You want to incentivize your sales manager responsible for Los Angeles. His sales Z₁ = e₁+ X₁ + Y depend on his effort e₁ (which he controls), the state of the LA economy X₁ and the state of the California economy Y (both of which are random and out of his control). You have a different sales manager for Orange county whose performance Z₂ = e₂ + X₂ + Y depend on the other manager's effort e₂ (which is effectively known in equilibrium), the state of the Orange county economy X₂ and Y as for the LA manager. All random variables X₁; X₂; Y are independent. On top of the LA manager's base wage "", you want to reward him for his absolute sales Z₁ and/or his relative sales compared to Orange county Z₁ - Z₂.

(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. Z₁ + (1 - )(Z₁ - Z₂). What level * minimizes the risk to the LA manager? What happens if X₂ is much more uncertain than Y? Interpret your result.