IBM Research | Ponder This | September 2007 challenges

# Ponder This

## September 2007

<<August September October>>

Ponder This Challenge:

A cable TV company has two channels of programming that it can offer (at negligible marginal cost) to a large pool of potential customers. Suppose the value (per unit time) of each channel to each potential customer is an independent random variable uniformly distributed on the interval (0,1) and that value is additive (so the value of both channels to the potential customer is the sum of the values of each individual channel). Assume a potential customer will
buy when the (additional) value is greater than the (additional) price.

1. Suppose the company prices each channel independently. What should it charge for each channel (to maximize revenue) and what will its expected revenue be (per potential customer per unit time)?

2. Suppose the company bundles the channels together so the potential customer has to buy both or neither. What should it charge (to maximize revenue) for the bundle and what will its expected revenue be (per potential customer per unit time)?

Define the consumer surplus to be the difference (assuming it is positive) between what a potential buyer would have been willing to pay for an item and the actual price. If the difference is negative the sale will not take place and the consumer surplus is defined to be 0.

3. What is the consumer surplus (per potential customer per unit time) assuming the cable company prices to maximize revenue for cases 1 and 2 above?

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Challenge: 09/05/2007 @ 02:30 PM EDT
Solution: 10/03/2007 @ 11:30 AM EDT
List Updated: 10/03/2007 @ 11:30 AM EDT

### People who answered correctly:

David Friedman (09.05.2007 @04:24:55 PM EDT)
V Balakrishnan (09.05.2007 @05:03:08 PM EDT)
Henry Bottomley (09.05.2007 @05:07:29 PM EDT)
Frank Yang (09.05.2007 @05:29:52 PM EDT)
Arthur Breitman (09.05.2007 @05:38:22 PM EDT)
Mark Pilloff (09.05.2007 @06:14:22 PM EDT)
Mark Perkins (09.05.2007 @07:02:05 PM EDT)
Celia Anteneodo (09.05.2007 @07:29:48 PM EDT)
Dan Dima (09.05.2007 @08:13:56 PM EDT)
Gary M. Gerkin (09.06.2007 @01:10:33 AM EDT)
Graeme McRae (09.06.2007 @01:47:42 AM EDT)
Vineet Gupta (09.06.2007 @05:46:42 AM EDT)
Jiri Hrdina (09.06.2007 @10:30:47 AM EDT)
Rong Fan (09.06.2007 @02:51:56 PM EDT)
Arthur Breitman (09.06.2007 @03:27:45 PM EDT)
John T. Robinson (09.06.2007 @05:58:08 PM EDT)
Øyvind Grotmol (09.06.2007 @07:01:37 PM EDT)
William Hasenplaugh (09.06.2007 @10:22:53 PM EDT)
Zhou Guang (09.06.2007 @11:04:58 PM EDT)
Andreas Eisele (09.07.2007 @12:12:31 AM EDT)
Hal Varian (09.07.2007 @01:32:18 AM EDT)
Cobus de Waal (09.07.2007 @09:02:44 AM EDT)
Ross Millikan (09.07.2007 @10:56:16 AM EDT)
Jiri Navratil (09.07.2007 @01:12:13 PM EDT)
Mithil Ramteke (09.07.2007 @03:08:03 PM EDT)
Joe Fendel (09.07.2007 @05:06:35 PM EDT)
Fred Batty (09.07.2007 @10:15:11 PM EDT)
Se Kwon Kim (09.08.2007 @07:51:17 AM EDT)
James Dow Allen (09.08.2007 @08:40:23 AM EDT)
Ed Shepard (09.08.2007 @01:42:38 PM EDT)
Christian Blatter (09.09.2007 @11:56:47 AM EDT)
lukas saul (09.10.2007 @01:42:45 AM EDT)
John Fletcher (09.10.2007 @01:27:25 PM EDT)
Dion Harmon (09.10.2007 @02:34:16 PM EDT)
Karl D'Souza and David Ehrlich (09.10.2007 @03:21:46 PM EDT)
Alan Murray (09.10.2007 @11:01:07 PM EDT)
Emmanuel Candalh (09.11.2007 @11:07:11 AM EDT)
Floyd Bullard (09.11.2007 @04:26:31 PM EDT)
Joshua Green (09.12.2007 @08:29:48 PM EDT)
Wolfgang Kais (09.13.2007 @11:53:36 AM EDT)
Maxim G. Smith (09.13.2007 @04:19:26 PM EDT)
Bhaskar Nallapureddy (09.14.2007 @03:58:23 AM EDT)
Don Rice (09.14.2007 @01:42:50 PM EDT)
Andrea Andenna (09.16.2007 @05:33:21 AM EDT)
Albert Stadler (09.18.2007 @03:10:03 AM EDT)
Gale Greenlee (09.18.2007 @11:56:31 AM EDT)
Daniel Bitin (09.28.2007 @09:10:30 AM EDT)
Phil Muhm (09.28.2007 @12:48:37 PM EDT)
Ervan Darnell (09.28.2007 @05:31:51 PM EDT)
Jamieson Cobleigh (09.28.2007 @08:57:51 PM EDT)
Rogerio Ponce (10.02.2007 @03:15:50 PM EDT)
Almudena Moratinos (10.03.2007 @10:52:32 AM EDT)

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