Question

Suppose there are two types of people, high ability and low ability. A high-ability person’s productivity is valued at wH = $100,000, while a low-ability person’s productivity is valued at wL = $50,000. Assume that the employer does not know the ability of a job applicant, but knows that the probability of an applicant being high ability is 50%. Assume next that only high ability applicants can send a signal, i.e., obtain a degree. The employer pays the expected wage.

i. What is the wage offer in a pooling equilibrium (no applicant attains a degree)?

ii. What is the wage offer in a separating equilibrium (only high-ability applicants attain a degree)?

iii. Suppose now both types can attain a degree, but it is costlier to attain for low-ability people and costs them cL = $60,000, while it costs high-ability people cH = $40,000. Is a separating equilibrium where only high-ability people send education as a signal possible? Explain.

Answer 1

a. In a pooling equilibrium, employer cannot distinguish between a high ability and low ability person. So, it offers a expected salary E(U)
probability of an applicant being high ability is 50%
E(U)=1/2*50,000+1/2*100,000
=$75,000

b. In a seperate equilibrium
high ability gets $100,000 and low ability gets $50,000

c. Yes, a seperating equilibrium is possible wherea person can send his educational qualifaction as a signal to the employer. A person with a higher degree sends high quality signals to the employer that he is more capable as he has spent more money and efforts for on attaining this degree.

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