QUESTION 6 [28 points] Chapter 6, Question 16 Medical arms race. 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. I If both hospitals install a machine, each earns $800 in revenue. 0 If only one hospital installs a machine, that hospital earns $1,800 in revenue. 0 The other hospital loses $300 in revenue as patients switch to the other hospital. a 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 prots 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