Suppose Mary is a worker and she can choose to exert high effort or low effort. Mary's individual costs and the probability of success

depends on Mary's effort level in the following way:

Effort Level || Mary's Cost Prob. of Success || Prob. of Failure

High 100 0.8 0.2

Low 10 0.5 0.5

Suppose Jack is Mary's immediate supervisor. Jack can choose a payment wG, perhaps in terms of bonus or promotion, if she sees the succeeds, and another payment wB, perhaps in terms of reduced pay or demotion, if she sees the fails.

(a) (5 pts) Express Mary's expected payoffs for both effort levels in terms of wG and wB.

(b) (5 pts) If Jack wants to induce high efforts from Mary, what does wG and wB need to satisfy?

(c) (5 pts) Suppose now the probability of success under high effort is only 0.6. How does your answers in parts (a) and (b) change?