Hospitals are faced with decisions regarding pricing, when negotiating with priv
ID: 1208416 • Letter: H
Question
Hospitals are faced with decisions regarding pricing, when negotiating with private insurance payers. They use information about the demand curve they face to decide on prices, quantities, and to anticipate revenue and profits. Consider a hospital that has a demand curve given by P=180-4Q. Their total cost curve is given by TC=95+2Q.
a)Please write down the expression for MR (marginal revenue) and MC (marginal cost)
b)What will be the optimal P and Q? What will be their total revenue and their profits that result?
The answer for (a) is MR=180 - 8Q and MC= 2. I can not figure out how to solve for MC or how to get that answer. Please help!
Explanation / Answer
P=180-4Q.
TR = PxQ =180Q -4Q2.
MR = dTR /dQ =180 - 8Q.
TC=95+2Q
Mc = dTC / dQ => 2
Equilibrium, MR = MC
180 - 8Q. =2
Q = 22.25
P = 180 - (4 x 22.25)
= 91
TR = 91 x 22.25 => 2024.75
TC = 95 + 2x 22.25 => 139.5
Profit = TR - TC = 2024.75 - 139.5 => 1885.25
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