Assignment:
Question HW#4 (No need to solve this question, just get info to solve HW#5)
Suppose Pat manages a large computer software company and Allen is a talented program designer. Pat would like to hire Allen to develop a new software package. If Allen works for Pat, Allen must choose whether or not to expend high e?ort or low e?ort on the job. At the end of the work cycle (say, 1 year), Pat will learn whether the project is successful or not. A successful project yields revenue of 6 for the ?rm, whereas the revenue is 2 if the project is unsuccessful. Success depends on Allen's e?ort as well as on a random factor. If Allen expends high e?ort, then success will be achieved with probability 0.5; if Allen expends low e?ort, then the project is unsuccessful for sure. The cost of high e?ort for Allen is 1. Compensation can be contingent on the project outcome, but not Allen's e?ort. Allen's utility function is u(x) = xα (x should include net compensation; in other words, wage minus cost of e?ort). Assume Allen is risk averse (so 0 < α < 1) and Pat is risk neutral. Allen's reservation wage is 1.
Econ 6680: Homework #5
Due Monday, November 23
1. Recall Pat and Allen from Homework #4. All of the information is the same as before except now assume that Allen is risk neutral (in other words assume that α = 1). Given that they are both risk neutral, Pat decides to sell the firm to Allen.
(a) What is the lowest price that Pat would accept for the firm?
(b) What is the highest price that Allen would be willing to pay for the firm (taking into account the fact that Allen can earn 1 elsewhere)?
(c) Given these prices, does Allen buy the firm from Pat?
(d) Intuitively, why does it make sense for Pat to sell the firm to Allen?
2. A new promotions manager has just be hired into the firm where you work. The promotions manager asks for your opinion about how to structure promotions. What factors do you tell the promotions manager to consider when determining the promotion structure? You also can give the promotions manager an overall recommendation for promotions (such as a tournament or a standard). If the promotion structure will apply to your next promotion, will that influence your answer? Why or why not?