Department of Managerial Economics and Decision Sciences
Question 1:
Optimal Mark-Up You are the manager of a small pharmaceutical company that received a patent on a new drug three years ago. Despite strong sales ($250 million last year) and a low marginal cost of producing the product ($0.50 per pill), your company has yet to show a profit from selling the drug. This is, in part, due to the fact that the company spent $1.7 billion developing the drug and obtaining FDA approval. An economist has estimated that, at the current price of $1.50 per pill, the own price elasticity of demand for the drug is -2. Based on this information, what can you do to boost profits? Explain.
Question 2:
Revenue Management by a Coffee Company The Blue Mountain Coffee (BMC) is the only supplier of high-end Kona blend coffee for a mid-size regional market. BMC's demand curve is Q = 200 - 2P, where P is the price of the coffee (measured in cents) and Q is daily volume (measured in thousands of pounds per day). Variable production costs of coffee are mainly due to roasting and are given by 10c/pound. All the other costs of BMC are fixed. For now, you may assume that BMC has enough roasting capacity on hand to sell as much coffee as it wants, on a daily basis.
The Deliverables
Please complete each of the following tasks. While you do not need to show every step of algebra that you used to arrive at your answers, please show enough of your work so that I can figure out the logic that you used to arrive at your answer. Please keep your answer to three pages or less.
Task 1:
What is the equation of the marginal revenue (MR) curve of the BMC?
Task 2:
Find the profit-maximizing quantity of newspapers sold, and the profit-maximizing price.
Task 3:
Suppose, now, that given the size of its roasting plant, BMC can produce at most 50 thousand pounds per day. In light of this limit, what is the profit-maximizing quantity of coffee sold? What is the profit-maximizing price? What is marginal revenue at the profitmaximizing quantity? (the number, not the formula)
Task 4:
Continuing from Task 3, suppose, now, that BMC has the opportunity to rent additional roasting capacity from a company that owns a roasting facility. With this extra capacity, BMC would be able to produce as much coffee as it wanted to up to a limit of 85 thousand additional pounds per day (on top of the 50 thousand it can make in its current facility). The rental rate is 40 cents for each pound.
Please answer the following two questions. Assuming, as we have above, that BMC's goal is to maximize its profit, should it:
A. Rent some additional capacity?
B. Decline the offer to rent the additional capacity?
C. Neither: it needs more information to determine if this is a good deal.
What is the lowest rental rate at which it is not worthwhile for BMC to rent extra capacity?