Consider a principal who wishes to hire an agent to work for them on a project. The project earns 750 if it is successful and 200 if it is not. The project is successful with probability 0.9 if the agent exerts high effort, and 0.5 if they exert low effort. The agent incurs a cost of 200 if they put in high effort, and 100 if low effort is exerted. Finally, the agent can choose to not work and would earn 50 in unemployment benefits from doing so. Assume that the agent will work hard if indifferent (i) between working hard and not working hard, and (ii) between working hard and not working.

Question:

In the case where effort is not observable, consider once again a wage contract (s,b) with salary s and bonus b conditional on the project being successful. Which of the following wage contracts would induce the agent to exert high effort?

(a) s = 150, b = 0

(b) s = 25, b = 250

(c) None of the options

(d) s = 0, b = 250

(e) s = 250, b = 0

Please show the calculation.