Question

In: Economics

9-Suppose you currently make $10/hour in the informal rural sector. You could make twice that in...

9-Suppose you currently make $10/hour in the informal rural sector. You could make twice that in the formal urban sector. However, the unemployment rate in the formal urban sector is currently at 30%. Describe, using simple algebra, why it’s economically rational to migrate to the city in search of a formal urban job. What would the unemployment rate have to be in order for urban migration to not be a rational decision?

Expert Solution

9. It is given that the wage rate in informal sector is $10/hour. And wage rate in formal urban sector is $20/hour. However unemployment rate in formal urban sector is 30%.

This means that if a person were to migrate, he will be unemployed with a probability of 30% or 0.3. Hence the probability that he will be employed in the formal sector is = 1 - 0.3 = 0.7.

Therefore if he migrates, he will be employed and get $20 with probability 0.7. And he will be unemployed and get $0 with probability 0.3. Therefore his expected earnings after migration to formal urban sector is

=(p* wage if job) + (1 - p * wage if not job)

where p is the probability of getting a job in the formal sector

=> (0.7*20) + (0.3*0)

=> 14 + 0 = 0

Thus expected earning if the person migrates is $14. This is still greater than $10 if he stayed in the informal sector. Thus it will be optimal for the person to migrate into formal urban sector.

__________________________________________________________________________________________________

Now we have to find the rate of employment at which it is not rational to leave the informal sector for a job in the formal sector. That is we have to find the probability of the person becoming unemployed in the formal sector at which it is not optimal to leave the informal sector.

This means that the expected earning from the formal sector should be equal to or lower than the earning in informal sector.

=> Expected earning from formal sector < or = earning from informal sector

=> expected earning from formal sector < or = 10

=> P*20 + ((1-P)* 0) < or = 10

where P is the probability of getting employed in formal sector

=> 20*P <= 10

=> P <= 1/2 or 0.5

Thus if the probability of employment is equal to or lower than 0.5, this means that it is not rational to leave the informal sector. This means that the probability of unemployment should be higher than 0.5. Hence if the unemployment rate is equal to or higher than 50%, migration would not be rational.

Rahul Sunny answered 1 year ago

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