Commodity Bundling

Introduction Firms often bundle the goods that they offer  Microsoft bundles Windows and Explorer  Office bundles Word, Excel, PowerPoint, 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 entree 3 Price goods separately: p E = p D = 3 Profits = 6 Better alternative: sell menus for $4 Profits = 8 Key idea: Make consumers more homogeneous by aggregation. Can be less extreme. Necessary condition: Negative correlation in values (Rank reversal ) dessert Two consumers Two goods (E,D) Valuations of consumers: (3,1), (1,3)

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

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

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

Extension: mixed bundling Alternative 1: bundle $7, profits = $21 Sell good 2 at $6 and bundle at $9 Total profits = $ Good 1 A B 6 C Good 2 12bundle A819 B639 C167

Self-selection Good 1 A B 6 C Good 2 12bundle A819 B279 C167 Try same as before: p B = 9 p 2 = 6 Does this work? What is the best?

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

Self-selection Each consumer has valuation v 1,v 2, v B =v 1 +v 2 Chooses alternative that gives higher CS:  Max ( v 1 – p 1, v 2 – p 2, v 1 + v 2 – p B ) Graphical representation: CS measured by vertical or horizontal distance to p B line p1p1 v1v1 v2v2 v 1 -p 1 p2p2 v 2 – p 2 p B represented by 45 0 line: p 1 +p 2 =p B CS = v 1 +v 2 -p b x+v 1 = p B v 2 – x = v 2 – (p B – v 1 ) = v 1 + v 2 –p B = CS v1v1 v2v2 x

All consumers in region A buy both goods All consumers in region A buy both goods Bundling: self-selection R2R2 R1R1 Consumer x has reservation price p x1 for good 1 and p x2 for good 2 Consumer x has reservation price p x1 for good 1 and p x2 for good 2 x p x2 p x1 y p y2 p y1 Consumer y has reservation price p y1 for good 1 and p y2 for good 2 Consumer y has reservation price p y1 for good 1 and p y2 for good 2 Suppose that the firm sets price p 1 for good 1 and price p 2 for good 2 Suppose that the firm sets price p 1 for good 1 and price p 2 for good 2 p1p1 p2p2 Suppose that there are two goods and that consumers differ in their reservation prices for these goods Suppose that there are two goods and that consumers differ in their reservation prices for these goods Each consumer buys exactly one unit of a good provided that price is less than her reservation price Each consumer buys exactly one unit of a good provided that price is less than her reservation price A B D C Consumers split into four groups Consumers split into four groups All consumers in region B buy only good 2 All consumers in region B buy only good 2 All consumers in region C buy neither good All consumers in region C buy neither good All consumers in region D buy only good 1 All consumers in region D buy only good 1

Bundling: self selection (cont.) R2R2 R1R1 c1c1 c2c2 Now consider pure bundling at some price p B Now consider pure bundling at some price p B pBpB pBpB Consumers now split into two groups Consumers now split into two groups E All consumers in region E buy the bundle All consumers in region E buy the bundle F All consumers in region F do not buy the bundle All consumers in region F do not buy the bundle Consumers in these two regions can buy each good even though their reservation price for one of the goods is less than its marginal cost Consumers in these two regions can buy each good even though their reservation price for one of the goods is less than its marginal cost

Mixed bundling R2R2 R1R1 p1p1 p2p2 Now consider mixed bundling Now consider mixed bundling pBpB pBpB Good 1 is sold at price p 1 Good 1 is sold at price p 1 Good 2 is sold at price p 2 Good 2 is sold at price p 2 The bundle is sold at price p B < p 1 + p 2 The bundle is sold at price p B < p 1 + p 2 Consumers split into four groups: buy the bundle buy only good 1 buy only good 2 buy nothing Consumers split into four groups: buy the bundle buy only good 1 buy only good 2 buy nothing p B - p 1 p B - p 2 Consumers in this region are willing to buy both goods. They buy the bundle Consumers in this region are willing to buy both goods. They buy the bundle Consumers in this region also buy the bundle Consumers in this region also buy the bundle Consumers in this region buy nothing Consumers in this region buy nothing Consumers in this region buy only good 1 Consumers in this region buy only good 1 Consumers in this region buy only good 2 Consumers in this region buy only good 2 This leaves two regions This leaves two regions In this region consumers buy either the bundle or product 1 In this region consumers buy either the bundle or product 1 In this region consumers buy either the bundle or product 2 In this region consumers buy either the bundle or product 2

Mixed bundling 2 R2R2 R1R1 p1p1 p2p2 pBpB pBpB p B - p 1 p B - p 2 x p 1x p 2x p 1x +p 2x Consider consumer x with reservation prices p 1x for product 1 and p 2x for product 2 Consider consumer x with reservation prices p 1x for product 1 and p 2x for product 2 Her aggregate willingness to pay for the bundle is p 1x + p 2x Her aggregate willingness to pay for the bundle is p 1x + p 2x Consumer surplus from buying the bundle is p 1x + p 2x - p B Consumer surplus from buying the bundle is p 1x + p 2x - p B Which is this measure Which is this measure Consumer surplus from buying product 1 is p 1x - p 1 Consumer surplus from buying product 1 is p 1x - p 1 The consumer x will buy only product 1 The consumer x will buy only product 1 All consumers in this region buy only product 1 All consumers in this region buy only product 1 Similarly, all consumers in this region buy only product 2 Similarly, all consumers in this region buy only product 2

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 B C D $50$450$500 $250$275$525 $300$220$520 $450$50$500

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

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

The example 4 Consumer Reservation Price for Good 1 Reservation Price for Good 2 Sum of Reservation Prices A B C D $50$450$500 $250$275$525 $300$220$520 $450$50$500 Take the monopoly prices p 1 = $250; p 2 = $450 and a bundle price p B = $500 $500 $250 All four consumers buy something and profit is $250x2 + $150x2 = $800 All four consumers buy something and profit is $250x2 + $150x2 = $800 Now consider mixed bundling Now consider mixed bundling Can the seller improve on this? Can the seller improve on this?

The example 5 Consumer Reservation Price for Good 1 Reservation Price for Good 2 Sum of Reservation Prices A B C D $50$450$500 $250$275$525 $300$220$520 $450$50$500 Try instead the prices p 1 = $450; p 2 = $450 and a bundle price p B = $520 $450 $520 $450 All four consumers buy and profit is $300 + $270x2 + $350 = $1,190 All four consumers buy and profit is $300 + $270x2 + $350 = $1,190 This is actually the best that the firm can do

Conclusions 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