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

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

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

i) Determine the optimal quantity to produce with the new technology and compute the profit of your business.

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?