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When Julia is a risk-neutral owner of a firm that manufactures and sells a single product. She is considering hiring Willie to work at her firm as a sales manager. If Willie is hired and works hard at his job, then expected sales will be relatively high. But, if he is hired and does not work hard at his job, then expected sales will be relatively low.

Willie is risk-averse, and his utility function is U(w, e) = (w) e, where w is the compensation that Julia will pay Willie, and e = e_L = 0 if Willie is completely lazy, and e = e_H = 1 if Willie works very hard. If Willie is not hired by Julia, then he can start his own business and earn reservation utility of 3.

Julias utility function is U(x, w) = x w, where x = x_L = 0 is low sales, x = x_H = 100 is high sales, and w is the compensation Julia will pay Willie.

Assume both Julia and Willie try to maximize their respective expected utility functions. In addition, assume Willie will work for Julia if working for Julia generates the same expected utility as working elsewhere.

The following table captures how Willies effort affects sales (5 pts):

	Probability x = xL	Probability x = xH
e = eL	30%	70%
e = eH	10%	90%

1. Suppose Julia cannot observe Willies choice of e. What contract will Julia offer if she wants Willie to work for her and choose e_H?

2. Suppose Julia faces competition from Gulia for Willies services (Willie can only work for one of them). Gulia is a risk-neutral owner of a firm that manufactures a similar competing product to Julias. Suppose Gulias utility function is the same as Julias. Also, suppose sales levels (x_L and x_H) and the relationship between Willies choice of e and sales levels are the same in Gulias firm as they are in Julias firm. Finally, suppose whoever hires Willie can observe his choice of e. If both Julia and Gulia want to hire Willie and have him choose e_H, what contract will they offer Willie?

3. Now suppose Julia is (again) the only employer, but Willie is not the only worker in the labor market. Specifically, Lewis is another potential candidate for the sales manager position at Julias firm. Suppose Lewis is identical to Willie in every way. Finally, whoever Julia hires, she can observe his choice of e. If Julia can only hire one of them, what contract will Julia offer Willie and Lewis?

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