Consider a worker who is paid a ?at rate w to perform a task. The worker gets to choose the amount of e?ort she exerts; the harder she works the more output she produces. In particular, her ?rm earns v for each unit of e?ort e the worker exerts. E?ort is costly for the worker, so she would like to avoid it; however, she also cares about the payo? to her ?rm because it’s a nice place to work and she believes in the work that she is going. Assume the worker’s utility function is the following, where π the payo? to the ?rm: u(e; w,v) = w –( θ/2)e^2 + σπ

Write π as a function of w,v and e.

What is the optimal amount of effort of each worker?

How is each parameter related to the optimal level of each worker?

Assume that σ depends on the amount the ?rm paid the worker such that δσ/δw (differential) > 0. If the firm increased w, would the worker exert more or less e?ort?

Assume that v and θ .Further assume that the ?rm can choose to pay the worker one of two amounts, either whigh or wlow . If the ?rm chooses whigh,,then σ.5.If the ?rm chooses wlow,then σ .

What work regime would the the worker prefer?

Which work regime would the firm prefer?