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Age t
Age t+1
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olih dqg zk| vrph dxwrprelohv duh wudghg pruh iuhtxhqwo| wkdq rwkhuv1
47
Wkh gl!fxow| lv wkdw wkh irup ri wkh whvw vwdwlvwlf ghshqgv rq wkh vljq ri wkh frqvwudlqwv whvwhg1
Wkh qxpehu ri uhjlrqv lq wkh sdudphwhu vsdfh zkhuh wkh whvw vwdwlvwlf wdnhv d glhuhqw irup jurzv
h{srqhqwldoo| lq wkh qxpehu ri frqvwudlqwv1 Vhh/ iru h{dpsoh/ Jrxulhurx{/ Kroo| dqg Prqiruw +4<;5,1
4;
715
71514
Qxphulfdo uhvxowv= sulfhv dqg uhvdoh udwhv
Fkrlfh ri sdudphwhu ydoxhv
Wr hydoxdwh wkh prgho qxphulfdoo|/ zh pxvw uvw fkrrvh vxlwdeoh sdudphwhu ydoxhv1
Wkh glvwulexwlrq ri frqvxphu w|shv lv dvvxphg wr eh xqlirup rq dfc 4@ o/ zklfk vhhpv
dssursuldwh jlyhq wkh sdshu*v irfxv rq wkh shdnv ri uhvdoh1 Xqghu wklv dvvxpswlrq wkh
yduldwlrq lq uhvdoh udwhv fdqqrw eh gxh wr kljk ghqvlw| ri w|shv wkdw suhihu d sduwlfxodu
ylqwdjh1 Lw vkrxog dovr eh qrwhg wkdw dq| ghqvlw| ?E fdq eh wudqviruphg lqwr wkh
xqlirup e| dssursuldwho| fkrrvlqj wkh xqlwv ri dqg uhghqlqj +4, dffruglqjo|148
Wkh sk|vlfdo olihwlph ri d fdu lv wdnhq wr eh A ' D |hduv1 Ghsuhfldwlrq lv dvvxphg
wr eh h{srqhqwldo/ zlwk d frqvwdqw udwh B=
%| ' %f E B| / | ' c c A 
Zh phdvxuh wkh wudqvdfwlrq frvw ri vhoolqj d xvhg yhklfoh zlwk wkh glhuhqfh ehwzhhq
lwv pdunhw sulfh dqg wkh wudgh0lq ydoxh1 Lq wkh prgho/ wkh udwlr ri wklv glhuhqfh wr
pdunhw sulfh lv htxdo wr b1 Lw wxuqv rxw wkdw wkh udwlr ri wudqvdfwlrq frvw wr sulfh
ulvhv zlwk yhklfoh*v djh dqg urxjko| grxeohv49 ryhu d yhklfoh*v olihwlph1 Dffruglqjo|/
zh vhw
|3
b| ' b 2 A 32 / | ' 2c c A 
+47,
Lq wkh prgho/ jrrgv ri doo djhv duh wudghg zlwk suredelolw| ri dw ohdvw k1 W|slfdoo|/
uhvdoh udwhv duh plqlpdo +l1h1 htxdo wr k, iru |rxqj ylqwdjhv 1 Zh fdq wkhuhiruh fkrrvh
wkh ydoxh ri k wr pdwfk wkh uhvdoh udwh iru 405 |hdu rog yhklfohv lq wkh gdwd14: Wklv
lpsolhv k ' f1
Wkh ydoxhv ri Rf / 4@ / b dqg B duh fkrvhq e| wwlqj wkh htxloleulxp sulfh suh0
glfwhg e| wkh prgho wr wkh qrupdol}hg sulfh vhulhv iru xvhg dxwrprelohv uhsruwhg e|
Sruwhu dqg Vdwwohu +4<<</ Wdeoh 7,1 Wkh uhvxowlqj ehqfkpdun sdudphwhu ydoxhv duh
Rf ' S/ 4@ ' S/ b ' ff.D/ B ' ffS1 Wkh xqlw ri phdvxuhphqw lv wkh vwuhdp
ri vhuylfh iurp wkh eudqg0qhz jrrg/ %f ' 1 Wr eh pruh vshflf/ wkh sulfh ri d qhz
fdu dssur{lpdwho| htxdov wr wkh suhvhqw ydoxh ri 8 |hduv ri lwv vhuylfh wr wkh phgldq
frqvxphu1 Wkh uhdo lqwhuhvw udwh lv vhw wr 3137/ zklfk lpsolhv q ' fbS1
71515
Qxphulfdo uhvxowv
Wkh vlpxodwlrqv iru sulfhv dqg txdqwlwlhv wudghg duh suhvhqwhg rq Iljxuh 81 Wkh uljkw
sorw vkrzv wkh htxloleulxp sulfh +wkh vrolg olqh, djdlqvw wkh sulfh vhulhv gdwd +-,1 Wkh
prgho wv wkh sulfh gdwd txlwh zhoo= wkh glvfuhsdqf| ehwzhhq suhglfwhg xvhg jrrgv
48
Li k Q ^3> kpd{ `/ wkhq k3 @ Q +k, lv xqlirup rq ^3> 4`1 Vlqfh wklv wudqvirupdwlrq lv prqrwrqlf/
lw lv wkh vdph dv uhghqlqj wkh xqlwv ri k1
49
Wklv fdofxodwlrq zdv shuiruphg xvlqj wudgh0lq dqg pdunhw ydoxhv uhsrwuwhg e| Hgpxqg*v=
kwws=22zzz1hgpxqgv1frp2xvhg2
4:
Dyhudjh uhvdoh udwh iru xvhg 4 |hdu rog yhklfohv lv 3138;/ dqg iru xvhg 5 |hdu rog yhklfohv lw lv
314771 Vrxufh= QSWV 4<<81
4<
1
Resale
rate
Normalized
price
0.9
Simulation
*
0.3
Data
0.8
0.7
0.6
0.2
0.5
0.4
0.3
0.1
0.2
0.1
0
5
10
0
15
0
5
10
15
Age
Age
Iljxuh 8= Htxloleulxp uhvdoh udwh dqg sulfhv/ ehqfkpdun fdvh
sulfhv dqg wkhlu ydoxhv lq wkh gdwd lv 6( ru ohvv1 Wkh wudgh lqwhqvlw| sorw vkrzv wkh
vlpxodwhg uhvdoh udwh dv d ixqfwlrq ri djh1 Uhvdoh udwh lv plqlpdo gxulqj wkh uvw 7
|hduv/ ehfdxvh frqvxphuv zkr gudz srvlwlyh wudqvdfwlrq frvwv gr qrw vhoo wkhlu jrrgv
xqwlo wkh djh ri 81 Uhvdoh udwh kdv d shdn dw 8 |hduv/ lv uhodwlyho| orz iru 9043 |hdu
rog fduv dqg ehfrphv uhodwlyho| kljk iru 44048 |hdu rog fduv1
Wr xqghuvwdqg krz wklv sdwwhuq dulvhv/ zh qhhg wr orrn dw wkh htxloleulxp ghflvlrq
uxohv vxppdul}hg lq Wdeoh 51 Hdfk urz ri wkh wdeoh fruuhvsrqgv wr d glhuhqw ghflvlrq
uxoh/ vwduwlqj zlwk wkh kljkhvw w|sh1 Wkh uvw froxpq vkrzv wkh lqwhuydo ri frqvxphu
w|shv zkr kdyh d sduwlfxodu ghflvlrq uxoh1 Iru h{dpsoh/ wkh wrs :19( ri frqvxphu
w|shv ex| jrrgv ri djh }hur dqg vhoo wkhp dw djh 8/ wkh qh{w :16( ex| jrrgv ri djh
}hur dqg vhoo wkhp dw djh 9/ hwf1/ dqg qdoo|/ wkh erwwrp 48( ri frqvxphu w|shv gr
qrw sduwlflsdwh lq wkh pdunhw1
Zh zloo ghprqvwudwh xvlqj Wdeoh 5 wkdw uhodwlyho| kljk uhvdoh udwhv iru 44048 |hdu
rog fduv duh gxh wr uhodwlyho| vkruw kroglqj wlphv iru wkhvh fduv1 Dffruglqj wr +46,/
ghpdqg iru jrrgv ri djh | htxdov wkh qxpehu ri frqvxphuv zkrvh ex|lqj srlqw lv |
dqg zkr duh fxuuhqwo| dw wklv ex|lqj srlqw1 Wkh orqjhu lv wkh kroglqj wlph iru wkh
jrrg/ wkh ohvv lv wkh vwhdg| vwdwh qxpehu ri frqvxphuv dw wkh ex|lqj srlqw14; Wdnh/
iru h{dpsoh/ ; |hdu rog fduv1 Frqvxphuv zkr ex| wkhvh fduv krog wkhp iru hlwkhu
4;
Dffruglqj wr +43,/ wkh qxpehu ri frqvxphuv dw wkh ex|lqj srlqw
i +k> Vk , @
q+k,
=
4 +4 , k
Wklv h{suhvvlrq lv prqrwrqlfdoo| ghfuhdvlqj lq kroglqj wlph k 1
53
Shufhqwloh ri
w|sh glvwulexwlrq
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54
8 ru 9 |hduv +Wdeoh 5,1 Wkhuhiruh/ lw wdnhv wkhp xs wr4< 809 |hduv wr uhwxuq wr wkh
ex|lqj srlqw1 Frpsduh wkhp/ vd|/ wr wkh frqvxphuv zkr ex| 47 |hdu rog fduv1 Wkhlu
kroglqj wlph lv mxvw 4 |hdu/ dqg wkh| wxuq ryhu pxfk idvwhu= qh{w shulrg doo ri wkhp
uhwxuq wr wkh ex|lqj srlqw1 Dv d uhvxow/ ghpdqg iru 47 |hdu rog fduv lv kljkhu/ dqg vr
lv wkh uhvdoh udwh1 Dv vkrzq lq wkh odvw froxpq ri Wdeoh 5/ wkh kroglqj wlphv dw wkh
h{wuhphv ri wkh w|sh glvwulexwlrq duh vkruwhu wkdq lq wkh plggoh1 Ehfdxvh frqvxphuv
lq wkh plggoh ri wkh w|sh glvwulexwlrq wxuq ryhu vorzo|/ uhvdoh udwhv iru wkh jrrgv wkh|
ex| duh uhodwlyho| orz1
Urxjko| vshdnlqj/ wkh qxpehu ri frqvxphuv zkr ex| d sduwlfxodu ylqwdjh lv lq wkh
qxphudwru ri wkh uhvdoh udwh/ dqg wkhlu kroglqj wlph lv lq wkh ghqrplqdwru153 Kroglqj
wlph lv qrw wkh rqo| idfwru wkdw dhfwv ghpdqg iru d sduwlfxodu ylqwdjh1 Ghpdqg iru
jrrgv ri djh | lv sursruwlrqdo wr wkh wrwdo qxpehu ri frqvxphuv zkrvh ex|lqj srlqw
lv |1 Iru h{dpsoh/ ghpdqg iru 8 |hdu rog jrrgv lv kljk/ ehfdxvh d wrwdo ri ;( ri wkh
srsxodwlrq ex|v 8 |hdu rog jrrgv1 Lq frqwudvw/ ghpdqg iru ; |hdu rog jrrgv lv orzhu/
ehfdxvh rqo| 718( ri frqvxphuv ex| wkhp1
Lw lv dovr wuxh wkdw wkh odujh txdqwlw| ri frqvxphuv dw d sduwlfxodu ex|lqj srlqw
fdq frxqwhudfw wkh hhfw ri vkruw kroglqj wlph/ lq zklfk fdvh wkh uhvdoh udwh qhhg
qrw kdyh d wurxjk dw plggoh djhv1 Wklv lv xvxdoo| wkh fdvh zkhq odujh wudqvdfwlrq
frvwv doprvw suhyhqw uhvdoh dqg kroglqj wlphv gr qrw ydu| d orw dfurvv frqvxphuv1
Zkhq kroglqj wlph lv doprvw wkh vdph iru hyhu|erg|/ wkh txdqwlw| ri frqvxphuv dw
wkh ex|lqj srlqw ehfrphv wkh ghflvlyh idfwru lq ghwhuplqlqj wkh uhvdoh udwh1
Zh zloo qrz wxuq wr frpsdudwlyh vwdwlfv h{huflvhv zklfk khos h{sodlq wkh uhodwlrq0
vkls ehwzhhq d fdu*v uholdelolw| dqg iuhtxhqf| dqg wlplqj ri lwv uhvdoh1
71516
Ghsuhfldwlrq hhfwv
Wkh hhfwv ri idvwhu ghsuhfldwlrq rq xvhg jrrgv sulfhv dqg uhvdoh sdwwhuqv duh lqyhv0
wljdwhg e| lqfuhdvlqj wkh ydoxh ri B iurp ffS wr ffH dqg frpsdulqj wkh uhvxowlqj
htxloleulxp zlwk wkh ehqfkpdun fdvh1 Wkh uhvxowv duh vkrzq rq Iljxuh 91 Fduv wkdw
ghsuhfldwh idvwhu kdyh pruh frqyh{ sulfhv dqg vkruwhu kroglqj lqwhuydov1 Khqfh ohvv
uholdeoh fduv duh wudghg pruh iuhtxhqwo| dqg hduolhu lq olih1
Wkh hylghqfh vkrzv vwurqj vxssruw iru wkhvh suhglfwlrqv1 Sruwhu dqg Vdwwohu +4<<<,
+Wdeohv 9/ : dqg ;, uhsruw wkdw xquholdeoh yhklfohv duh wudghg pruh iuhtxhqwo|1 Wkh|
dovr qg +s1 6, wkdw wkh udwh ri ghfolqh ri d xvhg fdu prgho*v sulfhv lv qhjdwlyho|
dqg vljqlfdqwo| fruuhodwhg zlwk wkh ohqjwk ri rzqhuvkls whqxuh1 Lq wkh prgho/ pruh
frqyh{ sulfhv lpso| vkruwhu kroglqj lqwhuydov1
4<
Li d frqvxphu gudzv d }hur wudqvdfwlrq frvw/ vkh uhwxuqv wr wkh ex|lqj srlqw qh{w shulrg1 Wkdw
lv zk| vrph frqvxphuv gr qrw uhdfk wkhlu vhoolqj srlqw1
53
Revhuyh wkdw wkh qxpehu ri frqvxphuv dw wkh ex|lqj srlqw/ i +k> Vk ,/ dssur{lpdwho| htxdov wr
olp i +k> Vk , @
$3
55
q+k,
=
k
Equilibrium prices
Benchmark case
Resale
rate
0.3
1
Normalized
price
0.8
0.6
0.2
Benchmark
0.4
0.1
0.2
0
5
10
0
15
0
5
10
Age
Faster depreciation
Resale
rate
0.3
Age
15
Decision rules
15
Age
Benchmark
10
0.2
5
0.1
0
5
10
Age
0
15
0.5
1
1.5
Consumer type
Iljxuh 9= Hhfwv ri idvwhu ghsuhfldwlrq
Wkhuh lv dovr hylghqfh wkdw uholdeoh yhklfohv duh wudghg odwhu lq olih1 Dffruglqj wr
Sruwhu dqg Vdwwohu +4<<</ Wdeoh 6,/ wzr pdnhv zlwk wkh kljkhvw uholdelolw| duh Krqgd
dqg Wr|rwd1 Wkh phgldq54 vhoolqj djh iru d xvhg Krqgd ru Wr|rwd lv :14 |hduv1 Lq
frqwudvw/ wkh phgldq vhoolqj djh iru d Srqwldf ru JPF/ wzr ri wkh ohvv uholdeoh pdnhv/
lv 914 |hduv1
Qrw vkrzq rq wkh jxuh lv wkh hhfw ri udlvlqj wkh sulfh ri wkh qhz jrrg/ zklfk
zrunv lq wkh rssrvlwh gluhfwlrq1 Doo rwkhu wklqjv ehlqj htxdo/ pruh h{shqvlyh fduv
kdyh ohvv frqyh{ sulfhv1 Wkhuhiruh/ wkh| duh wudghg ohvv iuhtxhqwo| dqg odwhu lq olih1
Sruwhu dqg Vdwwohu +4<<<, dovr qrwh wklv idfw dqg h{sodlq lw e| wkh srvlwlyh fruuhodwlrq
ehwzhhq lqlwldo sulfh dqg txdolw|1 Wkh dqdo|vlv khuh lpsolhv wkdw wkh hhfw pd| kdyh
ohvv wr gr zlwk txdolw| wkdq zdv ruljlqdoo| wkrxjkw1 Dffruglqj wr wkh prgho/ zkhq d
fdu lv pruh h{shqvlyh/ d kljkhu iudfwlrq ri lwv ruljlqdo sulfh lv sdvvhg rqwr wkh qh{w
rzqhuv155 Wklv pdnhv wkh sulfh vhtxhqfh ohvv frqyh{ dqg uhvdoh ohvv iuhtxhqw1
71517
Zduudqw| hhfwv
H{sludwlrq ri zduudqw| pxvw kdyh dq lpsruwdqw lpsdfw rq uhvdoh sdwwhuqv/ ehfdxvh
rzqhuv dqwlflsdwh uhsdlu frvwv zklfk dhfw wkhlu xwlolw| iurp wkh jrrg1 Lq wkh prgho/
% phdvxuhv wkh ydoxh ri vhuylfh qhw ri uhsdlu h{shqvhv/ vr wkh dssursuldwh zd| wr
54
Wkh phgldq lv frpsxwhg zlwk uhvshfw wr wkh glvwulewxlrq ri uhvdoh udwhv e| djh1 Vrxufh= QSWV
4<<81
55
Wklv uhvxow lv qrw gxh wr wkh dvvxpswlrq ri frqvwdqw olihwlph1 Li olihwlph zhuh hqgrjhqrxv/ pruh
h{shqvlyh fduv zrxog olyh orqjhu/ pdnlqj wkhlu sulfhv hyhq ohvv frqyh{1
56
Resale
rate
0.3
Equilibrium prices
Benchmark case
1
Normalized
price
0.8
0.6
0.2
Benchmark
0.4
0.1
0.2
0
5
10
Age
0
15
0
5
10
Age
15
Decision rules
Warranty expiration
15
Age
Resale
rate
0.3
10
Benchmark
0.2
5
0.1
0
5
10
Age
0
15
0.5
1
1.5
Consumer type
Iljxuh := Hhfwv ri zduudqw| h{sludwlrq
prgho zduudqw| h{sludwlrq zrxog eh wr vxewudfw uhsdlu frvwv iurp % ehjlqqlqj iurp
wkh 7wk |hdu ri yhklfoh*v olih1
Li uhsdlu frvwv duh odujh hqrxjk/56 zduudqw| h{sludwlrq fdq surgxfh d shdn ri uhvdoh
dw wkh h{sludwlrq gdwh/ dv vkrzq rq Iljxuh :1 Kljk0hqg frqvxphuv zkr kdyh odujh
pdujlqdo xwlolw| ri vhuylfh vwduw wr uhvhoo wkhlu jrrgv dw 6 |hduv +qrwh wkh gudpdwlfdoo|
qduurzhu kroglqj lqwhuydov iru wkhvh frqvxphuv,1 Wkh htxloleulxp sulfh ehfrphv pruh
frqyh{/ zlwk d nlqn dw 6 |hduv1 Wkh h{shfwdwlrq ri ixwxuh uhsdlu frvwv orzhuv wkh sulfhv
iru xvhg fduv wkdw duh vwloo rq zduudqw|/ pdnlqj wkh lqlwldo ghsuhfldwlrq ri |rxqj
yhklfohv hyhq idvwhu1 Wkh lqwxlwlrq iru wklv uhvxow lv wkh iroorzlqj1 Wkh ex|huv ri 406
|hdu rog fduv zloo rswlpdoo| krog wkhp iru d uhodwlyho| orqj wlph diwhu wkh zduudqw|
h{sluhv1 Khqfh wkh| h{shfw wr eh uhshdwhgo| klw zlwk uhsdlu frvwv dqg wkhlu zloolqjqhvv
wr sd| ghfuhdvhv1
Zduudqw| h{sludwlrq lv dqrwkhu uhdvrq zk| xquholdeoh fdu prghov pd| eh wudghg
hduolhu lq olih1 Li uhsdlu frvwv duh vljqlfdqw/ uhvdoh ehfrphv frqfhqwudwhg dw wkh gdwh
ri zduudqw| h{sludwlrq1
71518
Wudqvdfwlrq frvw hhfwv
Wudqvdfwlrq frvwv duh dqrwkhu lpsruwdqw ghwhuplqdqw ri uhvdoh udwhv1 Li wudqvdfwlrq
frvwv duh }hur/ hdfk jrrg lv wudghg hyhu| shulrg/ dqg uhvdoh udwh htxdov 4 iru hyhu|
xvhixo ylqwdjh1 Zkhq wudqvdfwlrq frvwv duh lqqlwh/ wkh jrrg lv wudghg li dq rqo| li
wkh frqvxphu gudzv d }hur wudqvdfwlrq frvw1 Wklv lpsolhv wkdw uhvdoh udwhv iru doo
56
Wr jhw d glvwlqfwo| glhuqw kroglqj sdwwhuq/ lw zdv dvvxphg wkdw uhsdlu frvwv uhgxfh { e| 48(1
57
λ=0
1
λ=0.01
1
0.8
0.8
0.8
0.6
0.6
0.6
0.4
0.4
0.4
0.2
0.2
0.2
0
0
0
1
5
λ=0.1
10
15
0
1
5
λ=0.2
10
15
0
0.8
0.8
0.6
0.6
0.6
0.4
0.4
0.4
0.2
0.2
0.2
0
0
1
5
λ=0.6
10
15
0
1
5
λ=0.8
10
15
0
0.8
0.8
0.6
0.6
0.6
0.4
0.4
0.4
0.2
0.2
0.2
0
0
5
10
15
0
5
5
10
15
0
5
10
15
0
5
10
15
1
0.8
0
0
1
0.8
0
λ=0.05
1
10
15
0
λ=0.4
λ=1.0
Iljxuh ;= Uhvdoh udwhv iru glhuhqw wudqvdfwlrq frvw ohyhov1
58
xvhixo ylqwdjhv duh htxdo wr k1
Iljxuh vkrzv krz wudgh lqwhqvlw| ghshqgv rq wudqvdfwlrq frvw ohyho1 Hdfk sorw
fruuhvsrqgv wr d glhuhqw ydoxh ri wudqvdfwlrq frvw ohyho b157 Iru vlpsolflw|/ zh ghsduw
iurp wkh vshflfdwlrq lq +47, dqg dvvxph wkdw b| ' SJ?r| iru doo |1
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