Bundling Strategy Considering Product Diffusion Processes

褚志鵬陳俞任國立東華大學企業管理學系暨運籌管理研究所

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中正大學經濟學系 演講

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when to bundle

Bundlingstrategy

The firm hope to gain more profit

How to price？

Diffusion Model

The diffusion

processes of the

bundling product

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Bundlingstrategy Bundlingstrategy

ProducerProducerThe scholars focus on the price strategy of the bundling, they set the optimal price not only using the basic of the economic theory

but also the mathematical method

(Adams & Yellen, 1976; Guiltinan, 1987; Eppen et al., 1991; Venkatesh & Mahajan,

1993; Robert & Hermann, 2000)

ConsumerConsumerThe scholars focus on the consumers evaluate

the processes of separate products or the preference of consumers behavior.

(Varadarajan, 1985; Yadav & Monroe, 1993; Yadav, 1994; Yadav, 1995; Harlam et al., 1995)

How to price

5

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The scholars investigate the diffusion of multiproduct most only discuss the relative of the multiproduct (Gupta, Jain & Sawhney,1999; Kim, Chang & Shocker,2000; Shocker, Bayus & Kim, 2004)

The multiproduct interaction on process of innovation diffusion (Peterson & Mahajan, 1978)

The diffusion processes of the bundling product

？

Bundlingstrategy

Diffusion Model

Hotelling’s model

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Key papers of the model construct

Delphine & Francis (1999)Persuasive advertising in Hotelling’s model

of product differentiation

Jay (2006)Tying in two-Sided Market with Multi-Homing

Bass (1969)A New Product Growth Model

for Consumer Durables

Multiproduct monopoly

Tying=bundling

Diffusion

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The Concept of Diffusion

Definition:

“The Information about an innovation (or product) is transmitted through certain channels over time among the members within a social system,” by which the communication channels consist of both the mass media and interpersonal communications (Rogers, 2003)

Communication Channels

The communication channels, which are the process by which people develop and share the information about the product with each other to reach a mutual understanding within the social system, consist of both the “mass media” and “word-of-mouth.”

Bass Diffusion Model

( )( )

1 ( )

f tp qF t

F t

f(t): PDFF(t): CDF

p: the coefficient of innovation q: the coefficient of imitation

Frank Bass

Connections result in Imitators According to the concept of Bass diffusion model, the adopters

of an innovation are categorized as:

◦ Innovators: the adopters who are influenced by mass media

◦ Imitators: the adopters who are influenced by interpersonal communications.

)]([)()(

)( tNmtFm

qp

dt

tdNtn

proportion of innovator (due to mass media)

proportion of imitator (due to word-of-mouth)

market potential

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Multiproduct monopolyMultiproduct monopolyFirmFirm

1.Pure components strategy1.Pure components strategySingle product aSingle product aSingle product cSingle product c

2.Pure bundling strategy2.Pure bundling strategyBundling product BBundling product B

FirmFirm

1.Pure components strategy1.Pure components strategySingle product aSingle product aSingle product cSingle product c

2.Pure bundling strategy2.Pure bundling strategyBundling product BBundling product B

ConsumerConsumer

1. Buy a, c, or B1. Buy a, c, or B2. If buy a or c, will not buy B2. If buy a or c, will not buy B

ConsumerConsumer

1. Buy a, c, or B1. Buy a, c, or B2. If buy a or c, will not buy B2. If buy a or c, will not buy B

aB c

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aaaa dxpVU

)1( cccc xdpVU

dppVV

xddxpVU

caca

iiBBB

)()(

)1(

buying single product a

buying single product c

buying bundling product B

Bca VVV ,, The common valuation for multiproduct

Bca PPP ,, The price for multiproduct

dThe cost of buying multiproduct

from consumer’s ideal choice

The coefficient of price from bundling product B

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dppVVxdpVU cacacccc )()()1(

dppVVdxpVU cacaaaaa )()(

)(,,)-1(

1 ijcaid

PPVn jij

ia

1))(2-1(

d

PPVN caB

Ba

)(,,)-1(

ijcaid

PPVN iji

ia

aaa xn

cca xn 1

cBa xN 1

caa xN

aca xN 1

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0 1

Pa Pc

Na(1) Nc(1)

NB(1)

xa xcn

a(1) n

c(1)

NBα

naα

ncα

nap

nap

Naα Ncα

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)T(

)T(

1

1)(

ii

ii

e

eTF

i

ii

iiAi FNMTY (1))(1

AM Potential of consumers for multiproduct

i Innovative factor of single product

i Imitative factor of single product

)T(

)T(

1

1

1(1)(1))(

ii

ii

e

eNFNTNF

i

iiiii

)1

())1(

))1((ln()(

1

11

iiiiii

iiiii NFN

NFNNFT

Potential of consumers for single product i

0 1

Pa Pc

Na(1)

Nc(1)

NB(1)

xa

xcn

a(1) n

c(1)

NBα

naα

ncα

nap

nap

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Model 1 : Market Equilibrium under multiproduct monopolyObject ： find the potential market

Model 2 : diffusion Model of Market EquilibriumObject ： find the timing point that the consumers will only willing purchase single product

Model 3 : bimodal profit function model Object ： find out the profit what the firm earn in the different timing of bundling

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product V Price(α=1)

Price(α=0.9) d

a 800 250 250

700c 600 200 200

B 1400 450 405

(α=0.9)

X0 X1 na(0.9) nc(0.9) NB(0.9) Na(0.9) Nc(0.9)

0.3643 0.85 0.3643 0.15 0.4857 0.85 0.6357

(α=1)

X0 X1 na(1) nc(1) NB(1) Na(1) Nc(1)

6/14(0.4286

)

11/14(0.7857

)

6/14(0.4286

)

3/14(0.2143

)

5/14(0.3571

)

11/14(0.7857

)

8/14(0.5714

)

大大大小 小

0 1

Pa Pc

Na(1) Nc(1)

NB(1)xa xcn

a(1) n

c(1)

NBα

naα

ncα

nap

nap

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(α=1)

Na(1) Nc(1)

0.7857 0.5714

na(1) nc(1) na(0.9) nc(0.9)

0.4286 0.2143 0.3643 0.15

)1

())1(

))1((ln()(

1

11

iiiiii

iiiii NFN

NFNNFT

Product

β γ

a 0.003 0.2

c 0.01 0.4

αT

1 0.9

Ta 21.72 20.13

Tc 7.91 6.70 1

Pa Pc

Na(1) Nc(1)

NB(1)xa xcn

a(1) n

c(1)

NBα

naα

ncα

nap

nap

TcTa

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caiMCCP iiii ,),(Pr

)]()[()(

)()(Pr

cacaca

cacaBB

MCMCCCPP

MCMCCCP

iC The manufacture cost of single product i

iMC The management and marketing cost of single product i

Cost coefficient of management and marketing

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If TB T≦ c then profit function 1Pra × Ya1(T) + Prc × Yc1(T) + PrB × NBα × MA

If Tc ≦ TB T≦ a then profit function2Pra × Ya1(T) + Prc × Yc1(T) + PrB × NBα × Mt － PrB ×{Yc1(T) － Yc1(Tc)}

TcTa

If Ta ≦ TB then profit function 3Pra × Ya1(T) + Prc × Yc1(T) + PrB × NBα × MA － PrB ×{Yc1(T) － Yc1(Tc)}

－ PrB ×{Ya1(T) － Ya1(Ta)}

naα ncα

Pa PcNBα

iiAi FNMTY (1))(1

00

Ta

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accumulated profit trendin the profit function 2(δ=1)

Product

β γ

a 0.003 0.2

c 0.01 0.4

B 0.013 0.3

αT

0.9

Ta 20.13

Tc 6.7

product V Price(α=0.9) d

a 800 250

700c 600 200

B 1400 405

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TB=8

TB=12

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TB=16

TB=20

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TB

Ultimate profit(10^

5)

8 3.38

12 3.21

16 3.50

20 4.16

α =0.9 δ =1

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α=0.9

α=0.8

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δ =0.4

δ =0.8

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If the cost of management and market in the bundling product B is low, then the optimal bundling time is the former critical time point.

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We proposed a diffusion process of bundling product. With this process, the firm could find the optimal timing to bundle two products at their life cycle.

Two critical time points are found. If the firm miss the first time point, the better strategy would be waiting for the next time point.

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Different critical time point of bundling◦Considering other factor

Stock, market strategy, finance of company Comparing the profit diffusion process of bundling

product B and unbundling

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