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. HQs 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.

1. 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?