Suppose that a business owner (Fred) has entered a contract with an employee (Sue) to work on a project that will happen at a particular future date. If Sue exerts effort e before this date the project will produce an amount S(e). Sue's efforts cost C(e).
After she has exerted her effort but before the project starts Sue will receive an offer to do something else with her time. Assume the value of this outside offer is given by V + ε, where ε has mean 0 and is distributed over the interval [a,b] according to f(ε).

Question

Suppose that a business owner (Fred) has entered a contract with an employee (Sue) to work on a project that will happen at a particular future date. If Sue exerts effort e before this date the project will produce an amount S(e). Sue's efforts cost C(e).
After she has exerted her effort but before the project starts Sue will receive an offer to do something else with her time. Assume the value of this outside offer is given by V + ε, where ε has mean 0 and is distributed over the interval [a,b] according to f(ε).

anonymous · Answer

1.	Set up and solve the planner's problem to determine the efficient level of effort. Note that Sue cannot do both things at once, and the planner will assign Sue to the alternative opportunity whenever V + ε > S(e).