2. (30 points) Alice and Bob are back at it for another Principal-Agent situation. Bob's learned...
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2. (30 points) Alice and Bob are back at it for another Principal-Agent situation. Bob's learned a little bit from his work for Alice and his cost function has changed. His new cost function if he exerts effort a is c(a) = a³. The output of the process is y and is formed via y = a + e where e is a mean zero random variable. As in class, Alice is restricted to a lincar wage contract, and we won't even worry about the possibility of a salary this time: w(y) = b.y. Bob's total expected payoff is TB (a) = E[w(y(a))]-c(a). Alice's expected payoff is TA = Ely - w(y)]. (a) (10 points) Find Bob's optimal level of effort given b. (b) (10 points) Given your answer to the previous question, find Alice's optimal bonus rate b. (c) (5 points) How does Bob's effort under the optimal wage contract compare to when his cost function is the one we used in class i.e. c(a)=a²? What explains this difference in cffort? Hint: Compare the two cost functions. (d) (5 points) Suppose that the change in Bob's cost function came at a cost. How much would Alice be willing to invest to change Bob's cost function from a² to a³? Hint: We know from class that if Alice can't set a negative base salary, her expected payoff is when Bob's cost function is a². 2. (30 points) Alice and Bob are back at it for another Principal-Agent situation. Bob's learned a little bit from his work for Alice and his cost function has changed. His new cost function if he exerts effort a is c(a) = a³. The output of the process is y and is formed via y = a + e where e is a mean zero random variable. As in class, Alice is restricted to a lincar wage contract, and we won't even worry about the possibility of a salary this time: w(y) = b.y. Bob's total expected payoff is TB (a) = E[w(y(a))]-c(a). Alice's expected payoff is TA = Ely - w(y)]. (a) (10 points) Find Bob's optimal level of effort given b. (b) (10 points) Given your answer to the previous question, find Alice's optimal bonus rate b. (c) (5 points) How does Bob's effort under the optimal wage contract compare to when his cost function is the one we used in class i.e. c(a)=a²? What explains this difference in cffort? Hint: Compare the two cost functions. (d) (5 points) Suppose that the change in Bob's cost function came at a cost. How much would Alice be willing to invest to change Bob's cost function from a² to a³? Hint: We know from class that if Alice can't set a negative base salary, her expected payoff is when Bob's cost function is a².
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Answer rating: 100% (QA)
a Bobs optimal level of effort can be found by maximizing his expected payoff function piBa Ewya ca Given wy by and y a epsilon we can express Bobs ex... View the full answer
Related Book For
International Marketing And Export Management
ISBN: 9781292016924
8th Edition
Authors: Gerald Albaum , Alexander Josiassen , Edwin Duerr
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