Alchian and Demsetz (1972) established that a manager's reward is most efficient if tied to the residual created by the team under his direction. But it is often, if not usually, impossible to measure precisely a manager's contribution to firm output or income, y. Gibbons, citing Baker's work, notes that firms may try to find observable measures, pi, which may be imperfect but serviceable proxies for y. Suppose both y and a set of possible proxies, pi, are functions of two activities, a1 and a2 that are under the manager's control.1 Further, our initial research suggests that y ≈ za1 + za2. Which of the hypothetical weights of pi for the target incentive system w = s + bp, is likely most efficient from the principal's perspective?

a. p1 = a1 + 2a2

b. p2 = a1 + .5a2

c. p3 = 2a1 + a2

d. p4 = a1 + a2

e. None of the above pi values and weights can be reasonable proxies for y