Your friend Tenfour Goodbuddy is an independent trucker whose truck is empty after his most recent haul. He has found a deal to take a load to Birmingham, with a return load included, for a total of $3000. Another deal would give him a load to Charlotte for $2500. Tenfour thinks there's a 50-50 chance of finding a $2500 return load from Charlotte. Otherwise he must return empty, with no revenue. Assume that the cost of a round trip to either city is the same, and that he sees no other loads presently available.
 
 

Tenfour has a twin brother Bubba Goodbuddy.  Sometimes one of the brothers will sell an opportunity to another.  If they both have the same utility function
u(X) =sqrt((x-(-5000))/(5000-(-5000))
CME(u)=-5000+(5000-(-5000)*u2
What is the least Tenfour would accept to sell his opportunity?
What is the most Bubba would pay to acquire this opportunity?

Suppose, instead, they both thad an exponential utility function,
u(X)=1.3069*(1-exp{-0.000144879*[X-(-5000)]})
CME(u)=-ln({1.3069-u}/1.3069)/0.000144879+(-5000)
Using this utility function,
What is the least Tenfour would accept to sell his opportunity?
What is the most Bubba would pay to acquire this opportunity?

 Solution