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±±¬²¹^, 7/y‹,Fb1„5?TXÖP_ ¯FÛŠVíoÀA

…^, Ĥ,Hj¶1._àk’mß¹

Bakos and Brynjolfsson(2000)ÑP_ ¯½ævƒø_Ý “íµI

FbN|^,úkø_ÞßÖß¹í¼Vz^,à‹iÒA…DQ1/¾‘6ú kFß¹íÇgÑÖ/u°íœ0}º(i.i.d. assumption) v^, ¼í|

_ìgµIÿuzFíß¹ ¯Aø_ß¹^, ìø_g

¥ÿuF‚íÀ ÓP_ ¯_
Í7,Bakos and Brynjolfsson úkiÒA…£¾‘6Rßí ícq£uÀÓP_ ¯.x^0íŸÄ
bPß¹íiÒA…Öü^, º%%

̶‹JI^: ªjzbPemÊf£v}Xƒæ˜ËÑí½æ^; 7Ûí æ˜ß—¼ç%%âŠVòçí
‘J¦)¤^, ]àµt−Ê©Ÿ>q26 bY¦G/‘
y6^, ç¼TXø_B×íP_ ¯v^, ¾‘6}Þ@Çg¤

øP_ ¯qFß¹í˚Ø^, Ĥ}ßÞÇgß¹íA…
¤Õ^, ‡ú¾‘6 Rßí½æ,Chuang and Sirbu(1999) N|^, ¾‘6úkß¹íÇg'ýx

Ö/u°íœ0}º^,ÄÑAb¦Éú/<ß¹E^,Fb.}ú¼F TXíFíß¹·£íÇg^,9õ,rÖß¹¾‘6íÇguÉ
^Anan- dalingam and Wu(2002) bM}&í!‹¹éý^, ʾ‘6íÇgÑÖ/ó

°}º^(i.i.d)/iÒA…ÑÉícq-^,ÀÓP_ ¯Ñ|_^,£à^{Bakos and} Brynjolfsson(1999) í!^, Í7^, ÀÓP_ ¯Éu|_j2íw2ø
à

‹uÝÖ ó°}º(non i.i.d) í¾‘6^,TX.°íî`“P_ ¯^(Cus- tomized Bundling)ikÀÓP_ ¯£_
»
cTXÀÓP_ ¯íÇø _½æu^,×b¾íP_ ¯ª?}¬¾‘6íã
Ì„

rÖíû˝Çá«n’mß¹Sà×b¾íP_ ¯ìgí½æ
¥<

d.øOVz·wÑ^,°vTX×b¾íP_ ¯£_
»^,¹S¦F‚¹¯

P_ ¯^,…}ikÀÖSà×b¾íP_ ¯CÀÖSà_
»^(Chuang and Sirbu, 2000; Fishburn, Odlyzko and Siders, 2000)
¥<d.°v6wÑ^, or¾‘6AвÏP_ ¯qíß¹^,7.uâ¼9l ¯ß^,¥šíìg œ„.cªJZ¾|_í!‹^,°v6?&Mw q4

Hitt and Chen (2001) N|^, TXø_CyÖíî`“P_ ¯ ⁽1/o r¾‘6AвÏß¹ƒ/øb¾⁾ ?Dªø¥Ó‹¼í‚â^, °v6?±

Qç¼Þ@æ”Û° ⁽Éú/<ß¹ECã
Ì„⁾ vF¨AíÌ^0 4
Ou^, b°j|_íP_ ¯b¾£g
º.âcq/<Ôìí¾‘6Ç gƒb
Hitt and Chen ¹Sà7ÊÝ(4¿g_2cí Spence-Mirrlees single crossing property
_SCP 4”s_½bí¿Ö^: íl^, úkLSøP _ ¯^, ò¾‘6íèGg
¯±òkQ¾‘6
ù^, úkLSs_.°×ü íP_ ¯^, ò¾‘6úk¥s_P_ ¯íÇgÏ毱×kQ¾‘6íÇ gÏæ
Í7,Anandalingam and Wu(2002)ºN|^, ¥<4”Êöõ0ä1.

_à
Fb6wÑ^,úk¼Vzªœ½bíu²ìƒbTX_î`“P_

¯^,1/Ê˛øí®¾‘6Çgƒƒ5-²ì|_íg

FbJ^{Hitt and} Chen(2001) íP_ ¯–1Ñ!^, SàÝ(4cbd•íj^, V«nÖ´

¼úk×b¾í’mß¹^, àS|_“w
»£ìgWÑ
…_.c_à kLSøÛ°}ºCu¾‘6Çgƒb^, °v65?ƒTXøP_ ¯íi ÒP_A… (marginal bundle cost of a bundle) £TXÖP_ ¯FßÞí oÀA…
°v^, ÄÑ_í‰bcÓ6’mß¹íb¾Ó‹7×(4AÅ^, Ä

¤…_ªJ_àk®ª?í’mß¹b¾
Ê#ìíÛ°£A…!Z5-^,

¤_ªJ²ì¼@TXÖýP_ ¯J£©P_ ¯íg

ù ìg_

…û˝í_3bqìuô/ ^Chuang £ Sirbu(2000) í_^, 3bí.

°Êk…dú¾‘6Û°¡b}ºSà.°cq

ø
¾‘6cq

cq¾‘6Þú(,ß—¼FTXí N ío^, F}Rßw2 kNí^, Ä

¤ k ÑøªW^, cq k Ã
ük¹
°vcq¾‘6}úFFRßí kN ío ªW§å^, |¿¡ío
§å§ø^, ¿¡|ý^, OERßío
§|(
ú

¾‘6Rß^, ¹èGg
Ñ£ío
^, BbªJcqø‘(4íÛ°
(^, à Ç3.4Fý^:

w (n)

w 0

kN

|

N n

0

)]

( 1 [ )

( ₀

kN w n

n

w = −

kN w₀

=

Ç 3. 4: _¾‘6íèGg

(

¥uø‘âs_¡b w0 £ _k F²ìíÛ°
(^, ©ø_¾‘6;WAÐ íw0 £_k ²ìw_íÛ°
(
óWѾ‘6íèGg
^,dWÑøb¾í –1
íl, N [ý¼uTXN ío

7©øío
ʾ‘6-2í§å^,

uJ¥ío•OdW⁰ƒ_N 5ÈíP0VH[
¾‘6|¿=ío
^, ¹n = 0 v^, wèGg
Ñ w0 ; ÇgŸ5£5(ío
^, ¾‘6íÇgJøìíªW -±
ç n = kNv ^, ¾‘6íÇgk⁰
Ĥ^, * n = 0 ƒ n = k(N − 1) , u _kN ío
u¾‘6Çgí
°vÊAâT0 (free disposal) ícq-^, âk¾‘6ªJ<J.;bío
7.ßÞA…^, Ĥ.}LSøíoíÇ guŠí
Ĥ* kN Çá^, ¾‘6úo
íÇg·uÉ
k Î7[ýÛ°

(íé0Õ^, °v6u¾‘6ÇgÝÉío
ªW
ÔWVz^, J k = 0.1 , 7 N = 100 , [ý¾‘6ÇgÝÉío
ѹ⁰í
¾‘6úní|¿=o
í Çg^, J-[ý^:

w(n) = max



0, w0· [1 − 1 k(n

N)]



, 0 ≤ n ≤ N − 1

{k, w₀}í ¯ªJ$Aø_¾‘6úß—ß¹íÛ°
(
…dcqkÑ øb ^¯k , w0 ÑøNb}º^, wœ0òƒbà-^:

fw0(w0) = λ · e^−λw0, w0 > 0

ù

¼cq

(,ß—¼DwFTX’mß¹í¼éN^,îJòìA… ^(FC) D QiÒA… ^(MC) ÑÔ
¼./Гí‘Kuw„‚ ⁽,YïÁ‰ A…⁾ b—DÚGìA…
7Éb¼í„‚—DÚGìA…^, |_ìgí²µÿ ÖkìA…^,C6BbªJzìA…çAÉ{CçA’³A…
¥šíc qUBbʪJe ^FC Ñ_2íÕÞ‰b

d_%Èu´à¼|_ìguBbFÉ-í^,ĤN¬P_ ¯íA

…MCB DÀ
A… MCA íÉ[V×Ûd_%ÈíæÊ^: MCJ = N^γ· MCA

w2_N [ý(,ß—¼TXP_ ¯F¨Öío
bñ^,7 γ†Ñd_

%ÈNb
à‹ γ < 1 , [ý(,ß—¼JTXøÖN íoíP_ ¯^,

wA…ø}ªTX N íÀ
íA…Zí^, Ĥ¼xd_%È
γ = 1 [ý .xd_%È^, 7 γ > 1†[ýæÊd_.%È

cq(,ß—¼ÖÍ.ø−õÒ˛wß¹í¾‘6íÛ°^, Ou%â

Ò|Œø−c_Ò,¾‘6Û°í }º
ĤJ°‚â”×í¼^, w

‚â”×íP_ ¯g
PB DÀ
g
PA , øD¾‘6íÛ°í}ºÉ

âk…dcq k = ¯k , Ĥ‚âƒbcD w0 É
Ê5?A…!Z5(^, ¼ í‚âƒbà-^:

Π = 

PB− MCB



f (w0)· dw0+

 n^∗



PA− MCA



f (w0)· dw0

ø¶}uP_ ¯í‚â^, ù¶MuÀ
í‚â
J¼c“P_

¯, w‚âÉø¶M^; JÉ“À
^, w‚âÉù¶M

ú
¾‘6í²ÏD
¼í‚â”×WÑ (ø⁾ ÀÓP_ ¯(Pure Bundling):

à‹(,ß—¼ÉTXÀÓP_ ¯^, du ^kkbox FTXí¿©^,

¾‘6í²Ïÿu¿©C.¿©
7²ìí!uªœ_Aúß—ß¹í,è Gg
DP_ ¯íg
^, à‹_Aúß—ß¹í,èGg
×k¼úP_

¯íìg^, †¾‘6}^, ¥5†.}
Bbø¾‘6úFo
íèGg

únd}^, ªJ)ƒw,èGg
WB: WB =

 _n

0 w(n) · dn + ∆c

w2∆_cuúk}FIíüúiÞí^k^,âk…dcqk < 1,Ä

¤^∆c = w0/2,½hì2WB: WB =

 _n

0 w(n) · dn + w0

2

è<¿©í¾‘6^, w¾‘6”ìUBuw,èGg
WBD¿©g
PBí gÏ^:

UB = WB− PB

k

0

買套裝組合

B : R

=0 UB

w0

不買

0 : R

Ç 3. 5: _¾‘6ÊÀÓP_ ¯-í²Ï

ÉUB > 0í¾‘6nª?˛P_ ¯
ĤBbzUB = 0í(å Ê_{{w0, k}}í Þ,^, àÇ_3.5Fý
J¾‘6í{w₀, k} ¯rÊUB = 0í¬i –RB, [ýwUB > 0, }²Ï¿©^; ¥5, rÊRB†.}˛
z WB Hp j UB = 0ªJ)ƒ^:

w0s = 2PJ

N ¯k + 1

ç(,ß—¼øP_ ¯íg
ìÑ PB , É w0 ≥ w0s í¾‘6n

ª?˛
Ĥ¼í‚âƒbÑ^:

Π_{P B} =

 _∞

w0s

[PB− MC_B]f (w0)dw0

=

 _∞

N ¯2PBk+1

[PB− N^γ· MCA]λe^−λw0dw0

= (PB− N^γ· MCA)· e^{−λN ¯2PBk+1}

(ù⁾ ÀÓÝP_ ¯(Pure Unbundling) :

(,ß—¼ú©ío
îJPAÑÀg
Þú¥_g
^,¾‘6|Ö?Ní o^, ¹¼TXí,Ì
õÒ,^, J°^à”×íÜ4¾‘6^, Ñ7®ƒ¾‘

6”ìUB|×^,FúF©øíF˛o
íèGg
w(n)@×k¼Fìíg

PA
Ĥ¾‘6F˛í|(øÀPo
^, ¹wF¾‘íiÒo
n^∗, @Å

—w(n^∗) = PAí‘K
à‹w0 > PA, ¹¾‘6|¿=o
íèGg
×kÀ

íg
^,†¾‘6í|_˛¾n^∗ªJ[ýÑ^: n^∗ = min



N,kN(w0− PA) w0



OâkBbcqkÃ
ük^1, Ĥ^, n^∗ = kN(w0− P_A)

w0

ÇÕ^,ú_{w0 < PA}í¾‘6Vz^,©F|¿=o
íèGg
·QkÀ
í g
^, Ĥ¥¾‘6.}LSøío

;W,H¾‘6í²Ï^,BbªJ)ƒ¼í‚âƒb^: Π_{P A} =

 _∞

w0=PA

[PA− MC] · n^∗· f(w₀)dw0

= [PA− MC]

 _∞

w0=PA

kN(w0 − PA)

w0 λe^−λw0dw0

(ú⁾ ¹¯P_ ¯(Mixed Unbundling) :

ʹ¯P_ ¯2^, ¾‘6}²ÏUw¾‘6”ìœ×í
¼.

âʾ‘6AB²Ï (self-selection) í¬˙2^, ²ìUw‚â|×íP_ ¯ g
DÀ
g

íl^,Bb.â²ìU¾‘6P_ ¯DÀ
í¾‘6”

ìóí‘K^, ¹j UB = UA , ª)^:

w˜0 =

¯kPA+ 2¯kNPA− 2P_B−

(¯kPA+ 2¯kNPA− 2P_B)²− 4(k − 1)¯kNP_A² 2(¯k − 1)

w_w0 ¬ w^˜0 í¾‘6øP_ ¯^, ¥5_{, w0} Qkw^˜0 í¾‘6ø˛

À

Ĥ¼í‚âƒbÑ^:

Π_Mix = [PA−MC]

 _w˜0

w0=PA

n^∗· f(w₀)dw0+ [PB−N^γ·MC]

 _∞

w0= ˜w0

f (w0)dw0

ú ìgõ„}&

…døþt7júø_TX^Nío
í(,ß—¼Vz^,¾‘6Û°Ô 4í}ºDÞßxX ÞßA…ú|_ìgµI²Ïíà
íl^, ¾‘6Û°

Ô4ʇd2BbJ f (w0, k) V·H
w2w BbcqwÑøNb}º
õÒ ,Vz^, BbêÛ --6 2^, è<S À
G‘ í¾‘6^, Fbúøí h o íèGg
}ºàÇ^3.6Fý^:

0 0.1 0.2 0.3 0.4

3 8 13 18 23 28 33 38 43 48 53

願付價格分配 exp~(0.1122)

0 0.2 0.4 0.6 0.8 1

3 8 13 18 23 28 33 38 43 48 53

願付價格累積分配 cumulative distribution of exp~(0.1122)

Ç 3. 6: w0 íõÒ}ºD,l

Ã
,Vz^, w}ºœéN ^Gamma }º^, O _Gamma }ºíœ0ò ƒbœµÆ^, Hp‚âƒb}ßÞ}í˚Ø
Ĥ5?_ Ý45(^, B bEJNb}ºV¡,Hí}º^, ,lí!‹λ = 0.1122, Cµ = 8.9127, [ý,lí Ì©íhoíèGg
Ñ^8.29217j
QOBbYW ^Chuang £ Sirbu(2000) íj¶^, J¾‘6©"ù4 Ìè<G‘ío
bñV,lk
Ìè<G‘ío
bñBbJø"ù4¹⁰íoÁ  Ì.è<G‘ío
bñ

0 0.05 0.1 0.15 0.2 0.25 0.3

0 1 2 3 4 5 6 7 8 9 10

願意付費的歌曲數 百分

比

3123 . 5

Ç 3. 7: kíõÒ}ºD,l

V[ý^,F)ƒí}ºàÇ^3.7Fý^:

w}ºéNG}º^,°ší^,ʇH_ Ý4íª5¾-^,Bbøk c qÑw Ìb ^¯k,wMÑ^0.51232

(,ß—¼í‚âÎ7§?¾‘6Û°Ô4íàÕ^, 6DwÞßA…

Du´xd_%ÈÉ
Bb5?.°d_%È-^, iÒA… ^MC ×üú¼

‚âíà
F)í!‹Ê-ÜÇáíÇ^3.8ƒÇ_3.11

íl^,ʳd_%È( γ = 1 ), ¹^N íoíP_ ¯wA…kÀ
í N I^, P_ ¯1„UÁýA…í8”-^,w‚â퉓àÇ^3.8Fý

ʳd_%È5-^, SàÀÓP_ ¯^, ¹cSà¿©íìgµIu œÏíµI^;ªœ<Õíu^,SÀ
ìg^,¹ÀÓÝP_ ¯µI¬wFµI^, Ñi‘µI (dominant strategy)
ç|Û¶}íd_%Èv( γ = 0.75 ),ÀÓ ÝP_ ¯µIEÑi‘µI^,àÇ_3.9Fý

çd_%ÈB#^, ®ƒ γ = 0.5 , 8”ÿ7Z‰
àÇ^3.10Fý^, iÒA

…J¬^5, ÀÓÝP_ ¯µIíi‘.y^, ¦7H5íu¹¯P_ ¯µ I^, 7çA…®ƒ²⁰ív`^, ¹¯P_ ¯DÀÓP_ ¯µI.}+ˇ^,·

No Eos(γ= 1)

0 50 100 150 200

0.01 0.1 1 5 10 20

MC

Profit

訂閱 單曲 混合

Ç 3. 8: ‚â”×-íP_ ¯µI^:Ìd_Ñ{(γ = 1)

Partial Eos(γ= 0.75)

0 50 100 150 200

0.01 0.1 1 5 10 20 MC

Profit

訂閱 單曲 混合

Ç 3. 9: ‚â”×-íP_ ¯µI^: ¶}d_Ñ{(γ = 0.75)

Partial Eos(γ= 0.5)

0 50 100 150 200

0.01 0.1 1 5 10 20

MC

Profit

訂閱 單曲 混合

Ç 3. 10: ‚â”×-íP_ ¯µI^:¶Md_Ñ{(γ = 0.5)

Perfect Eos(γ= 0)

0 50 100 150 200

0.01 0.1 1 5 10 20

MC

Profit 訂閱

單曲 混合

Ç 3. 11: ‚â”×-íP_ ¯µI^: êrd_Ñ{(γ = 0)

¬ÀÓÝ ¯µI
¤8$Êêrd_%È-yÑpé

Ü,ÀÓP_ ¯£ÀÓÝP_ ¯cu¹¯P_ ¯íÔW^, ¹¯

P_ ¯@Ñi‘µI^, ¹w‚â@.}ªwFµIQ
Í7…_ÊÍTv^, J¹¯P_ ¯µIÊ|_¢“ƒÀÓÝP_ ¯µI^, [ý w^˜0 ¡ÌÌ

×_, 7ñøíª?uPB 6¡ÌÌ×
²Í7 PB J¡ÌÌ×^,*P_ ¯F )í‚â¢.ÑÉ^, ÿD|_µI ⁽ÀÓÝP_ ¯⁾ ßÞ7pe
âkÊ PB

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°vúk(,ß—¼Vz^, Ê©øíoí¤

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ĤÊÇü2^, Bb)J¥

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Apple iTunesí‚âÖQ^,ÔO^iPodí
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‚â
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F:íÂu.Dí


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}í‚â}VAP_ ¯
õÒ,Vz^, (,ß—¼âk¤‘àí½æ^, Þ úíuø_.ªIíA…^; 7(,ß—¼J Ý--ݯ˝Uà íj

 |• øP_ ¯íß—^, £uw®Ad_%ÈíG¨
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2ÊChuang £ Sirbu(2000) í_2, ²ì ˜w0í‰b´¨
k, ÄÑFbcq k Ñø*Nb }ºíÓœ‰b