Adverse Selection

The table below shows the minimum wages that 3 types of workers: high skill (H), medium skill (M) and low skill (L), are willing to accept (reservation wages) and the value per hour they contribute to a firm. For example, a type H worker will work for the firm if offered wage rate $25/hour and will contribute value 40/hour to the firm. Assume there are an equal number of workers of each type.

Type

Reservation Wage

Value to Firm

H

25

40

M

20

16

L

10

13

The firm cannot tell which workers are which. It cannot identify, for example, which workers are type H workers. It also does not know what the reservation wages are. It does know the value of each type of worker to the firm.

Assume there are n workers of each type. Derive an expression for the deadweight loss arising from adverse selection in this example.

Type

Reservation Wage

Value to Firm

H

25

40

M

20

16

L

10

13

Explanation / Answer

So for n the benefit is 1.6 n for H

for n the benefit is 0.8 n for M

for n the benefit is 1.3 n for L

So for n the benefit margin is 0.6 n for H

for n the benefit is -0.2 n for M

for n the benefit is 0.3 n for L

If all are of H type, then the deadweight loss is = 0*H+0.8*M+ 0.3* L = 0.11 n (As H=L=M)

Type Reservation Wage Value to Firm Cost Benefit Benefit/Cost H 25 40 25n 40n 1.6 15 n M 20 16 20n 16n 0.8 -4 n L 10 13 10n 13n 1.3 3 n 18.33 23.00 55n 69n Loss If only H are selected By investing 55n 88 n 19 n

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