Question

Describe the first best equilibrium in the signaling model

Answer 1

WHAT IS SIGNALLING ?

Signalling is the idea that one party conveys information about itself to the other party. One party send a signal that would reveal some piece of relevant information to the other party.

BASELINE SIGNALING MODEL

Explained by an illustration~

• There are two types of workers, high ability and low ability.
• high ability workers is denoted by  λ.
• Employees do not observe that workers have their own ability too.
• High ability workers and low ability workers will always produce yH and yL respectively.
• Workers can invest in education, is denoted by  e { 0,1}
• The cost of obtaining education for high ability workers and low ability workers cH and cL respectively
• Crucial assumption (cL > cH)

Here it is seen that education is more costly for low ability workers. It is often called as  singal crossing assumption, as it makes sure that in the space of education and wages, the indifference curves of high and low types intersect only once.

For future reference, denote the decision to obtain education by e=1

First best equilibrium in singaling model is SEPERATING EQUILIBRIUM-

In Seperating equilirium, Different levels of schooling is chosen by high and low ability workers.

Now assume that,

yH - cH > yL > yH - cL

It is clearly possible since cH < cL.

Here equilibrium is  all high ability workers obtain education, and all low ability workers choose no education.

Wages are ~ w (e = 1) = yH and w (e = 0) = yL

Now worker with education has
productivity and worker with no education has productivity yH and yL respectively.
So no firm can increase its profit neither it would like to change its behaviour.

• Now high ability worker deviates to no education, he will obtain

w (e = 0) = yL, but
w (e = 1) - cH = yH - cH > yL

• low ability worker deviates to obtaining education, the market will perceive him as a high ability worker, and pay him the higher wage
  w (e = 1) = yH . But from (2), we have that
  yH - cL< yL

Therefore it is clearly seen that we need equilibrium.

PLEASE GIVE YOUR VALUABLE REVIEWS ABOUT THE ANSWER IN THE COMMENT BOX AND YOU CAN ALSO GIVE THUMBS UP IF YOU LIKE THE ANSWER.

THANK YOU.