Consider a simple model with 2 types: high (H) ability and low (L) ability. In t
ID: 1209052 • Letter: C
Question
Consider a simple model with 2 types: high (H) ability and low (L) ability. In this economy, those who do not go to college earn $10. Those who obtain 4 units of education (college) obtain W*. For H types, the cost of education is C_H = (1/2)U^2, where U is the number of education units obtained. For L types, the cost of education is C_L = U^2, where U is the number of education units obtained. A college education has no effect on the productivity of workers. 1. What is the lowest value that W* can be to make college worth it for H types? What is the lowest value that W* can be to make college worth it for L types? 2. Suppose W* = 20. Which type(s) get college educated? 3. A well-intentioned employer says, "since education has no effect on productivity, it is wasteful to make people go to 4 years of college. We can reduce the schooling requirement to 3 units and still pay W* = 20 to those workers. Thus, we will cut costs for those who go to college with no other repercussions." Evaluate this statement assuming all of the numbers provided above still hold and remembering our discussion from class.Explanation / Answer
1. Cost of 4 units of education for H = 0.5*4*4 = 8
Cost of 4 units of education for L = 4*4 = 16
Now a person without education recieves $10
So a H person will go for education if he recieves atleast 10+8 = $18
and a L person will go for education if he recieves atleast 10+16 = $26
2. If W* = 20 then only H type will go to college as W* is more than their minimum requirement
3. Cost of 4 units of education for H = 0.5*3*3 = 4.5
Cost of 4 units of education for L = 3*3 = 9
Now a person without education recieves $10
So a H person will go for education if he recieves atleast 10+4.5 = $14.5
and a L person will go for education if he recieves atleast 10+9 = $19
So as education is not improving productivity then we see that lowering the number of required units of education is beneficiary for both H and L type as they both can now go to college as W* is greater than minimum requirement.