Commodity Bundling Introduction n n Firms often bundle

Commodity Bundling

Introduction n n Firms often bundle the goods that they offer q Microsoft bundles Windows and Explorer q Office bundles Word, Excel, Power. Point, Access Bundled package is usually offered at a discount

Introduction • Definition: selling products together (bundle) • Typically at a price that is less than sum of components • Possible motives: - quality enhancing - Metering consumption (for price discrimination) - Strategic advantage (extend an advantage from one market to the other) - Price discrimination

Bundling – basic idea • Two consumers • Two goods (E, D) • Valuations of consumers: (3, 1), (1, 3) entree • Price goods separately: p. E = p. D = 3 Profits = 6 • Better alternative: • sell menus for $4 • Profits = 8 3 • Key idea: Make consumers more homogeneous by aggregation. 2 • Can be less extreme. 1 • Necessary condition: Negative correlation in values (Rank reversal ) 1 2 3 dessert

Bundling: an example n n n How much can Two television stations offered two old Hollywood How much can be charged for films be charged for If the films are sold Godzilla? q Casablanca and Son of Godzilla separately total Casablanca? Arbitrage is possible between the stations $7, 000 revenue is $19, 000 Willingness to pay is: to Willingness pay for Casablanca pay for Godzilla Station A $8, 000 $2, 500 Station B $7, 000 $3, 000 $2, 500

How much Bundling: an example 2 can be charged for the package? Now suppose that the two films are If and the films Willingness to sold Willingness to bundled sold are as pay a package total pay for as a package revenue is $20, 000 Godzilla Casablanca Total Willingness to pay Station A $8, 000 $2, 500 $10, 500 Station B $7, 000 $3, 000 $10, 000

Bundling n Extend this example to allow for q q costs mixed bundling: offering products in a bundle and separately

Extension: mixed bundling Good 1 1 2 bundle A 8 1 9 B 6 3 9 C 1 6 7 A • Alternative 1: bundle $7, profits = $21 8 B 6 • Sell good 2 at $6 and bundle at $9 • Total profits = $24 3 C 1 1 3 6 Good 2

Self-selection Good 1 • Try same as before: 1 2 bundle A 8 1 9 • p. B = 9 B 2 7 9 • p 2 = 6 C 1 6 7 • Does this work? • What is the best? A 8 6 B 2 C 1 1 6 7 Good 2

Implementation • p 1 = 8, p 2 =6, p. B = 8 • Sell goods indvidually and in bundles • Sell goods indvidually and put a coupon in box: Good 1 A -If buy good 1 at 8, get good 2 for free 8 6 B 2 - Selective discounting C 1 1 -If buy good 2 at 6, get coupon to buy good 1 at 2. 6 7 Good 2

Self-selection n n Each consumer has valuation v 1 , v 2 , v. B=v 1+v 2 Chooses alternative that gives higher CS: q Max ( v 1 – p 1 , v 2 – p 2 , v 1 + v 2 – p. B ) Graphical representation: • CS = v 1+v 2 -pb CS measured by vertical or horizontal • x+v 1 = p. B distance to p. B line v 2 – x = v 2 – (p. B – v 1 ) = v 1 + v 2 –p. B = CS v 2 – p 2 v 2 p 2 v 1 -p 1 v 1 v 2 x p. B represented by 450 line: p 1+p 2=p. B v 1

Bundling: self-selection Consumer y Each has consumer reservation price thatpy 1 the firm one Suppose that there. All areconsumers in. Supposebuys exactly for goodsets 1 and py 2 p for in All consumers price region B buy 1 two goods and that unit of abuy good for good 2 region A good 1 and price p R 2 good 2 2 x hasprovided that consumers differ inonly Consumer both 2 goods price for good price px 1 is less than her their reservation pricesreservation B A for good 1 and px 2 for these goods for good 2 reservation price y py 2 px 2 x All consumers in region C buy neither good All consumers in region D buy Consumers only good 1 split into four groups D C px 1 py 1 R 1

Bundling: self selection (cont. ) Now consider pure bundling at some All consumers in p. B E buy Consumers in theseprice two regions region R 2 can buy each good eventhe though bundle their reservation price for one of Ethe goods is less than its Consumers cost All marginal consumers in p. B c 2 F c 1 now split into two groups region F do not buy the bundle p. B R 1

Mixed bundling R 2 p. B p 2 p. B - p 1 In this region Now consider mixed consumers buy Consumers in Good this bundling 1 is sold either theonly bundle region buy at price p 1 or product 2 in this good 2 Consumers in. Good this 2 Consumers is sold region are willing to region also at price p 2 This leaves both goods. They buy the bundle buy two regions buy the bundle Consumers In this regionsplit consumers buy Consumers in this into four groups: either the bundle region buy nothing in this Consumers The bundle is sold buy the bundle or product 1 region at price p. Bbuy < p 1 only + pbuy only good 1 2 good 1 p. B - p 2 p 1 p. B R 1 buy only good 2 buy nothing

Mixed bundling 2 Similarly, all consumers in this region buy only product 2 R 2 The consumer x will buy only product 1 Consider consumer x with consumers reservation. All prices p 1 x for in Which is this Consumer surplus from Consumer surplus region from buy product 1 this and p 2 x for measure Her aggregate willingness buying product 1 isbundle the only is 1 product 2 product to pay for the bundle is p 1 x -pp 1 + p - p 1 x 2 x+ p 2 x. B x p. B p 2 p. B - p 1 p 2 x p. B - p 2 p 1 p. B p 1 x R 1 p 1 x+p 2 x

An Example Four consumers; two products; MC 1 = $100, MC 2 = $150 Consumer Reservation Price for Good 1 Reservation Price for Good 2 Sum of Reservation Prices A $50 $450 $500 B $250 $275 $525 C $300 $220 $520 D $450 $500

The example 2 Good 1: Marginal Cost $100 Price $450 $300 $250 $50 Price $450 $275 $220 $50 Quantity Total. Consider revenue simple Profit monopoly pricing 1 $450 $350 2 $400 $600 Good 1 should be sold 3 $750 $450 at $250 and good 2 at 4 $200 -$200 $450. Total profit Good 2: Marginal Cost + $150 is $450 $300 Quantity =Total $750 revenue 1 2 3 4 $450 $550 $660 $200 Profit $300 $210 -$400

The example 3 Consumer A B C D Now consider pure bundling Reservation Price for. The highest Price for bundle Good 1 price that Good 2 be can considered isbuy $500 All four consumers will $50 $450 the bundle and profit is 4 x$500 $100) $250 - 4 x($150 + $275 = $1, 000 $300 $220 $450 $50 Sum of Reservation Prices $500 $525 $520 $500

The example 4 Now consider mixed Take the monopoly prices p 1 = $250; p 2 = $450 and a bundle price p. B = $500 bundling All four consumers buy something and profit is Reservation Sum of Consumer Price + for$150 x 2 Price for Reservation Can the$250 x 2 seller improve Good 1 Good 2 Prices = $800 on this? A $50 $450 $500 B $250 $275 $525 $500 C $300 $250 $220 $520 D $450 $250 $500

The example 5 Try instead the prices p 1 = $450; p 2 = $450 and a bundle price p. B = $520 This is actually the best Reservation that the Reservation All four consumers buy Consumer do for Price+forfirm can Price and profit is $300 Good 1 $270 x 2 + $350 = $1, 190 A $50 Good 2 Sum of Reservation Prices $450 $500 B $250 $275 $520 C $300 $220 $520 D $450 $500

Conclusions n n n Increases homogeneity by aggregation Works if values are negatively correlated (rank-reversal) for at least some consumers. Bundling is a form of price discrimination (selective discounting) Self-selection needs to be considered Welfare effects ambiguous Necessary condition for welfare improvement: total output must increase