Charles is participating in an experiment. His payoff in the experiment is tied to his effort e doing a mundane task. There is also some risk involved by design-there is a chance p that Charles is going to get a fixed payment L regardless of his effort. Charles' payoff is thus: L with probability p w.e with probability 1-p Charles has to pay a cost C, which increases with his effort. First, let us assume that Charles'utility is the expected payoff net of this cost: U(e) = pl + (1 - pwe-cle) a. Derive the first order condition with respect to e. b. How does p affect Charles' effort e? How does L affecte? C