Question

A cable company offers two basic packages: sports and kids, and a combined package. There are three different types of users: parents, sports fans, and generalists. Assume that the cable company cannot discriminate among the three groups and must charge all customers the same price. The following table shows the maximum price that each type of consumer is willing to pay for each package. Sports Package Kids Package Parents 10 50 Sports fans 50 10 Generalists 40 40

	Sports Package	Kids Package
Parents	10	50
Sports fans	50	10
Generalists	40	40

If the cable company sells the packages separately, how much price should it charge for each package? What will be total revenue? What will happen if this price is slightly raised?

b. Rather than raising the single package price to increase revenue, suppose now the firm opts to offer mixed bundling where the customers can buy either a single package or a bundled package. Show that the cable company will earn a higher revenue with mixed bundling than the single pricing method in part a.

Answer 1

a. There are 3 categories of customers. For calculation purpose, let us assume only 3 customers from each category. If the packages are sold separately, then for sports package, the price can be fixed maximum at 40 where 2 customers will buy making the revenue of the company 80. At 50, only one customer will buy and any price less than 40 is a lost opportunity. Similarly, for kids package, the firm can price at 40 because it has 2 customers willing to buy at this rate. The revenue will be 80 again. The total revenue of the firm by selling 2 packages separately is 80 + 80 = 160. If the price is slighly riased to 41, then the company will face a loss in business and only earn 82 as only one category of customers are ready to pay more than 40.

b. If the firm opts to have a mixed strategy, it can cash in more of what the customers are willing to pay. Both packages combined, parents are willing to spend 60, Sports fans are willing to spend 60 and the generalists are willing to spend 80. Now, the price for the bundle can be set at 60 where all 3 customers will buy the cables. Now, the total revenue is 60*3=180 which is higher than the revenue from part a above. Hence the firm should choose this strategy to earn maximum.