Signalling in Labour Markets

Question 1

What is Signalling?

Answer 1

Workers choose Education Levels BEFORE receiving Job Offer from the employer

Question 2

What is Utility of a worker?

Answer 2

Ui = w - ai y

Question 3

How do you show wages are an increasing function of y?

Answer 3

w = Ui + ai y

- Indifference Curve equation

Question 4

Which Type has Steeper I.C and why?

Answer 4

Low Type has Steeper I.C than High Type

- Due to higher cost of education - al > ah

Question 5

What does a steeper I.C mean?

Answer 5

Since Unit cost of Education is higher –> Need a bigger Increase in wages to compensate for acquiring given level. of education than the high types

Question 6

What is Equilibrium in Full Info?

Answer 6

Workers paid w = Marginal Product of I
Level of Education for both types = 0
Point D for High Type
Point C for Low Type
Education serves no useful purpose
Employers Break Even

Question 7

Why is {D, C} Equilibrium in Full Info?

Answer 7

Suppose Contract at A {h, yh ; 1, yl} for High Type
- Better Contract Found at Q - above I.C
– Q offers Lower Wage - But offset by Lower educational costs
=> Q generates Supernormal Profits
- Competition –> Wage increased to h and education cut to 0 (Point D)

Question 8

Under Asymmetric Info, when do we have a Perfect Bayesian Equilibrium?

Answer 8

When workers’ actions lead to Evidence consistent w/ Employers beliefs

Question 9

Given beliefs: worker w/ y > y* is High type w/ Prob. p and Low Type w/ Prob. (1 - p), what happens in Eq.?

Answer 9

Employers willing to pay Average wage wbar (Average Productivity of workers) for workers w/ y > y*
If y < yC - both types obtain education
Employers expect to Break Even - by hiring random sample
These beliefs produce PBE

Question 10

Is there a better pooling equilibrium than {wbar, y*}?

Answer 10

Better Eq. w/ wbar and less education
- Best Eq. wbar and No education
- 0 Education becomes Signal worker is High type w/ Prob. p and Low Type w/ Prob. (1 - p)
Consistent w/ PBE - any contract between 0 and yC gives PBE
Low type better off - High Type cross-subsidise

Question 11

For separating Eq. what is the Self-selection Constraint for High type?

Answer 11

Uh ( y = yl) ≥ Uh (y = 0)

Question 12

For separating Eq. what is the Self-selection Constraint for Low type?

Answer 12

Uh ( y = 0) ≥ Uh (y = yl)

Question 13

Given Beliefs: y ≥ yl is High Type + y < yl is Low Type, what is the Separating Eq.?

Answer 13

Low Type choose 0 Education + Low Wage (Point E)
High Type choose y = yl + High Wage (Point F)
Self-selection constraints are satisfied
Separating PBE

Question 14

Under Separating Contracts, when would only the High Type choose to educate?

Answer 14

When yl ≤ y ≤ yh

Question 15

What do we assume for Separating Eq. to hold?

Answer 15

Epsilon Altruism - Low Type Indifferent between {1, 0} and {h, yl} so choose {1, 0} to allow employer to break even

Question 16

How does Intuitive Criterion eliminate Pooling Eq.?

Answer 16

If worker deviates from Pooling Eq. - then it must be High Type –> employer is convinced they deserve High Wage
Therefore- there is always a Profitable Deviation for High Type so can’t be Equilibrium

Question 17

What separating contract survives Intuitive Criterion?

Answer 17

Least-cost Separating Equilibrium survives

- Least expenditure on education by High type + 0 Education by Low Type (E, F)