Question

A number of utility-maximization models have been developed to describe the behavior of not-for-profit hospitals, generally assuming that the manager attempts to maximize his/her personal utility. Suppose the demand curve for hospital services is given by P= – Q + 300, and for simplicity assume constant MC=ATC=100.

a). Manager A currently is in charge of the hospital. Manager A likes to have a luxurious office and other perks, so his goal is to maximize profits, π, which due to the not-for-profit status of the hospital cannot be consumed directly, but can be later spent indirectly as discretionary spending. Please describe the relevant graph and calculate the optimal P, Q, and “π.”

Manager A retires, and Manager B comes on board. Manager B, a highly ethical TCNJ alum (a quality she honed at TCNJ), strives to improve the hospital’s image in the community in a sustainable way by having the hospital serve as many patients as possible without losing money.

b). What are in this case the optimal P, Q, and “π?”

c). It has come to Manager B’s attention that the quality of services provided in one of the hospital units is lacking, so Manager B has proposed to the Board (and the Board has approved!) investments in quality improvements, raising the ATC and MC by 50 units at any level of output. As a result of the improved quality of the hospital services provided, the demand for hospital services increases to P’= – Q + 320, What are now the optimal P, Q, and “π?”

Answer 1

P = -Q + 300

MR = 300 - 2Q

MC = 100

When the manager has to increase profits,

MR = MC

or 300 - 2Q = 100

or 2Q = 200

or Q = 100

P = -100 + 300 = 200

Profit π = (P - MC) * Q = (200 - 100) * 100 = 10,000

So the optimal Quantity is 100, The price is 200 and the Maximum profit is 10,000

b) When the objective is to serve the maximum people without losing money, it means that the hospital will keep on adding patients till the time the total price recovered by the hospital is equal to the Average Total Cost Incurred by the Hospital.

So in this condition,

P = ATC

or - Q + 300 = 100

or Q = 200

P = -200 + 300 = 100

Profit = (P - MC) * Q = (100 - 100) * 200 = 0

So in this case the optimal quantity will be 200, the optimal price will be 100 and the economic profit will be 0.

c) New Demand Curve is given as P’= – Q + 320

MC = ATC = 100 + 50 = 150

Since the Manager's objective is to still serve the maximum patients without losing money, so P’ = ATC

or – Q + 320 = 150

or Q = 170

P = ATC = 150

Profit = (P - MC) * Q = (150 - 150) * 170 = 0

So the optimal quantity now is 170, the optimal price is 150 and the economic profit is 0.

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