3. (12 points) There are two types of workers: low ability L and high ability H. The cost of obtaining a college degree is 40 for a type L worker and 20 for a type H worker. Suppose that the wage is 60 for workers without a college degree and w for workers with a college degree.

(a) What is the highest value of w for which type L workers do not obtain a college degree?

(b) What is the lowest value of w for which type H workers obtain a college degree?

4. (12 points) An economist seeks to calculate a differences-in-differences estimate for the effect of a training program on earnings. Workers are randomly assigned to a treatment group and a control group. Workers in the treatment group receive training, but workers in the control group do not. The training program takes place in 2005. The average wage of workers in the control group is 100 in 2004 and 200 in 2006. The average wage of workers in the treatment group is 110 in 2004 and 290 in 2006.

(a) What is the increase in the average wage for the control group between 2004 and 2006? What is the increase in the average wage for the treatment group between 2004 and 2006?

(b) What is the increase in the average wage for the treatment group minus the increase in the average wage for the control group?