For the remainder of this problem, set = 0.

(a) Now suppose that the Medicare system switches to a prospective payment system. For our purposes, lets say that the prospective payment system compensates doctors by a fixed payment provided that x > x, where x is some level set by the Medicare administrators. That is, the prospective payment system gives doctors a fixed dollar amount per patient, but requires that doctors provide at least a certain amount of care.

i. If the Medicare prospective payment system wants doctors to provide precisely the optimal level of care, what will they set as x?

ii. Provided that Medicare wants doctors to care for all patients (and not send patients away), what should they set as ?

iii. Demonstrate mathematically how doctors have limited incentive to provide care beyond x.

iv. Show that the total health benefits under this system are actually slightly smaller than those for under retrospective payment.

(b) Now suppose that that there are two types of patients divided into two diagnosis related groups (DRGs). Some patients are serious cases (S), and the other patients are not so serious (N). The cost of care is as above. Suppose further that the Medicare system compensates doctors with N = 10 for xN 1; and S = 60 for xS 3.

i. Calculate a doctors profits for each type of patient.

ii. If doctors can re-label patients describe what will happen.

iii. How didDRG Creep undo some of the gains of prospective payments, both in this model and in reality?