Consider a team of agents. Agent chooses effort 0 for = 1,2, ... , . There is no uncertainty and the total output = =1 . The cost of effort for agent is ( ) > 0. The effort levels are privately observed and chosen non-cooperatively.

(a) Show that with differentiable sharing rules () where () =1 = the first-best cannot be achieved.

(b) State the conditions that the second-best would satisfy in the situation (maintain the assumption of differentiable sharing rules () where () =1 = ). Show that the second best can always be sustained with a linear sharing rule.

(c) Suppose that = 2 and ( ) = 2 . Compute the second-best optimal sharing rules and the equilibrium effort levels. What is the net social surplus in the second best, and how does it compare with first best?