Firm A wants to hire Mary. Mary's utility function is given by U(w, e) = w...

  

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Firm A wants to hire Mary. Mary's utility function is given by U(w, e) = √w - e², where w is the wage and e is effort. Mary is currently working for another firm where she enjoys U(w, e) = 140 and she would be willing to switch jobs if offered the same level of utility. 1. If Mary exerts no effort (e = 0), her sales at the new job would be 100 000 with 0.7 probability but only 1 000 with 0.3 probability. In this case, what fixed wage does firm A need to offer her to get her to accept changing jobs? 2. Suppose firm A offers instead a fixed payment of F plus a 10% commission on any sales she makes. How much does F need to be for Mary to be indifferent between the two alternative payment schemes? (Assuming she behaves according to the expected utility model). Firm A wants to hire Mary. Mary's utility function is given by U(w, e) = √w - e², where w is the wage and e is effort. Mary is currently working for another firm where she enjoys U(w, e) = 140 and she would be willing to switch jobs if offered the same level of utility. 1. If Mary exerts no effort (e = 0), her sales at the new job would be 100 000 with 0.7 probability but only 1 000 with 0.3 probability. In this case, what fixed wage does firm A need to offer her to get her to accept changing jobs? 2. Suppose firm A offers instead a fixed payment of F plus a 10% commission on any sales she makes. How much does F need to be for Mary to be indifferent between the two alternative payment schemes? (Assuming she behaves according to the expected utility model).

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