I have a question about Angrist and Guryan’s model of the effects of teacher credentialing on teacher quality.

I have a question about Angrist and Guryan’s model of the effects of teacher credentialing on teacher quality. I need to find the average productivity of teachers under each of the following regimes, assuming that teachers receive w=30 and the potential teacher productivity w_i is distributed uniformly on the interval [0,40]http://economics.mit.edu/files/2202 <—See page 4 for utility equation1. Teaching credentials may be obtained at no cost by anyone2. People must take a test, which costs c=10 to become a teacher, and they pass the test if w_i>53. People must take a test which costs c=10, to become a teacher, but everyone passes the test4. People must take a test, which costs c=10, to become a teacher, and they pass with a probability w_i/40