Question

Question 5 1 pts A principal hires an agent to work on a project. The agent can either work hard (H) or not (N). If the agent works hard the project succeeds with prob. 0.92 and fails otherwise. If the agent doesn't work hard, the project succeeds with prob. 0.75. Assume the cost of working hard is $150 and cost of not is zero. The principal will pay the agent $100 if the project fails. What is the least amount the principal needs to pay for project success in order to induce the agent to choose H? 0 $974 0 $983 0 $995 0 $999

Answer 1

When Net Income for the Agent will be same under both cases, he will be INDIFFERENT. That will be the MINIMUM amount that should be paid for project success.

Net Income by working hard = Net Income by NOT working hard

Expected Income - Cost = Expected Income - Cost

[Sum of (Inflow*Probability)] - Cost = [Sum of (Inflow*Probability)] - Cost

Let Amount Payable for SUCCESS be S

[(S*0.92)+(100*0.08)]-150 = [(S*0.75)+(100*0.25)]

0.92S+8-150 = 0.75S+25

0.92S-0.75S = 25+150-8

0.17S = 167

Therefore, Amount that should be paid for winning = S = 167/0.17 = $982.35 = $983

Cross Verification:

Net Income if work hard = (0.92*983)+(100*0.08)-150 = $762.36

Net Income if NOT work hard = (0.75*983)+(100*0.25) = $762.25