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. • 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. Suppose hospitals A and B shared an owner, who maximized joint profits rather than individual ones. What do you predict will happen
3. 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.
• 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. Suppose hospitals A and B shared an owner, who maximized joint profits rather than individual ones. What do you predict will happen?
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