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제목 없음.pngA econ question regarding the performance pay

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4. Absolute vs relative performance pay: You want to incentivize your sales manager
responsible for Los Angeles. His sales Z A : 6A + X A + XC depend on his effort 9A
(which he controls), the state of the LA economy X A and the state of the California
economy XC (both of which are random and out of his control)- You have a different
sales manager for Orange county whose perfOrmance Z 3 = e 3 + X B + XC depend on
the other manager’s effort 83 (which is efl'ectively known in equilibrium), the state of
the Orange county economy X B and X0 as for the LA manager. All random variables
X A, X B,Xc are independent. On t0p of the LA manager’s base wage to, you want
to reward him for his absolute sales Z A and/or his relative sales compared to Orange
county Z A — Z B- (a) Which of these two Options exposes the LA manager to less risk, and therefore
requires the lower risk premium? (b) Now you consider also combinations of absolute sales, and relative sales, i.e. 6ZA+
(1 — 6)(ZA — Z3). What level of 6 minimizes the risk to the LA manager? What
happens as X B is much more uncertain than Xg? Interpret your result.

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