2 Quality Choice of Hospitals Suppose we have a hospital that is non-profit. Essentially, upon making choices, the hospital also cares about a "charitable component" when it comes to choosing its

quality level. Suppose this hospital has a profit function T= (PMC) D(Q) - FC(Q)+ NFP(Q) Where the hospital chooses quality Q. The number of consumers who visit the hospital is D(Q) - 2+ 4Q, which is a function of Q. The fixed cost of quality investment the hospital faces is FC(Q) = Q², which is a function of Q. The hos- pital receives payment P for treating one patient and faces marginal cost MC for treating one patient. Suppose P = 20 and MC = 8. The new component is NFP(Q), which is an increasing function of quality. Essentially, the hospital gets higher utility from offering higher quality as a "char- itable" component. a For now, suppose NFP(Q) = 0; that is, the hospital is a for-profit hospital. With P = 20 and MC = 8, what is the hospital's optimal level of quality? b Let us continue to assume that NFP(Q) = 0. Suppose a policy maker wants a quality outcome of Q* = 20. What should the policy maker choose P to be to achieve this outcome? c Now, suppose NFP(Q)= 4Q. With a payment of P = 20 and MC = 8, what is the optimal level of quality chosen by the hospital? How does this new optimal level of quality compare to the optimal level of quality found in the first question? Why is this new level of the hospital's quality higher or lower than in the first question? d Assuming NFP(Q) = 4Q, can a policy maker choose a payment level P that is less than 8, such that the hospital chooses an optimal level of quality that is greater than 0?