2. You are the division manager of a large company which uses a participative budgeting process in which division managers submit budget request to corporate headquarters each month. Assume monthly revenues are $100,000. Both you and corporate headquarters know that monthly costs to operate your division can range between $65,000 and $90,000, with the following probabilities for each of the possible cost values: Cost Amount Probability $65,000 1% $70,000 6% $75,000 1% $80,000 1% $85,000 $90,000 1% 90% Before submitting your budget request, you will learn your division's actual costs for the month. However, corporate headquarters will only know there are six possible cost values, each with the probabilities listed in the table above. Corporate headquarters is considering whether to use a rationing policy, in which you will receive funds equal to your request only if your request is equal to or below some cutoff point, or a trust policy, in which you will receive all requested funds. Your payoff is equal to the resources you receive from HQ less the actual costs to operate your division. Assume you are trying to maximize your expected payoffs. HQ's payoff is equal to the revenues your division generates less the resources it sends you to operate your division. Assume HQ is also trying to maximize its expected payoffs. a. What policy (rationing or trust) maximizes HQ's expected payoffs? Show supporting calculations. b. Suppose HQ has installed an information system that refines the range of potential costs into two smaller subsets. Specifically, the information system will indicate (with certainty) whether the actual costs are in the subset {$65k, $70k, $75k} or {$80k, $85k, $90k}. Both you and HQ will know whether your division's actual costs are in one of these subsets before you submit your budget request. As before, however, you will know the actual cost, but HQ will not. For example, you might learn that the actual cost is $70,000, but HQ will only know that the actual cost is in the subset {$65k, $70k, $75k}. Importantly, assume the information system constrains how much you request in your budget. For example, if the actual cost is $65k- and the information system correctly indicates actual costs are in the subset {$65k, $70k, $75k} - then you can request a maximum of $75k, and not $90k. Assume HQ seeks to maximize its expected payoffs. What policy will HQ use in each subset? Show supporting calculations. c. As discussed in class, information asymmetry plays a crucial role in our analysis of participative budgeting. Conventional wisdom holds that reducing information asymmetry will improve productive efficiency. That is, total welfare should increase as information asymmetry decreases. Does conventional wisdom hold in this problem?