Question

XYZ Cable Co. is trying to decide whether to bundle 2 channels: its “Sports” channel and its “History” channel. It has identified 2 type of customers who regularly subscribe to these channels, “Sports Nuts” and “History Buffs”.

Below is the willingness to pay of Sports Nuts and History Buffs for each of the channels.

		Willingness to Pay
	Number of Customers	Sports Channel	History Channel
Sports Nuts	10,000	$20	$4
History Buffs	2,000	$3	$10

Assuming that the incremental cost of serving 1 more customer for both channels is zero:

1. If you decide to have a separate price for each channel (2 prices), what is the optimal price and what are your profits? What is the consumer surplus? Show your calculations.

2. If you decide to bundle the 2 channels, what is the optimal price and what are your profits? What is the consumer surplus? Show your calculations.

Answer 1

1).

Consider the given problem here XYZ cable is trying to decide whether to bundle 2 channels “Sports” and “History” or not. It has identified 2 types of customer mentioned in the question and their respective willingness to pay for each channels.

If it charges $20 for sports channel and $10 for history, then only “sport nut” will subscribe for sport channel and history buffs will subscribe for history channel. So, the total profit under this case is given below.

=> A = $20*10,000 + $10*2,000 = $220,000.

If it charges $3 for sports channel and $4 for history, then both types of customer will subscribe for both the channels. So, the total profit under this case is given below.

=> A = $4*(10,000+2,000) + $3*(10,000+2,000) = $7*12,000 = $84,000.

=> A = $84,000 < $220,000.

So, the XYZ cable will charge $20 for sports channel and $10 for history channel.

Here the cable operator is exactly charging each customer’s willingness to pay, => the CS is zero.

2).

Given the information provided in the question the “sport nuts” customers want to pay maximum $24 for the bundle and the “history buffs” customers want to pay maximum $13 for the bundle. So, if $24 is charged for the bundle then only “sport nuts” customers will subscribe for the bundle. Under the situation the profit is given below.

=> A = $24*10,000 = $240,000.

So, if $13 is charged for the bundle then types of customers will subscribe for the bundle. Under the situation the profit is given below.

=> A = $13*(10,000+2,000) = $156,000 < $240,000.

So, here the XYZ cable will charge $24 for the bundle and only “sport nuts” customers will subscribe for the bundle, the cable will earn $240,000 as a profit. Here also cable operator is exactly charging each customer’s willingness to pay, => the CS is zero.