Jazzman's Caf hires Lucy as manager. The caf's profit function is = 5 + , where is Lucy's effort and is a random variable with expected value () = 0. The owner of the caf sets a wage function = + according to which Lucy will be paid. Lucy's expected utility is given by = () 50 2 0.5 2 , and her reservation utility is 0. a. If the commission rate is 20%, how much effort will Lucy supply? How much expected wage does she need to receive in order to achieve her reservation utility? What will be the caf owner's expected residual profit? b. Suppose the commission rate is 30%. Redo part (a).