Suppose a student athlete has two options: Play football for the Ohio State University or play football for the University of Michigan. The athlete anticipates that if he stays healthy he will play in the NFL and his salary will be $1,700,000 if he attends OSU and $1,250,000 if he attends UM. If he does not make it to the NFL, the athlete anticipates his salary will be $85,000 per year if he attends UM and $65,000 if he attends OSU. Finally, the student anticipates the odds of a career-ending injury at UM are 15% whereas at OSU the odds are 6%. Given this information, which school will the student attend, all else equal? Show all of your calculations which lead to your answer.
Congratulations to Xiaotian (Eric) Ma for being the first to figure out this week's question. In making the decision over which college to attend, a simple decision rule might be to choose the college that, on average, provides the higher expected income. The probability of injury will govern the likelihood that the young athlete will ever play professionally or settle for a regular career with his bachelor's degree.
Thus, the expected value of attending each college can be calculated as:
EV(OSU) = (0.94)($1,700,000) + (0.06)($65,000) = $1,601,900
EV(UM) = (0.85)($1,250,000) + (0.15)($85,000) = $1,075,250
As Eric points out, OSU provides the young athlete with the better income potential.