An economy has 2 types of workers: high quality workers and low quality ones. Th

ID: 1098825 • Letter: A

Question

An economy has 2 types of workers: high quality workers and low quality

ones. There are 20 of the ?rst type and 30 of the latter. Their respective

marginal productivity are 15 and 8.

(a) What would be the expected salary in this economy if ?rms cannot

di?erentiate between them?

A formation is available. Firms will consider workers to be of high quality

if they take it. Who will take the class if the cost is:

(b) 3 for high quality workers and 4 for low quality ones?

(d) 4 for high quality workers and 5 for low quality ones?

(a) Firms don't know the quality of the worker, so they will assume that

a worker is high quality with probability = 20/50 = 0.4 and

a worker is low quality with probability = 30/50 = 0.6

Expected salary = Expected productivity

= (Probability that a worker is high quality * Productivity of high quality worker) +

(Probability that a worker is low quality * Productivity of low quality worker)

= 0.4*15 + 0.6*8 = 6 + 4.8 = 10.8

(b) If the workers take the class they are considered high quality, else not.

Pay-off of high quality worker who takes class = Salary high quality - Cost = 15 - 3 = 12

Pay-off of high quality worker who does not takes class = Salary low quality = 8

Hence, high quality will take the class (12 > 8).

Pay-off of low quality worker who takes class = Salary high quality - Cost = 15 - 4 = 11

Pay-off of low quality worker who does not takes class = Salary low quality = 8

Hence, low quality will take the class (11 > 8).

Pay-off of high quality worker who takes class = Salary high quality - Cost = 15 - 6 = 9

Pay-off of high quality worker who does not takes class = Salary low quality = 8

Hence, high quality will take the class (9 > 8).

Pay-off of low quality worker who takes class = Salary high quality - Cost = 15 - 7 = 8

Pay-off of low quality worker who does not takes class = Salary low quality = 8

Hence, low quality may take or not take the class (8 = 8).

(d) If the workers take the class they are considered high quality, else not.

Pay-off of high quality worker who takes class = Salary high quality - Cost = 15 - 4 = 11

Pay-off of high quality worker who does not takes class = Salary low quality = 8

Hence, high quality will take the class (11 > 8).

Pay-off of low quality worker who takes class = Salary high quality - Cost = 15 - 5 = 10

Pay-off of low quality worker who does not takes class = Salary low quality = 8

Hence, low quality will take the class (10 > 8).

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