Tuesday, November 3, 2009

Buckeyes or Wolverines?

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.

2 comments:

Xiaotian said...

For the OSU,
salary=1,700,000*0.94+65,000*0.06
=1,601,900

For the UW,
salary=1,250,000*0.85+85,000*0.15
=1,075,250

Based on the above, the student should attend the OSU, for 1,601,900 is more than 1,075,250

Molly said...

Hello, Dr. Delemeester.
This is Qi Wu. In point of view, this student will choose the UM, if all else constantly.
From the midpoint method, I guess that if the absolutely value of elastic is higher, changes will be easier.
In OSU
% change in price= 2*($17,000,000-$65,000)/($17,000,000+$65,000) =1.8527

In UM
% change in price= 2*($1,250,000-$85,000)/($1,250,000+$85,000) =1.8023

From these calculations, we can know the student is willing to go to the UM.

Furthermore, as it offered, the odds of a career-ending injury at UM are higher that OSU.
So ,I guess that the student will attend in the UM.
Thank you very much.

Qi Wu