Managerial Economics & Organizational Architecture 5th Edition by James Brickley, Jerold Zimmerman, Clifford Smith

تمرين 35

Personal video recorders (PVRs) are digital video recorders used to record and replay television programs received from cable, satellite, or local broadcasts. But unlike VCRs, which they replace, PVRs offer many more functions, notably the ability to record up to 80 hours of programs and easy programming. A PVR consists of an internal hard disk and microprocessor. After the owner installs the hardware, the PVR downloads all upcoming TV schedules to the hardware via a phone or cable connection. Users merely enter the name of the show(s) they want recorded and the system finds the time and channel of the show and automatically records it. Users must subscribe to a cable or satellite system if they wish to record programs off these channels.
Besides ease of programming and much larger recording capacity than videotape, PVRs allow the user to watch a prerecorded show while the unit is recording a new program, pause watching live programs (for example, if the phone rings) and then resume watching the rest of the live broadcast, view instant replays and slow motion of live programs, and skip commercials. In effect, PVRs, like older VCRs, allow viewers to control when they watch broadcast programs (called "time shifting"). However, PVRs provide much sharper pictures and are much simpler to operate than VCRs, and PVRs allow the user to download the television schedule for the next week.
Two companies currently sell the hardware and provide the subscription service: TiVo and ReplayTV. Both firms started in 1997. As of 2008 TiVo had nearly four million subscribers and ReplayTV had been purchased by DirectTV. Companies are developing new technologies that make it even easier for users to "snip" commercials.
Cable companies have begun offering a combined cable box and PVR in one unit for a small additional monthly charge. This further simplifies setup and operation, and the user gets a single bill.
Suppose you are in charge of setting the price for commercial advertisements shown during Enemies, a top network television show. There is a 60-minute slot for the show. However, the running time for the show itself is only 30 minutes. The rest of the time can be sold to other companies to advertise their products or donated for public service announcements. Demand for advertising is given by:

where Q d = quantity demanded for advertising on the show (minutes), P = the price per minute that you charge for advertising, and V is the number of viewers expected to watch the advertisements (in millions).
a. All your costs are fixed and your goal is to maximize the total revenue received from selling advertising. Suppose that the expected number of viewers is one million people. What price should you charge How many minutes of advertising will you sell What is total revenue
b. Suppose price is held constant at the value from part ( a ). What will happen to the quantity demanded if due to PVRs the number of expected viewers falls to 0.5 million Calculate the "viewer elasticity" based on the two points. Explain in words what this value means.