Law and Economics assignment

Economics 348

Assignment 2: Contracts

Due: Friday February 13

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), where S'(e) > 0, S"(e) < 0. Sue's efforts cost C(e), where C'(e) > 0,

C"(e) > 0.

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).

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); i.e., whenever ε > S(e) – V.

2. Now suppose Fred and Sue have agreed to divide the amount Sue creates such that Sue gets

S(e)/2 and Fred gets S(e)/2. Sue will leave Fred and go to her alternative whenever it is in her

personal best interest to do so, i.e. whenever V + ε > S(e)/2. Derive the first order condition

that describes Sue's choice of effort. (Sue chooses e and whether or not to leave Fred. Fred

does not get to choose anything in this model.)

3. Using the information from Part 2, determine whether Sue will exert too much or too little

effort and whether she will be too likely to leave Fred or too likely to stay with Fred, relative to

the optimal outcomes in Part 1.

4. Suppose now that Fred and Sue can divide the amount Sue creates such that Sue gets αS(e)

and Fred gets (1 – α)S(e). Is there a value of α that will lead Sue to make the optimal choices?

Will Fred like this solution?