1. You are a division manager who submits a budget to corporate headquarters (HQ) at the start of each month. After receiving your budget request, HQ sends you resources to operate your division. HQ's payoff is equal to the revenues your division generates less the resources HQ send you to operate your division. Assume HQ tries to maximize its expected payoff. Your payoff is the difference between what HQ sends you and the actual costs to operate your division. Assume you also try to maximize your expected payoff. When in operation, your division generates $100,000 in expected revenues each month. The costs of operating your division can be either $45,000 or $75,000. Suppose only you learn whether the actual costs to operate your division are $45,000 or $75,000; HQ knows only that the actual costs to operate your division can be one of these. HQ can implement either a trust policy, in which HQ sends whatever you ask for in the budget request, or a rationing policy, in which HQ sends $45,000 if you ask for $45,000 in the budget request, and $0 otherwise; under the rationing policy, HQ sends nothing if you ask for $75,000 in the budget request. a. When analyzing a very similar example in class, our analysis incorporated both the probability that the actual costs to operate the division are $45,000 (50%) and the probability that the actual costs are to operate the division are $75,000 (50%). What would the probability that the actual costs to operate the division are $75,000 need to be in order for HQ to be indifferent between using the trust policy and the rationing policy? b. Now suppose the division has two departments (business units). For each department, the actual cost to operate the department is either $45,000 or $75,000, and each are equally likely (50%). Also, each department, if open, generates $100,000 in revenues. Assume the two departments are independent, in that the actual costs to operate one department are either $45,000 or $75,000 (each equally likely) regardless of the actual costs to operate the other department, and vice versa. As the division manager, you learn the actual costs to operate each department before submitting a budget request. HQ's payoff is the generated revenues less the resources sent to the division manager to operate the division (any open departments). Your payoff is the resources from HQ less the actual costs to operate the division. Suppose HQ requires you to submit two budget requests, one for each department. For each budget request, HQ can use either a trust policy or a rationing policy. Under the trust policy, HQ sends whatever you ask for in each budget requests Under the rationing policy, HQ sends $45,000 if you ask for $45,000 in the budget request for that department, and S0 otherwise. Which policy does HQ prefer, and what is HQ's payoff under the preferred policy? c. Building on part b, now suppose HQ requires the division manager to submit one budget request that covers both departments. For the budget request, HQ can use either a trust policy or a rationing policy. Under the trust policy, HQ sends whatever you ask for in the budget request. Under the rationing policy, HQ will send $120,000 if you ask for $120,000 or less in the budget request, and SO otherwise Which policy does HQ prefer, and what is HQ's payoff under the preferred policy? d. When comparing your answers to parts b and c, does HQ prefer the division manager to submit two separate budget requests (one for each department), or submit one budget request that covers both departments? That is, is HQ's payoff bigger in part b or c? Why do you think this occurs?