Question

1. Given the following demand function for a community hospital: P = 5000 – 0.5Q, where P is the price for hospital services, and Q is the quantity of hospital services per volume demanded. Its marginal cost function is P = 1000 + 1.5Q, where P is the marginal cost of producing hospital services, and Q is the quantity of hospital services provided. The hospital has an average total cost of $2000 per service provided.

A. Use the Twice As Steep Rule to form marginal revenue function.

B. If the community hospital is a for-profit hospital, what is the equilibrium price and quantity?

C.        If the community hospital is a not-for-profit hospital, what should be the price charged and quantity served?

Answer 1

A.P=5000-0.5Q

We know that P=AR

The twice as steep rule indicates that the slope of AR will be half the slope of MR but the intercept will remain the same or slope of MR=2*(Slope of AR).

Slope of MR=2*0.5=1

MR=5000-Q

B.If the hospital is maximising profits then it will set price such that MR=MC

MC=1000+1.5Q

At equilibrium

5000-Q=1000+1.5Q

2.5Q=4000

Q=1600

P=5000-0.5(1600)=4200

C.If the hospital is not for profit then its price will be set equal to MC

5000-0.5Q=1000+1.5Q

2Q=4000

Q=2000

P=5000-0.5(2000)=4000

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