The profit benefits of bundle pricing
of complementary products
Ruiliang Yan, Subir Bandyopadhyay
School of Business and Economics, Indiana University Northwest Gary, IN
46408, USA
Journal of Retailing and Consumer Services
Available online 30 April 2011
1
Contents
• Motivation
• Model
- Pricing strategy without bundling
- Pricing strategy with bundling
• Conclusion
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Complementary good
A complementary good is a good with a negative cross elasticity of
demand
That is, demand for one complementary good creates demand for the
other – firms can gain additional marketing power through bundling, and
vendors can obtain optimal prices.
For example, if they price the base good at a relatively low price,
consumers are more likely to consider the secondary product.
•
•
•
•
-
Examples include:
Peanut butter and jelly
Printers and ink cartridges
DVD players and DVDs
Computer hardware and computer software
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Motivation
•
Various examples of complementary product bundling describe the
different approaches that firms have taken to this strategy.
- Michelin started publishing the Michelin guide, it provided tourists with
information about gas stations, hotels, and restaurants, as well as maps and
driving directions. But it also encouraged the use of automobiles, which boosted
its tire business, making tourist guides and automobile tires seemingly strange
complements.
- For example of A perfect complement, demand for hot dogs creates parallel
demand for buns, as well as for ketchup, mustard, and other related items.
•
In an attempt to provide a framework that can help firms find optimum
bundling product categories and pricing strategies that maximize their
profits, this study develops a profit-maximization model.
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Goal
• They propose a profit-maximization model to address three main
research questions:
①
②
③
What is the optimal pricing strategy when there is no bundling?
What is the optimum product and pricing strategy when the firm uses
bundling?
What is the value of a bundling strategy to the firm if the market is
large and consumers are sensitive to price?
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Pricing strategy without bundling
•
the demand functions are linear with regard to self- and cross-price
sensitivities
:
:
:
:
:
:
demand for product i (1 or2)
the market base (i.e., potential demand if offered free of charge)
the price for product 1
the traditional retail channel price for product 2
self-price sensitivity
the degree of complementarity between the two products
(larger indicates a higher degree of complementarity)
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Pricing strategy without bundling
• Profit function
- The production costs for products 1 and 2 are c1 and c2, respectively
•
we can obtain the optimal pricing strategy without bundling
Theorem 1. When a firm sells complementary products, there exists an optimal
pricing strategy, that decreases as the degree of complementarity increases.
- the firm charges a lower price for the two products when their degree of
complementarity increases, because when the degree of complementarity is high,
a price increase for one product significantly decreases demand for the other
product
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Pricing strategy with bundling
•
This bundling price
is lower than the total price if a consumer buys the two
products separately, or
.
We assume the firm generates higher demand from a larger bundling discount
•
Demand for bundled products
•
: is the bundling discount price sensitivity
•
the profit earned by the firm with a bundling policy
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Pricing strategy with bundling
• the optimal bundling pricing strategy for this firm
Proposition 1. When a firm sells complementary products through a
bundling pricing strategy, there exists an optimal bundling pricing
strategy, that decreases as the degree of complementarity increases.
•
The firm charges a lower price for bundled products with a higher degree of
complementarity, because the lower bundling price effectively stimulates market demand
when the two products are close complements.
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Analysis
Proposition 2. When a firm sells complementary products through bundled pricing,
the bundle discount
decreases as the products’ complementarity
increases.
•
the firm should offer a greater discount in its bundled price, because the larger discount
is more likely to stimulate market demand.
Proposition 3. The firm’s profit with a bundling price strategy
is greater than its
profit without a bundling price strategy
when
. The value of
bundling increases with the degree of complementarity between two products.
•
when business managers sell highly complementary products, a bundling price strategy is
optimal; when the products have low degree of complementarity, separate sales are the
optimal strategy
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Analysis
Proposition 4. When a firm sells complementary products through bundle
pricing, the value of the bundle price always increases with bundling
discount price sensitivity.
•
managers might use advertising or other marketing promotions to inform customers of
its generous bundling policy, which increases their sensitivity to the related discount
Proposition 5. When a firm sells complementary products through bundled
pricing, the value of the bundle price always increases with the size of
market.
•
In large cities or populous areas, managers should actively use bundle pricing policies to
improve their business
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Numerical examples
•
•
Pricing strategies always decrease with an increase in the degree of
complementarity between two products
The gap between no bundling and bundling equals the bundling discount rate,
which always decreases with the increase in the degree of complementarity
between two products
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Numerical examples
•
•
we further show that a firm’s profit always decreases with the degree of
complementarity between two products.
The gap between these cases reflects the value of the bundling policy
when the degree of complementarity between two products increases, the value
of the bundling policy increases for the firm
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Conclusion
• A firm using bundling to sell its products should offer a larger
discount and charge a lower price when the degree of
complementarity between the two products is high.
• A bundling policy is always valuable for the marketer when the
products are close complements.
• The value of the bundling policy always increases with market size
and bundling discount price sensitivity.
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THANKS
Q&A
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