Problem 1. 6.8 from Cabral: Sal’s satellite company broadcasts
TV to subscribers in LA and NY. Demand functions are
QNY=50-(1/3)PNY
QLA=80-(2/3)PLA
where Q is in thousands of subscriptions per year and P is the
subscription price per year.
The cost of providing Q units of service is given by
TC=1000+30Q,
where Q= QNY + QLA.
a) What are the profit-maximizing prices and quantities for the NY and LA markets?
b) As a consequence of a new satellite that the Pentagon developed, subscribers in LA are now able to get the NY broadcast and vice versa so Sal can charge only a single price. What is the profit-maximizing single price that he should charge?
c) In which situation is Sal better off? In terms of consumers’ surplus which situation do people in LA prefer and which do people in NY prefer? Why?
Problem 2. 6.10 from Cabral: SpokenWord: Your software company has just completed the first version of Spoken Word, a voice activated word processor. As marketing manager, you have to decide on the pricing of the new software.
You commissioned a study to determine the potential demand for SpokenWord. From this study, you know that there are essentially two market segments of equal size, professionals and students (one million each).
Professionals would be willing to pay up to $400 and students up to $100 for the full version of the software. A substantially scaled-down version of the software would be worth $50 to students and worthless to professionals.
It is equally costly to sell any version. In fact, other than the initial development costs, production costs are zero. Although you know there are two market segments, you cannot directly identify a consumer as belonging to a specific market segment.
(a) What are the optimal prices for each version of the software?
Suppose that, instead of the scaled-down version, the firm sells an intermediate version that is valued at $200 by professionals and $75 by students.
(b) What are the optimal prices for each version of the software? Is the firm better off by selling the intermediate version instead of the scaled-down version?