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=180-9Q. Their total cost curve is given by TC=90+3Q.

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?

c) Please shade in and indicate on the graph the areas that represent the total revenue and the total costs at these optimal P and Q. (Indicate them clearly)

Answer 1

a) Expression for MR and MC------

#CALCULATING MR-------

P=180-9Q

TR=P*Q=180Q-9Q2

MR= derivative of TR

MR= 180-18Q

#CALCULATING MC-------

TC=90+3Q

MC= derivative of TC= 3

MC=3

b) OPTIMAL P&Q-----

optimal point occurs where MR=MC

180-18Q=3

177=18Q

Q=9.83 or 10 hospitals

putting this value in demand equation-----
P=180-9*10=$90
# TOTAL REVENUE and PROFIT--------

putting Q=10 in TR equation-----

TR=180(10)-9(10)2=$900
TC=90+3(10)=$120
profit=TR-TC

900-120=$780
c) GRAPHIC PRESENTATION OF TR-TC------

schedule----

Q TR TC

0 0 90

5 675 105

10 90 120

20 0 150