The city of Braavos has population 10,000, and none of its citizens has health insurance. The Iron Bank (IB) sees an opportunity to expand operations into the health-care business. Currently, the citizens' an- nual health care costs are uniformly distributed between 0 and $10,000. Each citizen's cost of care is known to them, and is the same every year, but is private. IB could care for any consumer at lower cost; an indi- vidual whose care currently costs c can be provided the same care by IB for only .8c. The market will work as follows: IB chooses a price p and will offer full care for the next year to anyone who signs up at this price. Citizens know their own cost c and sign up if p < c. (a) For a given price p, how many customers will sign up? (b) What will the average c be for these customers, and what will IB's average cost and total costs be? (c) What is IB's profit as a function of p, and what is the profit- maximizing p