You attempt to hire Fred to work on a project that will yield $700 in revenue if

Question

You attempt to hire Fred to work on a project that will yield $700 in revenue if it succeeds and $100 if it fails. If Fred exerts great effort, his opportunity cost of working is $210. If Fred works little effort, his opportunity cost of working is $150. If Fred exerts great effort, the project will succeed with probability 0.6. If Fred exerts little effort, the project will succeed with probability 0.3. You must design a contract for Fred such that Fred gets paid “x” if the project succeeds and “y” if the project fails, so that Fred takes the contract and gives great effort.

(a) Calculate Fred’s expected value of giving great effort in terms of “x” and “y.” Make sure to include the cost of Fred’s effort in your answer.

(b) Now, calculate Fred’s expected value of giving little effort in terms of “x” and “y.” Again, make sure to include the cost of Fred’s effort in your answer.

(c) If Fred takes the contract, it must induce Fred to give great effort instead of little effort. Given this information, what is the minimum value of “x y”?

(d) You must now convince Fred that taking the contract is better than not taking the contract. (The expected value to Fred of not taking the contract is zero.) Determine the values of “x” and “y” that would make Fred indifferent between taking the job and giving great effort, taking the job and giving little effort, and not taking the job at all.

Explanation / Answer

a) EV= 0.6x + 0.4y - 210

b) EV= 0.3x + 0.7y - 150

c) 0.6x + 0.4y - 210 >= 0.3x + 0.7y - 150

or 0.3x - 0.3 y >= 210-150

or x-y >= 200

So x-y (minimum) = 200

d) For taking job and giving great effort

EV = 0.6x +0.4y-210

For taking job and giving little effort

EV= 0.3x+0.7y-150

For not taking job

EV = 0

Equating all three EV's

0.6x+0.4y-210 = 0.3x+0.4y -150= 0

Solving the equations ,we get

x-y =200 and

9x+11y =3600

so x =290 and y = 90

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