15.Consider a two-hospital town with hospitals, unimaginatively named A and B. The hospitals are considering installing a new imaging machine to attract more patients. The population of the town is small enough that it really only needs one of these machines. Purchasing a machine costs $1,000.

If both hospitals install a machine, each earns $800 in revenue.

If only one hospital installs a machine, that hospital earns $1,800 in revenue. The other hospital loses $300 in revenue as patients switch to the other hospital.

If neither hospital installs a machine, then revenue does not change for either one.

(a)Consider hospital A's decision to buy one of these fancy new machines. A's profits will depend on what B decides to do. Suppose hospital B buys a machine. How much will A earn if it also decides to buy a machine? How much will A earn if it does not? What should A do if B buys a machine?

(b)Now consider A's optimal choice if B decides not to buy a machine. How much will A earn if it buys a machine? How much will A earn if it does not? What is A's best response if B does not buy a machine?