ajaz_eco204_2009_Bundling

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Unformatted text preview: University of Toronto, Department of Economics, ECO 204 20092010 S. Ajaz Hussain ECO 204 2009 2010 S. Ajaz Hussain (Draft) Bundling (To appear again in a chapter) Please help improve the course by sending me an email about typos or suggestions for improvements _____________________________________________________________________________________ Note: Please don't memorize these solutions in the expectation that similar questions will appear on tests and exams. Instead, try to understand how to derive the answer as you'll be tested on techniques and applications, not on memorization. Moreover, tests and exams will cover topics and techniques that may not be in these practice problems. You are urged to go over all lectures, class notes and HWs thoroughly. Bundling Also see Bundling Model and Bundling Model 2003 for 3 segments and 2 good model (easily extendible to more general case) We have demonstrated that by extracting consumer surplus price discrimination is more profitable than uniform pricing. In this note, we examine another mechanism for extracting consumer surplus: bundling. Among other results, we will show that a business can earn greater profits from bundling diverse products together as opposed to selling diverse products individually this is in stark contrast to marketing where diverse products are individually targeted to specific segments. For example, marketers will target a word processing software at "literary" types and spreadsheet software at "technical" types; in contrast, economists argue that it may be more profitable to sell the word processing and spreadsheet software together as a bundle, targeted at both the literary and the technical types. There are two types of bundles: pure and mixed. Pure Bundling is when the business offers two (or more) products as a bundle only but not individually. In most countries pure bundling is illegal: for example, McDonald's cannot offer burgers and fries as a value meal only it must also offer burgers and fries individually. That is, most countries want consumers to have a choice. Yet, there are ways to get around this: a business can sell a pure bundle by "tying" products: designing products that are only compatible with one another. For example, Microsoft sells the Xbox and Xbox games as a pure bundle (you can't play Xbox 1 Draft Bundling Note University of Toronto, Department of Economics, ECO 204 20092010 S. Ajaz Hussain games on a Play Station console) in this case, Microsoft can get away with pure bundling by designing products that are only compatible with one another. Similarly, BMW warranties are void if the car is serviced by nonBMW mechanics; as such, BMW owners must "purchase" a bundle of BMW car + BMW service. Mixed Bundling is when the business offers two (or more) products as a bundle and individually. For example, McDonald's offers burgers and fries as a value meal and offers burgers and fries individually; travel agencies sell all inclusive vacation packages and travel, lodging, food, etc individually; baseball teams sell season passes (bundling all games) and individual game tickets; etc. Note to self: For chapter version, discuss negatively correlated preferences (show matrix) and give movie studio example that shows a segment having a WTP < MC. For a more rigorous treatment do WTP1 + WTP2 = WTP_1+2 approach In this note we learn how to set optimal mixed bundling prices: the profit maximizing price of the bundle and the individual products. For chapter version, do movie studio example. Here are the assumptions: the firm produces a diverse set of products which are not tied to each other (i.e. can be used independently of each other) and the segments have negatively correlated preferences a segment prefers (say) product A over (say) product B and another segment prefers product B over product A. For Summer 2010 chapters, integrate WTP with consumer theory: use utility functions to derive max WTP these must be independent of prices that is, what is that price at which demand = 1. Suppose a company produces two products. The of good 1 is $20 and the Market research shows there are four segments with the following WTP: Segment A B C D MC WTP Good 1 10 50 60 90 20 WTP Good 2 90 50 40 10 30 of good 2 is $30. 2 Draft Bundling Note University of Toronto, Department of Economics, ECO 204 20092010 S. Ajaz Hussain Assume each segment will purchase 1 unit. The first step is to locate the segments' WTP and the company's on a chart see graph below. Note how the segments' WTP are clearly negative correlated as these are dispersed around the line . Segments' WTP in relation to MC We should: Sell the bundle to segments with Do not sell anything to segments with Sell good 1 to segments with Sell good 2 to segments with and and and and Consider the point where the curves cross. This is "origin" point for the discussion below: i.e. B and C are located Northeast of the crossing point, D is located Southeast of the crossing point and A is located Northwest of the crossing point. Observe that segment A's WTP for good 1 is below the of good 1, while segment D's WTP of good 2 is below the of good 2. This tells us that the company will lose money selling good 1 to segment A and selling good 2 to segment D. The optimal strategies are: Sell the bundle to segments in the Northeast quadrant (above, but not on, both Do not sell anything to segments in the Southwest quadrant (below or on both Sell good 1 to segments in the Southeast quadrant (above the on the for good 2 line) lines) lines) for good 1 line and below or 3 Draft Bundling Note University of Toronto, Department of Economics, ECO 204 20092010 S. Ajaz Hussain Sell good 2 to segments in the Northwest quadrant (above the on the for good 1 line). for good 2 line and below or Put another way, we should come up with a set of prices for the bundle, good 1, and good 2 such that: Segments B and C chooses the bundle but not the individual products Segment A chooses good 2 but not the bundle Segment D chooses good 1 but not the bundle Bundle Individual Products Price ? P good 1 = ? P good 2 = ? A Not Buy Not Buy Buy B Buy Not Buy Not Buy C Buy Not Buy Not Buy D Not Buy Buy Not Buy Let us first price the bundle. To sell the bundle to segments B and C observe that: Segment B C MC Good 1 WTP 50 60 20 Good 2 WTP 50 40 30 Bundle WTP 100 100 50 Since both bundle WTP = $100 the only bundle price point is $100. Bundle Price 100 Bundle quantity purchased 2 Profits = (P MC)Q (100 50)(2) = 100 Next we need to determine the price of goods 1 and 2 to ensure that segments B and C buy the bundle but not the individual goods, and, segments A and D buy the goods individually but not the bundle. For good 1, aiming to extract as much CS as possible from segment D, we set the price at $90. Likewise, aiming to extract as much CS as possible from segment A, we set the price at $90. What will each segment do? It depends on their CS: remember, consumers purchase so long as CS 0. Here is a summary (CS = WTP Price): 4 Draft Bundling Note University of Toronto, Department of Economics, ECO 204 20092010 S. Ajaz Hussain Bundle Individual Products Price 100 P good 1 = 90 P good 2 = 90 A 100 100 = 0 10 90 = 80 90 90 = 0 B 100 100 = 0 50 90 = 40 50 90 = 40 CS C 100 100 = 0 60 90 = 30 40 90 = 50 D 100 100 = 0 90 90 = 0 10 90 = 80 From this we can tell the segments will: Bundle Individual Products Price 100 P good 1 = 90 P good 2 = 90 A Buy Not Buy Buy B Buy Not Buy Not Buy C Buy Not Buy Not Buy D Buy Buy Not Buy We almost have the desired result: segments B and C will buy the bundle but not the individual goods. However, segments A and D are indifferent between the bundle and for segment A good 2 and for segment D good 1. Since we want segments A and D not to buy the bundle, we have to "nudge" these two segments away from the bundle. The easiest way to do this is to give them positive CS when purchasing the goods individually since their CS from the bundle is 0, this will induce them to buy the individual goods. Hence, suppose we lower the price of goods 1 and 2 from $90 to $89.99: Bundle Price 100 P good 1 = $89.99 P good 2 = $89.99 A 100 100 = 0 10 89.99 = 80.01 90 89.99 = 0.01 B 100 100 = 0 50 89.99 = 40.01 50 89.99 = 40.01 CS C 100 100 = 0 60 89.99 = 30.01 40 89.99 = 50.01 D 100 100 = 0 90 89.99 = 0.01 10 89.99 = 80.01 Individual Products Now segment A will purchase good 2 individually because then the CS is 0.01 which is greater than the CS = 0 of a bundle; segment D will purchase good 1 individually because then the CS is 0.01 which is greater than the CS = 0 of a bundle. 5 Draft Bundling Note University of Toronto, Department of Economics, ECO 204 20092010 S. Ajaz Hussain Bundle Price 100 P good 1 = 89.99 P good 2 = 89.99 A Not Buy Not Buy B Buy Not Buy C Buy Not Buy D Not Buy Buy Individual Products Buy Not Buy Not Buy Not Buy Thus, the optimal mixed bundle prices are: Price of good 1 = $89.99 Price of good 2 = $89.99 Price of the bundle = $100 The total profits are: 89.99 20 1 89.99 30 1 100 100 50 2 B 69.99 69.99 $239.98 6 Draft Bundling Note ...
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This note was uploaded on 05/02/2011 for the course ECO 204 taught by Professor Hussein during the Fall '08 term at University of Toronto.

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