Moral Hazard in Teams Suppose there is a team with n agents. Team production function is given by y = F(e, θ) = θ Pn i=1 ei where θ = team productivity, λi = individual cost parameter and ei is the effort exerted by the agent i. Agents payoff is given by ui = mi- 1 2 λie 2 i (mi = monetary earnings).
(a) Suppose ei is observable. Find the first best level of effort and output for the team.
(b) Assume ei is not observable and each agent gets constant shares: si(y) = siy. How much effort will each agent exert as a function of their share?
(c) Find the optimal shares from a planner's perspective (who wants to maximize total surplus) in the presence of moral hazard. Compare this outcome to your answer in part (a) for a symmetric case.