BUSINESS 412 – Compute the total revenue, the total cost, and the profit

Computational and
analytical questions
You must show and explain
your work

1.
You are the
manager of the surgery department at a hospital which serves mostly Medicare
patients. The hospital performs 1,000 surgical operations per year using the
traditional method. The Medicare payment for a surgical operation using the
traditional method is 2,250 dollars and the cost to the hospital per operation
is 1,750 dollars.

a)
Compute the total
revenue, the total cost, and the profit at the end of each year if the hospital
continues to use the traditional method for surgical operations.

b)
You have the
option to purchase a Robotic Surgery Machine to perform the surgical
operations. The Medicare payment for a surgical operation using the Robotic
Surgery Machine is 2,500 dollars and a surgical operation using a Robotic
Surgery Machine has a lower cost per operation of 1,500 dollars.

i)
Compute the total
revenue, the total cost, and the profit at the end of each year if the hospital
performs the surgical operations with the Robotic Surgery Machine.

ii)
For simplicity,
assume the life of the machine is three years. In addition, assume the machine
has a cost of 1,250,000 dollars and the opportunity cost of funds (interest
rate) is 10% per year. Should the hospital buy the machine?

2.
Assume the market
for a commodity is described by the demand and supply functions

Demand:

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Supply:

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a)
Determine the
equilibrium price and quantity in this market.

b)
Derive the
inverse demand and supply functions, draw a graph to illustrate your answer,
and compute the consumer surplus and the producer surplus.

3.
You are the
manager of a business in a competitive market and your production technology is
described by the total cost function

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In addition,
assume the market price is p = 15 dollars.

a)
Determine the
optimal quantity to produce and compute the profit of your business.

b)
Assume
you have the opportunity to make an investment which would improve your
production technology and would result in the new total cost function given by
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i)
Determine the
optimal quantity to produce with the new technology and compute the profit of
your business.

ii)
Assume the
business will operate for only one period, either with the old or the new
technology. If the cost of the investment to improve your technology is 300
dollars, should you make the investment?