In problems 9 and 10 above you have encountered numerical examples where private information in…
In problems 9 and 10 above you have encountered numerical examples where private information in the hands of a manager is or is not in the best interests of the firm. Sketch two corresponding institutional settings, one where the firm wants the manager to be informed and one where it does not. Is it possible a firm might want to exclude some information from the accounting library for strategic or control purposes?
(problems 9: Return to Example 17.5. Suppose no information is available, and the firm desires supply of input H. Determine an optimal pay-forperformance arrangement, and contrast it with the case where the information is privately obtained by the manager but not communicated. How much would the firm pay for the manager to observe the environment before acting? Does this amount depend on whether communication is feasible? Why?
((Example 17.5: Consider the setting in Table 17.6. Set cH = 3, 000 and the manager’s risk aversion measure at ρ = .0001 (along with the usual normalization of cL = M = 0). The information arrives just before the manager acts. Notice we have π(g) = π(b) = .50. Moreover, under y = b inputs L and H are equally productive, while input H is more productive under y = g. This suggests an input policy of H in the good (g) environment and L in the bad (b). Absent any contracting frictions, this would lead to an expected cost to the firm of .50cH + .50cL = 1,500. Now suppose this critical information is public. The optimal contract, denoted I ∗ xy in Table 17.6, leads to a risk premium of 28.42 (and overall expected cost to the firm of 1,528.42).10 Notice incentives are applied only in the good environment, where input H is desired. Contrast this with the case where the information is available (to guide the input choice), but is not used in the payment arrangement. This is contract I ∗ x which, due to its information diet, needlessly maintains strong incentives in the bad environment.
Conversely, suppose the manager privately observes the information. Not asking him to self-report results in the noted I ∗ x setting. Contract I ∗ xy (where we interpret the public information as the self-reported variable) implements the desired input and candid self-reporting by the manager. Relative to the public information story we again see less aggressive use of the information. We even see incentives are active in the bad environment, as the privately informed manager must be deterred from opportunistic reporting.11 Finally, and in sharp contrast, placing the private information in the hands of the firm returns us to the public information setting. You can readily verify that if the firm self-reports its private observation, in time for the manager to act thereon, it will gladly self-report with candor when the I ∗ xy contract is in place.
(Problem 10: Return to Table 17.7, and assume the manager is as specified in problem 4 above. Input H is desired, regardless of any information. Initially suppose no information is available, either publicly or privately. Determine and interpret an optimal pay-for-performance arrangement. (Assume the manager can post a large performance bond.) Next, suppose the g or b environment is privately revealed to the manager before acting; this revelation cannot be communicated to the firm. Determine and interpret an optimal pay-for-performance arrangement. How much would the firm pay to keep the manager from observing this information? Does the manager benefit from having the private information? Why?