Question

Suppose someone offers to sell you a Bryce Harper autographed jersey for $1000. You think there is an 80% chance the jersey is authentic. If it is authentic, your friend who is a Phillies and Harper fan, will buy it for $3000. If your utility function is U = √W + 2000, what is the maximum you are willing to pay to get the jersey appraised?

Answer 1

There is 80% chance that it is authentic and hence there is 80% chance that he will sold it for 3000 and There is 20% chance that it is not authentic and hence he will get 0 for it.

Hence p = 0.8 and W = 3000 and q = 0.2 and W' = 0

Now his Expected Utility = pU(W) + qU(W') = 0.8*(W^1/2 + 2000) + 0.2*(W'^1/2 + 2000)

= 0.8(3000^1/2 + 2000) + 0.2(0^1/2 + 2000)

= 2043.82

Hence, Maximum amount he is willing to pay to get it be Z and is must be that amount such tht U(Z) must equal to utility derived above(i.e. 2043.82)

=> U(Z) = 2043.82

=> Z^1/2 + 2000 = 2043.82 => Z^1/2 = 2043.82- 2000

=> Z =1920.19.

Hence Maximum amount he is willing to pay to get the Jersey appraised is $1920(approx)