Price bundling: Difference between revisions

Revision as of 18:23, 11 September 2016

This article describes a pricing strategy used by sellers, typically in markets that suffer from imperfect competition, significant transaction costs or imperfect information.
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Definition

Price bundling is a strategy whereby a seller bundles together many different goods/items being sold and offers the entire bundle at a single price.

There are two forms of price bundling -- pure bundling, where the seller does not offer buyers the option of buying the items separately, and mixed bundling, where the seller offers the items separately at higher individual prices. Mixed bundling is usually preferable to pure bundling, both because there are fewer legal regulations forbidding it, and because the reference price effect makes it appear even more attractive to buyers.

Motivation behind price bundling

Exploit different valuations by different buyers

Toy example

Suppose there are two buyers, $A$ and $B$ , and two products, $X$ and $Y$ . Suppose buyer $A$ values product $X$ at $20$ units above the cost of production, and values $Y$ at $15$ units above the cost of production. Suppose buyer $B$ values $Y$ at $20$ units above the cost of production, and $X$ at $15$ units above the cost of production. Here is a simple $2\times 2$ of the value the buyers place.

	Value place on product $X$ above the cost of production (i.e., reservation price - cost of production)	Value placed on product $Y$ above the cost of production	Value placed on a bundle of $X$ and $Y$ above the cost of production = Sum of preceding two columns
Buyer $A$	20	15	35
Buyer $B$	15	20	35

The ideal thing for the seller would be to practice price discrimination: charge each buyer the maximum that buyer is willing to pay. However, this may be forbidden by law or otherwise difficult to implement.

Instead, the seller can pursue the following bundling strategy: charge slightly under $35$ units above production cost for the combination of $X$ and $Y$ . Since both buyers value the combination at $35$ units above the cost of production, this deal appeals to both buyers. This allows the seller the obtain the entire social surplus as producer surplus. (It isn't true in general that bundling allows the seller to capture the entire social surplus -- that is a special feature of this situation because both buyers have similar reservation prices for the total bundle. However, bundling does allow the seller to capture more of the social surplus in many situations).

The seller can even make this a mixed bundling strategy: offer both $X$ and $Y$ individually for $20$ units above the cost of production, and offer the combination for slightly less than $35$ units above the cost of production.

Generalization

Consider the same two-buyer situation as above, but with more arbitrary numbers. Denote by $p_{A,X},p_{A,Y},p_{B,X},p_{B,Y}$ the prices that buyers are willing to pay over and above the cost of production. Thus, for instance, $p_{A,X}$ is the maximum price that buyer $A$ is willing to pay for $X$ over and above the cost of production of $X$ .

Here are the three basic cases:

Type of situation	Seller's pricing strategy	Seller's profit from buyer $A$	Seller's profit from buyer $B$	Seller's total profit
No price discrimination or price bundling	Charge $\min\{p_{A,X},p_{B,X}\}$ above cost of production for $X$ and $\min\{p_{A,Y},p_{B,Y}\}$ above cost of production for $Y$	$\min\{p_{A,X},p_{B,X}\}$	$\min\{p_{A,Y},p_{B,Y}\}$	$\min\{p_{A,X},p_{B,X}\}+\{p_{A,Y},p_{B,Y}\}$
Pure price bundling	Charge $\min\{p_{A,X}+p_{A,Y},p_{B,X}+p_{B,Y}\}$ above cost of production for the bundle of $X$ and $Y$	$\min\{p_{A,X}+p_{A,Y},p_{B,X}+p_{B,Y}\}$	$\min\{p_{A,X}+p_{A,Y},p_{B,X}+p_{B,Y}\}$	$2\min\{p_{A,X}+p_{A,Y},p_{B,X}+p_{B,Y}\}$
Price discrimination	Charge each buyer the maximum the buyer is willing to pay for each product	$p_{A,X}+p_{A,Y}$	$p_{B,X}+p_{B,Y}$	$p_{A,X}+p_{A,Y}+p_{B,X}+p_{B,Y}$

External links

Weblog entries/articles

Particular weblog entries/articles of interest:

@@ Line 38: / Line 38: @@
 |-
 | No price discrimination or price bundling || Charge <math>\min \{ p_{A,X}, p_{B,X} \}</math> above cost of production for <math>X</math> and <math>\min \{ p_{A,Y}, p_{B,Y} \}</math> above cost of production for <math>Y</math> || <math>\min \{ p_{A,X}, p_{B,X} \}</math> ||  <math>\min \{ p_{A,Y}, p_{B,Y} \}</math> || <math>\min \{ p_{A,X}, p_{B,X} \} + \{ p_{A,Y}, p_{B,Y} \}</math>
+|-
+| Pure price bundling || Charge <math>\min \{ p_{A,X} + p_{A,Y}, p_{B,X} + p_{B,Y} \}</math> above cost of production for the bundle of <math>X</math> and <math>Y</math> || <math>\min \{ p_{A,X} + p_{A,Y}, p_{B,X} + p_{B,Y} \}</math> || <math>\min \{ p_{A,X} + p_{A,Y}, p_{B,X} + p_{B,Y} \}</math> || <math>2\min \{ p_{A,X} + p_{A,Y}, p_{B,X} + p_{B,Y} \}</math>
 |-
 | Price discrimination || Charge each buyer the maximum the buyer is willing to pay for each product || <math>p_{A,X} + p_{A,Y}</math> || <math>p_{B,X} + p_{B,Y}</math> || <math>p_{A,X} + p_{A,Y} + p_{B,X} + p_{B,Y}</math>
-|-
-| Pure price bundling || Charge <math>\min \{ p_{A,X} + p_{A,Y}, p_{B,X} + p_{B,Y} \}</math> above cost of production for the bundle of <math>X</math> and <math>Y</math> || <math>\min \{ p_{A,X} + p_{A,Y}, p_{B,X} + p_{B,Y} \}</math> || <math>\min \{ p_{A,X} + p_{A,Y}, p_{B,X} + p_{B,Y} \}</math> || <math>2\min \{ p_{A,X} + p_{A,Y}, p_{B,X} + p_{B,Y} \}</math>
 |}