Product bundling and shared information goods: A pricing exercise

Abstract

In this article, the author describes an exercise in which two pricing problems (product bundling and the sharing of digital information goods) can be understood using the same analytical approach. The exercise allows students to calculate the correct numerical answers with relative ease, while the teaching plan demonstrates the importance of the distribution of reservation prices across consumers in determining the optimal pricing strategies.

Keywords:

• Bundling
• pricing
• shared information goods

JEL code:

• A2

Acknowledgements

The author thanks the numerous MBA students at Wilfrid Laurier University both in Waterloo and in Toronto who, through their participation in earlier versions of the exercise, have helped him develop and refine it. He also thanks Logan McLeod, Steffen Ziss, the referees, and the editor for their insightful comments and suggestions.

Notes

1. If the distribution of reservation prices is unknown or uncertain, mixed bundling becomes more attractive as a pricing strategy because setting both individual and bundle prices allows the seller to cover more of the reservation price space.

2. Consumer d would be willing to purchase the bundle but receives a higher consumer surplus from purchasing only good x. Consumer e will not purchase the bundle but receives a positive consumer surplus from purchasing good x.

3. More formally, let M be the set of potential consumers for goods x and y: M = {1, 2…m}, where each consumer has reservation prices r_x and r_y with r_x ∈ [0, R_x] and r_y ∈ [0, R_y]. Any mixed bundling strategy {p_B, p_x, p_y} must satisfy: (1) (2) (3) (4) If (1) was not satisfied, demand for the bundle would be zero. Constraint (2) guarantees that the bundle price (p_B) generates a positive number of consumers for whom the bundle generates a non-negative consumer surplus. Constraint (3) guarantees that individual prices (p_x,p_y) create demand for at least one individual product by generating a non-negative consumer surplus which is greater than the consumer surplus generated by the bundle. Lastly, (4) guarantees that {p_B, p_x, p_y} will create a positive demand for the bundle; that is, there will be some consumers for whom the bundle generates the highest (non-negative) consumer surplus.

4. In the case of digital music file sharing, see Liebowitz (2006), Oberholzer‐Gee and Strumpf (2007), and Zentner (2006).

5. Specifically, the idea of using a symphony orchestra and patron types as the basis for the exercise comes from an example given in Brandenburger and Krishna (1995, 2).

6. The pricing exercise can also be downloaded in an editable format from http://web.wlu.ca/sbe/morrison/pricingex.htm. A complete solution guide for instructors is also available upon request; please e-mail the author.

7. Individual concert prices are lowered by one dollar in order to guarantee a positive demand. WAMs and Sophisticates will receive a consumer surplus of $1 from purchasing a single concert versus a consumer surplus of zero from purchasing the bundle.

8. If we allow mixed sharing strategies that make consumers indifferent between the purchase of a sharing version and multiple purchases of the no-sharing version, then the mixed sharing strategy can generate the same revenues as a no-sharing strategy for the reservation prices in table 8.

9. A copy of the student spreadsheet I use is available for download along with the pricing exercise at http://web.wlu.ca/sbe/morrison/pricingex.htm.