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 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 education has no effect on the productivity of workers.

Note: In what follows, to keep things simple, assume that all costs and benefits are obtained in only 1 period, so that we won't have to worry about discounting.

 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 types 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.