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Electronic copy available at: http://ssrn.com/abstract=1283955
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%hi( p*per -e.e/op( * theor2 o3 re.e*/e- pre3eren5e( o.er one6(o7n *n- other(6 monet*r2 p*2o9(: ;e intro-<5e =more */tr<i(ti5 th*n> ?!"#@!* p*rti*/ or-erinA o.er pre3eren5e(! *n- interpret it 7ith Bno7n p*r*metri5mo-e/(: ;e */(o intro-<5e *n- i//<(tr*te =more Aenero<( th*n> ?!$#@! *p*rti*/ or-erinA o.er opport<nit2 (et(: Ce.er*/ re5ent -i(5<((ion( o3 */tr<i(m3o5<( on t7o p/*2er exten(i.e 3orm A*me( o3 5omp/ete in3orm*tion in 7hi5hthe Er(t mo.er ?FG@ 5hoo(e( * more or /e(( Aenero<( opport<nit2 (et 3or the(e5on- mo.er ?CG@: Here re5ipro5it2 5*n Ie 3orm*/iJe- *( the *((ertion th*t*n !$# 5hoi5e I2 the FG 7i// e/i5it !"# pre3eren5e( in the CG *n-! 3<rKthermore! th*t the e9e5t on pre3eren5e( i( (tronAer 3or *5t( o3 5ommi(ion th*n*5t( o3 ommi(ion I2 FG: ;e (t*te *n- pro.e propo(ition( on the oI(er.*I/e5on(eL<en5e( o3 the(e *((ertion(: %hen 7e te(t tho(e propo(ition( <(inA exi(tKinA -*t* 3rom in.e(tment A*me( 7ith -i5t*tor 5ontro/( *n- Ct*5Be/IerA A*me(*n- ne7 -*t* 3rom Ct*5Be/IerA miniKA*me(: %he te(t re(</t( pro.i-e (<pport3or the theor2 o3 re.e*/e- */tr<i(m:
M:C: Cox! Oni.er(it2 o3 AriJon*! P5oxQe//er:*riJon*:e-<R$: Frie-m*n! Oni.er(it2 o3 C*/i3orni*! C*nt* Cr<J! -*nQ<5(5:e-<RS: C*-ir*P! Oni.er(it2 o3 AriJon*! .(*-ir*PQe5on/*I:*riJon*:e-<:
T:
;h*t *re the 5ontent( o3 pre3eren5e(U Veop/e (<re/2 5*re *Io<t their o7n m*teri*/7e//KIeinA! e:A:! *( proxie- I2 in5ome: AI(tr*5t theor2 *n- 5ommon (en(e h*.e/onA re5oAniJe- the po((iIi/it2 th*t in (ome 5ontext( peop/e */(o 5*re *Io<t other(67e//KIeinA! I<t <nti/ re5ent/2 *pp/ie- 7orB h*( neA/e5te- th*t po((iIi/it2: E.i-en5e3rom the /*Ior*tor2 *n- Ee/- ?*( (<r.e2e- in Fehr *n- XY5hter ?Z[[[@ 3or ex*mp/e@h*( IeA<n to per(<*-e e5onomi(t( to -e.e/op (pe5iE5 mo-e/( o3 ho7 *n- 7hen *per(on6( pre3eren5e( -epen- on other(6 m*teri*/ p*2o9( ?CoIe/! Z[[\@:An-reoni *n- Gi//er ?Z[[Z@ report =-i5t*tor> experiment( in 7hi5h * h<m*n
(<IPe5t -e5i-e( on *n *//o5*tion 3or him(e/3 *n- 3or (ome *non2mo<( other (<IPe5t7hi/e 3*5inA * /ine*r I<-Aet 5on(tr*int: %heir *n*/2(i( 5onErm( 5on(i(ten52 7ith theAener*/iJe- *xiom o3 re.e*/e- pre3eren5e ?XA]V@ 3or * /*rAe m*Porit2 o3 (<IPe5t(:%he2 5on5/<-e th*t */tr<i(m 5*n Ie mo-e/e- *( <ti/it2 m*ximiJinA Ieh*.ior:^n thi( p*per 7e t*Be three 3<rther (tep( -o7n the (*me p*th: Fir(t! 7e 5re*te
nonK/ine*r opport<nit2 (et(: C<5h (et( en*I/e the (<IPe5t to re.e*/ more *Io<tthe tr*-eo9 Iet7een her o7n *n- *nother6( in5ome! e:A:! 7hether her in-i9eren5e5<r.e( h*.e po(iti.e or neA*ti.e (/ope! *n- 7hether the 5<r.*t<re i( Jero or po(Kiti.e: Ce5on-! 7e Ai.e the other (<IPe5t *n initi*/ mo.e th*t 5*n Ie more or /e((
Date _ ;orBinA V*per! #o.emIer Z[[\:;e th*nB Cte.e XPer(t*-! Cte3*n %r*<I *( 7e// *( p*rti5ip*nt( in the ^ntern*tion*/ GeetinA o3
the E5onomi5 C5ien5e A((o5i*tion ?ECA@ Z[[` *n- the #orth Ameri5*n ]eAion*/ ECA GeetinAZ[[` 3or he/p3</ 5omment(:
T
Electronic copy available at: http://ssrn.com/abstract=1283955
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Aenero<(: %hi( *//o7( <( to -i(tinA<i(h 5on-ition*/ */tr<i(mapo(iti.e *n- neA*ti.ere5ipro5it2a3rom <n5on-ition*/ */tr<i(m: ^t */(o *//o7( <( to 5/*ri32 the oI(er.*I/e5on(eL<en5e( o3 5on.ex pre3eren5e( *n- o3 5h*nAe- pre3eren5e(: %hir-! 7e -i(tinKA<i(h *5ti.e 3rom p*((i.e initi*/ mo.e(R i:e:! 7e -i(tinA<i(h *monA *5t( o3 omi((ion!*5t( o3 5ommi((ion! *n- *I(en5e o3 opport<nit2 to *5t! *n- their 5omp*r*ti.e imKp*5t( on re5ipro5it2:;e IeAin in Ce5tion Z I2 -e.e/opinA repre(ent*tion( o3 pre3eren5e( o.er o7n
*n- other(6 in5ome! *n- 3orm*/iJe the i-e* th*t one pre3eren5e or-erinA i( =more*/tr<i(ti5 th*n> ?MAT @ *nother: ;e in5/<-e the po((iIi/it2 o3 neA*ti.e reA*r- 3orthe other6( in5omeR in thi( 5*(e MAT re*//2 me*n( =/e(( m*/e.o/ent th*n:> Cpe5i*/5*(e( in5/<-e the m*in p*r*metri5 mo-e/( o3 other reA*r-inA pre3eren5e( th*t h*.e*ppe*re- in the /iter*t<re:Ce5tion b intro-<5e( opport<nitie( *n- 5hoi5e(! *n- i//<(tr*te( 5on5ept( 7ith (e.K
er*/ t7o p/*2er A*me( o3 5omp/ete in3orm*tion 3rom the re5ent /iter*t<re: Ce5tion` 3orm*/iJe( the i-e* th*t one opport<nit2 (et i( more Aenero<( th*n ?!"#@ *nKother! *n- then <(e( it to 3orm*/iJe re5ipro5it2: Axiom ] *((ert( th*t more Aenero<(5hoi5e( I2 the Er(t mo.er in-<5e more */tr<i(ti5 pre3eren5e( in the (e5on- mo.er:An interpret*tion <rAe- in * pre.io<( p*per ?Cox! Frie-m*n! *n- XPer(t*-! Z[[`@i( th*t pre3eren5e( *re emotion*/ (t*teK-epen-ent! *n- the Er(t mo.er6( Aenero(Kit2 in-<5e( * more Iene.o/ent ?or /e(( m*/e.o/ent@ emotion*/ (t*te in the (e5on-mo.er: Axiom C *((ert( th*t the re5ipro5it2 e9e5t i( (tronAer 3o//o7inA *n *5t o35ommi((ion ?<p(ettinA the (t*t<(KL<o@ th*n 3o//o7inA *n *5t o3 omi((ion ?<pho/-inAthe (t*t<(KL<o@! *n- th*t the e9e5t on pre3eren5e( i( 7e*Be(t 7hen the Er(t mo.eri( <n*I/e to */ter the (t*t<( L<o:Ce5tion \ report( (ome Aener*/ theoreti5*/ propo(ition( on the 5on(eL<en5e( o3
5on.ex pre3eren5e( *n- Axiom( ] *n- C: %o i//<(tr*te the empiri5*/ 5ontent o3 thetheor2! 7e -eri.e te(t*I/e pre-i5tion( 3or the 7e//KBno7n in.e(tment A*me! 7hi5h3e*t<re( * 5omp/ete !"# or-erinA o3 /ine*r opport<nit2 (et(: ;e */(o -eri.ete(t*I/e pre-i5tion( 3or Ct*5Be/IerA -<opo/2 A*me(: %he(e A*me( *re e(pe5i*//2<(e3</ Ie5*<(e * (m*//er o<tp<t I2 the Ct*5Be/IerA ce*-er in-<5e( * more Aenero<(opport<nit2 (et 3or the Fo//o7er! *n- Ie5*<(e the opport<nit2 (et( h*.e * p*r*Io/i5(h*pe th*t en*I/e( the Fo//o7er to re.e*/ * 7i-e r*nAe o3 po(iti.e *n- neA*ti.etr*-eo9( Iet7een o7n in5ome *n- ce*-er6( in5ome: Come Be2 pre-i5tion( in.o/.e *.*ri*nt A*me! 5*//e- the Ct*5Be/IerA miniKA*me! in 7hi5h the ce*-er h*( on/2 t7o*/tern*ti.e o<tp<t 5hoi5e(! one o3 7hi5h i( 5/e*r/2 more Aenero<( th*n the other:%he next three (e5tion( te(t the i//<(tr*ti.e pre-i5tion( on exi(tinA in.e(tment
A*me -*t*! on exi(tinA Ct*5Be/IerA -*t*! *n- on ne7 Ct*5BeIerA miniKA*me -*t*:;ithin the /imit*tion( o3 the -*t*! the re(</t( *re *// 5on(i(tent 7ith the pre-i5tion(:%he /*(t (e5tion (<mm*riJe( *n- point( to 3<rther empiri5*/ *n- theoreti5*/ 7orB:A// 3orm*/ proo3( *n- other m*them*ti5*/ -et*i/( *re 5o//e5te- in Appen-ix A:^n(tr<5tion( to (<IPe5t( in the miniKCt*5Be/IerA A*me *ppe*r in Appen-ix d:
Z:
cet Y = (Y!; Y"; :::; Y! ) ! !# repre(ent the p*2o9 .e5tor in * A*me th*t p*2(e*5h o3N " 2 p/*2er( * nonKneA*ti.e in5ome: A-mi((iI/e pre3eren5e( 3or e*5h p/*2eri *re (mooth *n- 5on.ex or-erinA( on the po(iti.e orth*nt #!# th*t *re (tri5t/2in5re*(inA in o7n in5ome Y": %he (et o3 *// *-mi((iI/e pre3eren5e( i( -enote- :
]ESEAcE$ Ac%]O^CG b
An2 p*rti5</*r pre3eren5e $ ! 5*n Ie repre(ente- I2 * (mooth <ti/it2 3<n5tionu : #!# % # 7ith po(iti.e i#$ p*rti*/ -eri.*ti.e %&
%'!= u'! * 0: %he other Er(t
p*rti*/ -eri.*ti.e( *re Jero 3or (t*n-*r- (e/E(h pre3eren5e(! I<t 7e *//o7 3or thepo((iIi/it2 th*t the2 *re po(iti.e in (ome reAion( ?7here the *Aent i( =Iene.o/ent>@*n- neA*ti.e in other( ?7here (he i( =m*/e.o/ent>@:;e (h*// 3o5<( on t7oKp/*2er exten(i.e 3orm A*me( o3 5omp/ete in3orm*tion! *n-
to (tre*m/ine not*tion 7e (h*// -enote o7n ?=m2>@ in5ome I2 Y" = m *n- the otherp/*2er6( ?=2o<r>@ in5ome I2 Y!" = y: %h<( pre3eren5e( *re -eEne- on the po(iti.eL<*-r*nt #"# = f(m; y) : m; y " 0': %he p/*2er6( m*rAin*/ r*te o3 (<I(tit<tion!$%(m; y) = u(=u) i(! o3 5o<r(e! the neA*ti.e o3 the (/ope o3 the in-i9eren5e5<r.e thro<Ah the Ai.en point: On3ort<n*te/2! the !$% i( not 7e// -eEne- *tpoint( 7here the *Aent i( (e/E(h! *n- -i.erAe( to +( *n- I*5B 3rom )( 7hen7e p*(( 3rom (/iAht Iene.o/en5e to (/iAht m*/e.o/en5e: %here3ore it i( 5on.enientto 7orB 7ith 7i//inAne(( to p*2! &#' = 1=!$%! the *mo<nt o3 o7n p*2o9 the*Aent i( 7i//inA to Ai.e <p in or-er to in5re*(e the other *Aent6( p*2o9 I2 * <nit:&#' mo.e( 3rom (/iAht/2 po(iti.e thro<Ah Jero to (/iAht/2 neA*ti.e 7hen the *AentAoe( 3rom (/iAht Iene.o/en5e to (/iAht m*/e.o/en5e:;h*t (ort o3 3*5tor( miAht *9e5t&#'U A prime 5*n-i-*te i( re/*ti.e in5ome!
*( me*(<re- 3or nonKJero *//o5*tion( in #"# I2 the r*tio o3 other6( in5ome to o7nin5ome! d = y=m: ^t i( e*(i/2 (ho7n ?(ee Appen-ix A:T@ th*t on/2 re/*ti.e in5omed m*tter( 3or homotheti5 pre3eren5e(! i:e:! &#' i( 5on(t*nt */onA e*5h r*2 R* =f(t; td) : t * 0' * #"# 7hen pre3eren5e( *re homotheti5:^t i( int<iti.e th*t &#' -e5re*(e( in d! th*t i(! ^6m 7i//inA to p*2 /e(( to
in5re*(e 2o<r in5ome 7hen ^6m re/*ti.e/2 poor: %he int<ition i( 3orm*/iJe- in the5on.exit2 *((<mption impo(e- e*r/ier: ]e5*// th*t pre3eren5e( *re 5on.ex i3 e*5h<pper 5onto<r (et ?i:e:! the (et o3 *//o5*tion( pre3erre- to *n2 Ai.en *//o5*tion@ i( *5on.ex (<I(et o3 #"#: A L<*ntit*ti.e me*(<re o3 5on.exit2 i( pro.i-e- I2 5<r.*t<reo3 the in-i9eren5e 5<r.e(! <(inA Er(t *n- (e5on- p*rti*/ -eri.*ti.e( o3 * <ti/it23<n5tion u repre(entinA the pre3eren5e( ?e:A:! Xr*2! Teef! pp:T`KTf@: C<r.*t<rei( the re5ipro5*/ o3 the r*-i<( o3 the 5ir5/e th*t i( (e5on-Kor-er t*nAent to thein-i9eren5e 5<r.e thro<Ah * Ai.en point *n- i( Ai.en I2
?Z:T@ ( =u((u
") ) 2u()u(u) + u))u"((u"( + u
"))$+"
%he 5on.exit2 *((<mption i( th*t ( + 0 *t e.er2 point #"#: #eA*ti.e ( rege5t(-e5re*(inA &#'! e:A:! the (/ope mo.e( to7*r-( [ *( * Iene.o/ent p/*2er6( o7nin5ome in5re*(e( */onA *n in-i9eren5e 5<r.e: h3 5o<r(e ( = 0 in * reAion 7herein-i9eren5e 5<r.e( *re (tr*iAht /ine(! *n- more neA*ti.e ( me*n( th*t the &#'5h*nAe( more L<i5B/2 7ith 5h*nAe( in re/*ti.e in5ome d */onA *n in-i9eren5e 5<r.e:#ote th*t Ioth&#' *n- ( *re intrin(i5 3or pre3eren5e(: %h*t i(! i3 7e 5hoo(e
*nother <ti/it2 3<n5tion w = h , u to repre(ent the (*me pre3eren5e( ?(o h"(t) * 0-t ! Range(u)@! then <(inA w in the 5omp<t*tion( 3or &#' *n- ( Ai.e( <( the(*me .*/<e( th*t 7e Aet <(inA u:;e *re no7 prep*re- to 3orm*/iJe the i-e* th*t one pre3eren5e or-erinA on #"#
i( more */tr<i(ti5 th*n *nother: %7o -i9erent pre3eren5e or-erinA( A;/ ! o.erin5ome *//o5*tion .e5tor( miAht repre(ent the pre3eren5e( o3 t7o -i9erent p/*2er(!or miAht repre(ent the pre3eren5e( o3 the (*me p/*2er in t7o -i9erent emotion*/(t*te( ?Cox! Frie-m*n! *n- XPer(t*-! Z[[`@:
` ! ! A#$
&,-./0/1. 2313 For * Ai.en -om*in * #"# 7e (*2 th*t A !)# / on i3&#'#(m; y) "&#'$(m; y); 3or *// (m; y) ! :
%he i-e* i( (tr*iAht3or7*r-: ^n the Iene.o/en5e 5*(e ?7here <ti/it2 i( monotonein5re*(inA in y@ more */tr<i(ti5 th*n ?!)#@ me*n( th*t A h*( (h*//o7er in-i9erKen5e 5<r.e( th*n / in (m; y) (p*5e! (o A in-i5*te( * 7i//inAne(( to p*2 more m th*n/ 3or * <nit in5re*(e in y: ^n the m*/e.o/en5e 5*(e!&#' i( /e(( neA*ti.e 3or A! (oit in-i5*te( * /e((er 7i//inAne(( to p*2 3or * <nit -e5re*(e in y:h3 5o<r(e! !)# i( * p*rti*/ or-erinA on ! not * tot*/ or-erinA! 3or nontri.i*/
-om*in( th*t 5ont*in more th*n * (inA/e point: ;hen pre3eren5e( *re homoKtheti5 then it (<i5e( to 5he5B 3or !)# on * thin (<I(et o3 ! t2pi5*//2 * (inA/ein-i9eren5e 5<r.e: ;hen no p*rti5</*r -om*in i( in-i5*te-! the !)# or-erinAi( <n-er(too- to re3er to the entire po(iti.e orth*nt = #"#:
"56789, 2323 cine*r ^neL<*/it2K*.er(e Vre3eren5e( ?3or N = 2 on/2R Fehr *n-C5hmi-t! Teee@: cet pre3eren5e( J = A;/ Ie repre(ente- I2 u% (m; y) = (1 +7% )m) 7% y; 7here
7% = 8% ; !" m 9 y
= ):% ; !" m " y;
*n- 0 9 :% + 8% ! 0 9 :% 9 1: Ctr*iAht3or7*r-/2! A !)# d i9 7# + 7$:
"56789, 2333 #on/ine*r ^neL<*/it2K*.er(e Vre3eren5e( ?3or N = 2; do/ton *n-h5Ben3e/(! Z[[[@: cet pre3eren5e( J = A;/ Ie repre(ente- I2 u% (m; y) = ;% (m;<);7here
< = m=(m+ y); !" m+ y * 0
= 1=2; !" m+ y = 0
^t 5*n Ie e*(i/2 .eriEe- th*t A !)# / i9 ;#!=;#" + ;$!=;$":
"56789, 2343 j<*(i G*xiKmin Vre3eren5e( ?3or N = 2; Ch*rne(( *n- ]*Iin!Z[[Z@: cet pre3eren5e( J = A;/ Ie repre(ente- I2
u% (m; y) = m+ =% (1) >% )y; !" m 9 y;
= (1) >% =% )m+ =% y; !" m " y
*n- =% ! [0; 1]! >% ! (0; 1): ^t i( (tr*iAht3or7*r- ?*/tho<Ah * Iit te-io<(@ to .eri32th*t A !)# / i9
=# " =$max!
1
1 + (># ) >$)=$;1) >$1) >#
":
"56789, 2353 EAo5entri5 A/tr<(im ?CES) Vre3eren5e( ?Cox *n- C*-ir*P! Z[[`@:cet pre3eren5e( JkA;/ Ie repre(ente- I2
u% (m; y) =1
8(m, + 7% y
,); !" 8 ! ()(; 1)!f0'
= my-! ; !" 8 = 0:
^3 0 9 7$ + 7# then A !)# d: SeriE5*tion i( (tr*iAht3or7*r-_ &#'% =7% (m=y)
!!,;J =A;d imp/2 &'##=&#'$ = 7#=7$ " 1: >EAo5entri5it2> imKp/ie( WTP (m;m) + 1:
]ESEAcE$ Ac%]O^CG \
%he exponent 8 + 1 -etermine( the 5<r.*t<re *n- hen5e the 5on.exit2 o3 pre3Keren5e(: Ctr*iAht3or7*r- */AeIr* 2ie/-(
( =7(8) 1)m,#!y,#!(m, + 7y,)
((m,y)" + (7my,)")32
+ 0:
hn * r*2 R* = f(m;md) : m * 0' 7e h*.e
( =(8) 1)d,#!7(d,7 + 1)m(d" + (d,7)")
32
+ 0:
%h<( the 5<r.*t<re -e5re*(e( ?in *I(o/<te .*/<e@ */onA * Ai.en r*2 *( 1=m! i:e:!m( i( 5on(t*nt */onA the r*2: Appen-ix A:Z (ho7( th*t the (*me i( tr<e 3or *n2homotheti5 pre3eren5e(: Hen5e re/*ti.e 5<r.*t<re m( (ometime( i( more <(e3</th*n 5<r.*t<re (:%he theoreti5*/ /iter*t<re on (o5i*/ pre3eren5e( h*( pre.io<(/2 Ieen 5h*r*5teriJe-
I2 (pe5i*/ *((<mption( th*t *ppe*r to Ie in5on(i(tent 7ith the 5/*((i5*/ *ppro*5hto pre3eren5e ?*n- -em*n-@ theor2 ?Hi5B(! TebeR C*m<e/(on! Te`f@: %he pre5e-inAex*mp/e( he/p to 5/*ri32 thi( L<e(tion: %he /ine*r *n- non/ine*r ineL<*/it2 *.er(ionmo-e/(! L<*(iKm*ximin mo-e/! *n- eAo5entri5 */tr<i(m *// h*.e in-i9eren5e 5<r.e(th*t *re 5on.ex to the oriAin: %h<( the2 ret*in * 5entr*/ 5h*r*5teri(ti5 o3 5/*((i5*/pre3eren5e theor2_ 5on.ex <pper 5onto<r (et(: Ctri5t ineL<*/it2 *.er(ion re.er(e(the 5/*((i5*/ monotoni5it2 ?>more i( pre3erre- to /e((>@ *((<mption in the reAion7here one6( o7n in5ome i( (m*//er: For #kZ! the m*xiKmin propert2 i( imp/ie-I2 5on.exit2 *n- monotoni5it2: A pre3eren5e 3or ei5ien52 ?or /*rAer tot*/ o3 *//*Aent(6 p*2o9(@ i( 5on(i(tent 7ith *// o3 the pre5e-inA p*r*metri5 mo-e/(! *n- there.e*/e- */tr<i(m mo-e/! in (o 3*r *( ;%V 5*n Ie po(iti.e *n- /e(( th*n the nee-to p*2 in the re/e.*nt opport<nit2 (et:
b:
$eEne *n opport<nit2 (et F ?or (2non2mo<(/2! * 3e*(iI/e (et or I<-Aet (et@*( * 5on.ex 5omp*5t (<I(et o3 #"#: F i( 5/o(e- ?*( * 5omp*5t (et in #"#@ *n-there3ore it 5ont*in( it( #"#KIo<n-*r2! -enote- EF R in-ee- F i( the 5on.ex h<// o3EF : Con.exit2 o3 F me*n( th*t e*5h Io<n-*r2 point h*( * (<pportinA h2perp/*ne?i:e:! t*nAent /ine@ -eEne- I2 *n o<t7*r-KpointinA norm*/ .e5tor! *n- F i( 5ont*ine-in * 5/o(e- neA*ti.e h*/3(p*5eR (ee 3or ex*mp/e ]o5B*3e//*r! Tef[! pp:T[[: At (omeIo<n-*r2 point( F ?in3orm*//2 5*//e- 5orner( or BinB(@ the (<pportinA h2perp/*nei( not <niL<eR ex*mp/e( 7i// Ie note- /*ter:At reA</*r Io<n-*r2 point( there i( * <niL<e (<pportinA h2perp/*ne *n- the
imp/i5it 3<n5tion theorem A<*r*ntee( * (mooth 3<n5tion f 7ho(e i(oL<*nt -eEne(the Io<n-*r2 /o5*//2: %he m*rAin*/ r*te o3 tr*n(3orm*tion!$# 5*n Ie expre((e-*( * r*tio o3 the Er(t p*rti*/ -eri.*ti.e(! ex5ept 7hen the t*nAent i( .erti5*/: ;eo3ten nee- to 7orB ne*r .erti5*/ t*nAent(! (o 7e <(e the nee- to p*2 ?*#'@! -eEne-*( *#'(F) = 1=!$#(F) = f)=f(: %he *#' i( (inA/eK.*/<e- ex5ept *t BinB(*n- 5orner( o3 the Io<n-*r2! 7here it( .*/<e( /ie in (ome inter.*/:C<r.*t<re 5*n */(o Ie -eEne- *t reA</*r Io<n-*r2 point(! <(inA the (*me 3orm</*
?T@ 3or( 7ith u rep/*5e- I2 f : AA*in( *n-*#' *re intrin(i5! in-epen-ent o3 the
l ! ! A#$
5hoi5e f <(e- to repre(ent the Io<n-*r2 (eAment: Appen-ix A (ho7( th*t 5on.exopport<nit2 (et( h*.e nonneA*ti.e 5<r.*t<re *t *// reA</*r Io<n-*r2 point(:T
Come ex*mp/e( m*2 he/p Ex i-e*(:
"56789, 3313 Ct*n-*r- I<-Aet (et: cet F =#(m; y) ! #"# : m+ py + I
$3or
Ai.en p; I * 0: %hen EF 5on(i(t( o3 portion( o3 the *xe( toAether 7ith the /ine(eAment
#(m; y) ! #"# : m+ py = I
$! *( (ho7n in FiA<re T: %he *#' i( p */onA
the I<-Aet /ine! i( 0 */onA the y *xi( *n- i( ( */onA the mK*xi(: *#' *((<me( *//.*/<e( o<t(i-e the inter.*/ (0; p) *t the 5orner (0; I=p)! *n- t*Be( *// .*/<e( in theinter.*/ [p;+() *t the 5orner (I; 0) ! EF : A( <(<*/! 5<r.*t<re i( not -eEne- *tthe 5orner(! 7hi/e *t *// reA</*r Io<n-*r2 point( ( = 0:
"56789, 3323 ]inA te(t ?cieIr*n-! Tee`R (ee */(o Connem*n(! .*n $iPB *n- .*n;in-en! Z[[\@: cet F =
#(m; y) ! #"# : m" + y" + R"
$3or Ai.en R * 0! *( (ho7n
in FiA<re Z:Z hn the 5ir5</*r p*rt o3 the Io<n-*r2! *#' i( y=m *n- the 5<r.*t<rei( 1=R:
"56789, 3333 O/tim*t<m A*me ?Xmth! C5hmittIerAer! *n- C5h7*rJe! TenZ@: %here(pon-er6( opport<nitie( in the .10 </tim*t<m A*me 5on(i(t o3 t7o i(o/*te- point(_the oriAin (0; 0) *n- the propo(*/ (x; 10)x): Cin5e thi( (et i( not 5on.ex it -oe(n6tL<*/i32 *( *n opport<nit2 (et I2 o<r -eEnition:
"56789, 3343 ^n.e(tment A*me ?derA! $i5Bh*<t! *n- G5C*Ie! Tee\@: %he Fir(tGo.er ?FG@ *n- Ce5on- Go.er ?CG@ e*5h h*.e *n initi*/ en-o7ment o3 oT[: %heFG (en-( *n *mo<nt s ! [0; 10] to CG! 7ho re5ei.e( 3s: %hen the CG ret<rn( *n*mo<nt r ! [0; 3s] to the FG! re(</tinA in p*2o9( m = 10 + 3s ) r 3or CG *n-y = 10 ) s + r 3or FG: %he FG6( 5hoi5e o3 s (e/e5t( the CG6( opport<nit2 (etF. =
#(m; y) ! #"# : m + 10 + 3s; 10) s + y + 10 + 2s;m+ y + 20 + 2s
$: FiA<re
b (ho7( F. 3or s = 3; 9: C<r.*t<re ( = 0 on e*5h (eAment o3 the Io<n-*r2! *n-*#' = 1 on the (eAment o3 the Io<n-*r2 5orre(pon-inA to r ! (0; 3s):
"56789, 3353 Goon/iAhtinA A*me ?AIIinB! ^r/enI<(5h! *n- ]enner! Z[[[@: ^n thi(.*ri*nt on the in.e(tment A*me! the FG (en-( s ! [)5; 10] to CG! 7ho re5ei.e(g(s) = 3s 3or po(iti.e s *n- g(s) = s 3or neA*ti.e s: %hen the (e5on- mo.ertr*n(3er( t ! [!!%#.$ ; 10+ g(s)] re(</tinA in nonKneA*ti.e p*2o9( m = 10+ g(s)) 1t1*n- y = 10)s+t 3or po(iti.e t *n- y = 10)s+3t 3or neA*ti.e t; *( (ho7n in FiA<re`: %he (e5on- mo.er6( opport<nit2 (et i( the 5on.ex h<// o3 the 3o<r 5orner point((m; y) = (0; 0); (10 + g(s)) (10) s)=3; 0); (10 + g(s); 10) s); *n- (0; 20 + 2s): %he*#' */onA the Io<n-*r2 o3 the opport<nit2 (et i( 1 *Io.e *n- )1=3 Ie/o7 theEr(t mo.er6( I<-Aet /ine! i( 0 */onA the y *xi(! *n- i( ( */onA the mK*xi(: AA*in!5<r.*t<re *t *// reA</*r Io<n-*r2 point( i( ( = 0:
"56789, 3363 Vo7er to t*Be A*me ?do(m*n *n- .*n ;in-en! Z[[Z@: %he pt*Be*<thorit2p p/*2er 5hoo(e( * t*Be r*te M ! [0; 1]: %hen the re(pon-er 7ith in5ome I5hoo(e( * -e(tr<5tion r*te 1 ) >: %he re(</tinA p*2o9( *re m = (1 ) M)>I 3or the
T;h2 po(iti.e 5<r.*t<re 3or 5on.ex opport<nit2 (et( I<t neA*ti.e 5<r.*t<re 3or 5on.ex pre3Keren5e(U hne *n(7er i( th*t the opport<nit2 (et i( the ?inter(e5tion o3@ /o7er 5onto<r (et( o3 the K3<n5tion(! 7hi/e 5on.ex pre3eren5e( re3er to the <pper 5onto<r (et( o3 :
Z^n the oriAin*/ (t<-ie( !" # ! $ ! % ! ! !
]ESEAcE$ Ac%]O^CG f
re(pon-er *n- y = M>I 3or the t*Be *<thorit2: %h<(! 7ith 3ree -i(po(*/ the re(ponK-er6( opport<nit2 (et i( the 5on.ex h<// o3 three point(_ the oriAin (0; 0); (0; MI) *n-((1) M)I; MI)! *( (ho7n in FiA<re \:
"56789, 3373 Xi3t ex5h*nAe /*Ior m*rBet( ?Fehr! qir5h(teiAer! *n- ]ie-/! Teeb@:%he emp/o2er o9er( * 7*Ae w * 0 *n- the 7orBer then 5hoo(e( *n e9ort /e.e/ e * 07ith * L<*-r*ti5 5o(t 3<n5tion c(e): %he En*/ p*2o9( *re m = w ) c(e) 3or the7orBer *n- y = ke)w 3or the emp/o2er! 7here the pro-<5ti.it2 p*r*meter k = 10in * t2pi5*/ A*me: ;ith 3ree -i(po(*/ the 7orBer6( opport<nit2 (et i( (imi/*r to the(e5on- mo.er6( in the in.e(tment A*me! ex5ept th*t the northe*(tern Io<n-*r2 i(* p*r*Io/i5 *r5 in(te*- o3 * (tr*iAht /ine o3 (/ope )1: A/(o! i3 the emp/o2er o9er(* 7*Ae in ex5e(( o3 hi( en-o7ment ?= 10 in FiA<re l @ then the opport<nit2 (etin5/<-e( p*rt o3 the L<*-r*nt rm * 0 * ys: ^t i( (tr*iAht3or7*r- I<t * Iit me((2 toexten- the -eEnition o3 opport<nit2 (et to in5/<-e (<5h po((iIi/itie(:
"56789, 3383 CeL<enti*/ SCG p<I/i5 Aoo- A*me 7ith t7o p/*2er(: E*5h p/*2erh*( initi*/ en-o7ment I: FG 5ontriI<te( c! ! [0; I] to the p<I/i5 Aoo-: CGoI(er.e( c! *n- then 5hoo(e( hi( 5ontriI<tion c" ! [0; I]: E*5h <nit 5ontriI<te- h*(* ret<rn o3 a ! (0:5; 1]! (o the En*/ p*2o9( *re m = I + ac! ) (1) a)c" 3or CG *n-y = I + ac" ) (1) a)c! 3or FG: ;ith 3ree -i(po(*/ 3or CG! CG6( opport<nit2 (et i(the 5on.ex h<// o3 the 3o<r point( (m; y) = (I+ac!; 0); (I+ac!; I) (1)a)c!); (aI+ac!; (1 + a)I ) (1) a)c!) *n- (0; (1 + a)I ) (1) a)c!)! *( (ho7n in FiA<re f: A/onAthe V*reto 3rontier! *#' i( 5on(t*nt *t (1) a)=a:
"56789, 3393 Ct*5Be/IerA Fo//o7er6( hpport<nit2 Cet ?e:A:! S*ri*n! TeeZ@: ConK(i-er * -<opo/2 7ith Jero Exe- 5o(t! 5on(t*nt *n- eL<*/ m*rAin*/ 5o(t! *n- nontri.Ki*/ /ine*r -em*n-: ;itho<t 3<rther /o(( o3 Aener*/it2 one 5*n norm*/iJe (o th*t theproEt m*rAin ?pri5e min<( m*rAin*/ 5o(t@ i( M = 24) q
") q
#! 7here q
"! [0; 24]
i( the ce*-er6( o<tp<t 5hoi5e *n- q#! [0; 24 ) q
"] i( the Fo//o7er6( o<tp<t to Ie
5ho(en: %h<( p*2o9( *re m = Mq#*n- y = Mq
": %he Fo//o7er6( opport<nit2 (et
there3ore i( Io<n-e- I2 * p*r*Io/i5 *r5 openinA to7*r-( the yK*xi(! *( (ho7n inFiA<re n: A 5*/5</*tion o3 *#' *n- 5<r.*t<re *ppe*r( in Appen-ix A:`: On/iBethe e*r/ier ex*mp/e(! the *#' .*rie( (mooth/2 3rom neA*ti.e to po(iti.e .*/<e(*/onA the Io<n-*r2 o3 the opport<nit2 (et: A((<minA 3ree -i(po(*/ I2 the ce*-erimp/ie( th*t the opport<nit2 (et i( the 5on.ex h<// o3 the *r5 in #"#:
`:
]e5ipro5it2 i( Be2 to o<r *n*/2(i(: %he i-e* i( th*t more Aenero<( 5hoi5e( I2 onep/*2er in-<5e more */tr<i(ti5 pre3eren5e( in * (e5on- p/*2er: %o 3orm*/iJe! 5on(i-er* t7o per(on exten(i.e 3orm A*me o3 5omp/ete in3orm*tion in 7hi5h the Er(t mo.er?FG@ 5hoo(e( *n opport<nit2 (et C ! 2! *n- the (e5on- mo.er ?CG@ 5hoo(e(the p*2o9 .e5tor (m; y) ! C: ^nt<iti.e/2! opport<nit2 (et G i( more Aenero<( th*n?!"#@ opport<nit2 (et F i3 it i( oIt*ine- I2 (hrinBinA the y)*xi( ?FG6( potenti*/p*2o9(@ *n- (tret5hinA the mK*xi( ?CG6( potenti*/ p*2o9(@! or I2 (imp/2 t*BinA */*rAer (et: ;e oIt*in * p*rti*/ or-erinA !"# on the (<I(et( o3 #"# <(inA
&,-./0/1. 4313 hpport<nit2 (et G * #"# i( more Aenero<( th*n opport<nit2 (etF i3 G 5ont*in( "F 3or (ome (mooth tr*n(3orm*tion " : #"# )% #"# (<5h th*t
n ! ! A#$
(m; y) 3)% (R(m); S(y)) 7ith R(0) " 0 " S(0)! R"(m) " 1 *n- 0 + S"(y) + 1: ^n thi(5*(e 7e 7rite G !"# F:
^niti*//2! the (e5on- mo.er Bno7( the 5o//e5tion 2 o3 po((iI/e opport<nit2 (et(:Vrior to her *5t<*/ 5hoi5e (he /e*rn( the *5t<*/ opport<nit2 (et C ! 2; *n- *5L<ire(pre3eren5e( A/ : ]e5ipro5it2 i( 5*pt<re- 3orm*//2 in$5/17 !3 Let the 'rst mover choose the actual opportunity set for the secondmover from the collection 2: If F;G ! 2 and G !"# F , then A0 !)# A1 :%here i( * tr*-ition*/ -i(tin5tion Iet7een (in( o3 5ommi((ion ?*5ti.e 5hoi5e@ *n-
(in( o3 omi((ion ?ret*ininA the (t*t<( L<o@: h3 5o<r(e! (ometime( there i( no 5hoi5e*t *// *n- the (t*t<( L<o 5*nnot Ie */tere-: ^nt<iti.e/2! the (e5on- mo.er 7i//re(pon- more (tronA/2 to Aenero<( ?or <nAenero<(@ 5hoi5e( th*t o.ert<rn the (t*t<(L<o th*n to tho(e th*t <pho/- it! *n- 7i// re(pon- /e*(t 7hen the Er(t mo.er h*(no re*/ 5hoi5e:b %he(e -i(tin5tion( *re 5*pt<re- 3orm*//2 in$5/17 *3 Let the 'rst mover choose the actual opportunity set G for the secondmover from a collection 2! 8ith G !"# F for some F ! 2: Let A0;A0" andA0$ respectively denote the second mover9s ac:uired preferences 8hen F is the status:uo, 8hen G is the status :uo, and 8hen the choice set is the singleton 2 = fG':Then A0 !)# A0" !)# A0$ : =n the other hand, if the 'rst mover chooses theless generous set F ! then the ac:uired preferences satisfy A1 $ !)# A1" !)#A1 :;e 7i// (*2 th*t either Axiom holds strictly i3 the ineL<*/itie( in the !)#
-eEnition ?Z:T@ *n- the !"# -eEnition ?`:T@ *re (tri5t:^t (ho</- Ie emph*(iJe- th*t the re5ent pre3eren5e mo-e/( note- in Ex*mp/e(
?Z:b K Z:l@ h*.e no room 3or Axiom( R *n- S: ^n tho(e mo-e/( pre3eren5e( *re*((<me- Exe-! <n*9e5te- I2 more or /e(( Aenero<( opport<nit2 (et( 5ho(en I2 theEr(t mo.er: A5t<*/ 5hoi5e( I2 * Er(t mo.er *re not 5entr*/ e.en in the pre5ipro5it2pmo-e/( o3 Ch*rne(( *n- ]*Iin ?Z[[Z! Appen-ix@! F*/B *n- Fi(5hI*5her ?Z[[\@! *n-$<37enIerA *n- qier(teiAer ?Z[[`@: %ho(e mo-e/( 3o5<( on hiAherKor-er Ie/ie3(reA*r-inA other p/*2er(6 intention( ?or! in ce.ine ?Teen@! reA*r-inA other p/*2er(6t2pe(@: Cox! Frie-m*n! *n- XPer(t*- ?Z[[`@ imp/i5it/2 5on(i-er Axiom ]! I<t on/27ithin the p*rti5</*r p*r*metri5 3*mi/2 o3 CEC <ti/it2 3<n5tion( note- in Ex*mp/eZ:Z:#*t<r*/ !"# or-erinA( *re 3*ir/2 5ommon: For ex*mp/e! 7ith the (t*n-*r-
I<-Aet (et in EA<re ?b:T@! *n in5re*(e in o7n in5ome I toAether 7ith * re*/ in5re*(ein the pri5e o3 tr*n(3er( ?(o I=p -e5re*(e(@ /e*-( to * more Aenero<( I<-Aet (et! *(i//<(tr*te- in EA<re e: ^n-ee-! R"(m) i( (imp/2 the in5ome r*tio *n- *n- S" 9 1rege5t( the -e5re*(e in I=p: ciBe7i(e! it i( 5/e*r 3rom EA<re( ?bKf@ th*t /*rAer s inthe ^n.e(tment *n- Goon/iAhtinA A*me(! (m*//er t*Be r*te T in the Vo7er to %*BeA*me! /*rAer I in the Xi3t Ex5h*nAe c*Ior G*rBet *n- * /*rAer 5ontriI<tion c! inthe SCG p<I/i5 Aoo-( A*me *// 5re*te !"# opport<nitie( 3or the (e5on- mo.er:d<t * 3e7 min<te( (t<-2 o3 tho(e EA<re( re.e*/( th*t re5ipro5it2 *n- 5on.exK
it2 7i// Ie -ii5</t to -i(ent*nA/e: ^n the ^n.e(tment A*me! 3or ex*mp/e! /*rAer smo.e( the (e5on- mo.er6( initi*/ en-o7ment -o7n */onA the -*(he- /ine! in5re*(KinA hi( re/*ti.e in5ome: ^n-ee-! the r*2 thro<Ah the en-o7ment point 3or s = 2h*( (/ope d = 8=16 = 1=2! 5omp*re- to d = 5=25 = 1=5 3or s = 5: Hen5e i3 the
b%hi( int<ition Aoe( I*5B *t /e*(t to A-*m Cmith6( Theory of Moral Sentiments! Tf\e! p: TnT:
]ESEAcE$ Ac%]O^CG e
(e5on- mo.er6( pre3eren5e( *re (tri5t/2 5on.ex *n- homotheti5 then * /*rAer s imKp/ie( Are*ter&#' e.en 7hen tho(e pre3eren5e( *re not *t *// *9e5te- I2 the Er(tmo.er6( more Aenero<( 5hoi5e: %he other A*me( */(o 5ong*te 5on.exit2 *n- re5iKpro5it2: %he <n-er/2inA proI/em i( th*t more Aenero<( 5hoi5e( I2 -eEnition 5re*teIetter re/*ti.e opport<nitie(! hen5e /o7er d *n- ?I2 5on.exit2@ Are*ter&#':
\:
A( in (t*n-*r- re.e*/e- pre3eren5e theor2! o<r m*int*ine- *((<mption i( th*te.er2 p/*2er */7*2( 5hoo(e( * mo(t pre3erre- point in the opport<nit2 (et F : d25on.exit2! (<5h point( 3orm * 5onne5te- (<I(et o3 the Io<n-*r2 o3 F ! *n- i3 eitherpre3eren5e( A or opport<nitie( F *re (tri5t/2 5on.ex then th*t (<I(et i( * (inA/eton!i:e:! there i( * <niL<e 5hoi5e F ! EF : ^n thi( 5*(e *// point( in F nfF' *re re.e*/e-to Ie on /o7er AKin-i9eren5e 5<r.e( th*n F: %he empiri5*/ pre-i5tion i( th*t noother I<n-/e in F 7i// e.er Ie 5ho(en 7hen F i( *.*i/*I/e:#ot *// Io<n-*r2 point( *re 5*n-i-*te( 3or 5hoi5e in o<r (et <p: %he Er(t re(</t
i( th*t! -<e to (tri5t monotoni5it2 in o7n p*2o9 m! on/2 =e*(tern> point( 7i// Ie5ho(en! (in5e the2 h*.e /*rAer o7n p*2o9: %o 3orm*/iJe! -eEne the e*(tern Io<n-*r2*( E2F = f(m; y) ! F : -x * m; (x; y) =! F': %he #orth point N1 *n- the Co<thpoint S1 *re the point( in E2F 7ith re(pe5ti.e/2 the /*rAe(t *n- the (m*//e(t y5omponent:
Proposition \:T. C<ppo(e th*t either pre3eren5e( A or the opport<nit2 (et F *re(tri5t/2 5on.ex! *n- /et F Ie the A)5ho(en point in F: %hen F ! E2F :
A// proo3( *re 5o//e5te- in Appen-ix A:
%he next re(</t (ho7( th*t! *( *-mi((iI/e pre3eren5e( Ao 3rom m*xim*//2 m*/e.oK/ent thro<Ah ne<tr*/ to m*xim*//2 Iene.o/ent <n-er the!)# or-erinA! the p/*2er6(5hoi5e( tr*5e o<t the E*(tern Io<n-*r2 o3 the I<-Aet (et 3rom Co<th to #orth: %op<t it *nother 7*2! 5on(i-er the r*2 o3 (/ope d: A( d in5re*(e( 3rom [ to (! theinter(e5tion o3 the r*2 7ith the E*(tern Io<n-*r2 tr*5e( o<t the 5ho(en point(: %henot*tion d3 in-i5*te( the (/ope o3 the r*2 thro<Ah F! i:e:! d3 = y=m i3 F = (m; y):
Proposition \:Z. C<ppo(e th*t either pre3eren5e( A *n- /! or the opport<nit2 (etF ! *re (tri5t/2 5on.ex: cet F# *n- F$ Ie the point( in F 5ho(en 7hen pre3eren5e(*re re(pe5ti.e/2 A *n- /: %hen
?T@ / !)# A imp/ie( d3B " d3$ :?Z@ ^3 F ! E2F /ie( on * r*2 7ith (/ope Iet7een d3$ *n- d3B ! then there *re
pre3eren5e( $ 7ith / !)# $ !)# A (<5h th*t F i( the $K5ho(en pointin F:
?b@ %here *re *-mi((iI/e pre3eren5e( 3or 7hi5h S1 i( the 5ho(en point! *n- otherpre3eren5e( 3or 7hi5h * point *rIitr*ri/2 5/o(e to N1 i( the 5ho(en point inF :
Vropo(ition( \:T *n- \:Z -e*/ 7ith * Exe- opport<nit2 (et: h3ten 7e nee- preK-i5tion( o3 ho7 *n *Aent 7ith Ai.en pre3eren5e( 7i// 5hoo(e in * ne7 opport<nit2(et: %extIooB re.e*/e- pre3eren5e theor2 o9er( (<5h pre-i5tion( in the 5*(e o3 (t*nK-*r- I<-Aet (et( *n- 5on.ex monotone pre3eren5e(: ;e 7i// Aet 7e*Ber pre-i5tion(Ie5*<(e 7e -e*/ 7ith more Aener*/ opport<nit2 (et( *n- 7ith pre3eren5e( th*t *re
T[ ! ! A#$
5on.ex I<t not ne5e((*ri/2 monotone in other6( in5ome y: %he 3o//o7inA ex*mp/ei//<(tr*te( thi(:
"56789, 5333 FiA<re e (ho7( (t*n-*r- I<-Aet (et( F 7ith I = 1; p = 1 ?(o/i-/ine@ *n- G 7ith I = 2; p = 4 ?-*(he- /ine@: C<ppo(e th*t * p/*2er 7ith pre3eren5e($ pi5B( F 3rom F : ;h*t 5*n 7e pre-i5t *Io<t hi( 5hoi5e W 3rom GU ^3 ith*ppen( th*t F i( in G then textIooB re.e*/e- pre3eren5e theor2 te//( <( th*t Wi( not in F R it m<(t Ie on the (eAment o3 the G I<-Aet /ine th*t /ie( o<t(i-e F :O(inA homotheti5it2! 7e 5*n (trenAthen the pre-i5tion_ W /ie( on the (<IK(eAmentIet7een Y = tF *n- the 5orner ?*( in-i5*te- in the FiA<re@ *( in the 3o//o7inAVropo(ition:
Proposition \:`. cet *n *Aent 7ith (tri5t/2 5on.ex *n- homotheti5 pre3eren5e( A5hoo(e F *n- W 3rom (ome opport<nit2 (et( F *n- G; re(pe5ti.e/2: cet Y =tF ! EG Ie the mo(t -i(t*nt point 3rom the oriAin on the r*2 thro<Ah F in theopport<nit2 (et G! *n- /et Z ! E2G (o/.e *#'%1 (F) = *#'%0(Z): %hen! 3orpre3eren5e( A;
?T@ i3 F ! G then W ! F 4 or W = F;?Z@ d5 + d3 i9 *#'%1 (F) + *#'%0(Y )! *n-?b@ d5 " d6 i9 d6 + d3 :
Vropo(ition( TKb -o not in.oBe Axiom( ] *n- C: %he(e *xiom( (ometime( (h*rpen*n- (ometime( 7e*Ben the pre-i5tion( o3 (t*n-*r- re.e*/e- pre3eren5e theor2! *(i//<(tr*te- in the re(t o3 thi( (e5tion:
"56789, 5353 ;h*t h*ppen( in ex*mp/e \:b i3 pre3eren5e( A *re */tere- I2 the5hoi5e o3 G o.er FU ;ere G /e(( Aenero<( th*n F ! then re5ipro5it2 *((<mption R7o</- imp/2 th*t the 5hoi5e W 7o</- (hi3t (o<th7*r-! to7*r-( the 5orner (2; 0)o3 the I<-Aet (et! i:e:! the e*r/ier pre-i5tion 7o</- ho/- a fortiori: Ho7e.er! G!"# F 3or re*(on( exp/*ine- in the (e5on- to /*(t p*r*Ar*ph o3 the pre.io<((e5tion: Con(eL<ent/2! i3 the other p/*2er i( re(pon(iI/e 3or the 5h*nAe in I<-Aet(et! Axiom R imp/ie( th*tW 7i// (hi3t north7*r-: %he pre-i5tion re-<5e( to (*2inAth*t W i( north o3 the Co<th 5orner: d<t thi( te//( <( nothinAR no 5hoi5e */onA theE*(tern portion o3 EG i( r</e- o<t: %he proI/em here i( th*t the re5ipro5it2 e9e5t-oe(n6t rein3or5e the <(<*/ (<I(tit<tion e9e5t in re.e*/e- pre3eren5e theor2! I<tr*ther 5o<nter*5t( it *n- 7e h*.e no in-i5*tion 7hi5h e9e5t i( (tronAer:
Ch*rper pre-i5tion( o3ten *ri(e 3rom 5/o(er ex*min*tion o3 (pe5iE5 A*me(: ;ei//<(tr*te Er(t 7ith the ^n.e(tment A*me o3 ex*mp/e b:`:
Proposition \:l. cet the FG in the ^n.e(tment A*me 5hoo(e F. *( the CG6( opporKt<nit2 (et! *n- /et r(s) Ie the CG6( re(pon(e: A/(o /et the (*me CG Ie Ai.en the(*me opport<nit2 (et F. in * -i5t*tor A*me! *n- /et r7(s) Ie hi( re(pon(e there:A((<me th*t&#' + 1 *n- E&#'=E+ " 0: %hen_
?T@ 5on.exit2 imp/ie( th*t r7(s) i( in5re*(inA in s;?Z@ Axiom R imp/ie( th*t r(s) i( in5re*(inA in s;?b@ Axiom S imp/ie( th*t r(s) " r7(s) 3or s = [! T! Z! :::! T[:
%he (t*n-*r- Ct*5Be/IerA A*me in Ex*mp/e b:e i( e(pe5i*//2 <(e3</ 3or o<r p<rKpo(e(: FiA<re n (<AAe(t( ?*n- Appen-ix A:` .eriEe(@ th*t (m*//er o<tp<t 5hoi5e( I2
]ESEAcE$ Ac%]O^CG TT
the Ct*5Be/IerA ce*-er 5re*te !"# opport<nit2 (et( 3or the Fo//o7er: d2 Axiom] 7e expe5t thi( to in-<5e!)# pre3eren5e( in the Fo//o7er: An oI(er.*I/e 5on(eKL<en5e o3 (<5h * (hi3t i( * (m*//er -e.i*tion q8 o3 Fo//o7er6( o<tp<t q1 3rom (e/E(hIe(t rep/2: d<t o3 5o<r(e 7e m<(t */(o t*Be into *55o<nt pre3eren5e 5on.exit2! *n-*/(o the 5h*nAinA 5<r.*t<re o3 the opport<nit2 (et: %he(e e9e5t( *re (orte- o<t inthe next propo(ition:
Proposition \:f. ^n the (t*n-*r- Ct*5Be/IerA A*me o3 ex*mp/e b:e! /et Q8(q9) =q1 ) q71 Ie the -e.i*tion o3 the Fo//o7er6( o<tp<t 5hoi5e q1 3rom the (e/E(h Ie(trep/2 q71 = 12)
!"q9 7hen the ce*-er 5hoo(e( o<tp<t q9: hne h*(
dQ8dq9
= )1
2w )
dw
dq9q9
7here w =&#'(Mq1 ;Mq9):
?T@ ^3 Fo//o7er6( pre3eren5e( A *re Exe- *n- /ine*r then&#' o3 the optim*/point i( 5on(t*nt 7ith re(pe5t to q9 *n- *:%
*;"i( po(iti.e i3 *n- on/2 i3
pre3eren5e( *t the point *re m*/e.o/ent:?Z@ ^3 Fo//o7er6( pre3eren5e( A *re Exe- *n- 5on.ex! then&#' i( -e5re*(inA in
q9 *n-*:%
*;"5ont*in( *n *--ition*/ term th*t i( po(iti.e pro.i-inA q9 + 12!
w + 1! w( " 0 *n- w( + w) " 0:?b@ ^3 Fo//o7er6( pre3eren5e( (*ti(32 Axiom ! (tri5t/2! then&#' i( -e5re*(inA
in q9 *n-*:&
%
*;"5ont*in( *n *--ition*/ po(iti.e term:
?`@ ^3 Fo//o7er6( pre3eren5e( (*ti(32 Axiom * (tri5t/2 then&#' i( -e5re*(inAin q9 *n-
*:'%
*;"h*( *n *--ition*/ po(iti.e ?neA*ti.e@ term i3 the (t*t<( L<o
i( (m*//er ?/*rAer@ th*n q9:
Vropo(ition \:f (ho7( th*t *n in5re*(e in q9 h*( three -i9erent e9e5t(_5 A re5ipro5it2 e9e5t! item( bK` in the Vropo(ition: ^3 Axiom ] ho/-( (tri5t/2!then the /e(( Aenero<( opport<nit2 (et -e5re*(e( the Fo//o7er6(&#'! inK5re*(inA q1 *n- q8: Axiom C mo-er*te( or inten(iEe( thi( e9e5t! -epen-inAon the (t*t<( L<o:
5 A pre3eren5e 5on.exit2 ?or (<I(tit<tion@ e9e5t! item Z in the Vropo(ition:%he 5hoi5e point i( p<(he- north7e(t! 7here ?(<IPe5t to (ome te5hni5*/L<*/iE5*tion(@&#' i( /e((! *A*in in5re*(inA q1 *n- q8:
5 An opport<nit2 (et (h*pe e9e5t ?in (ome 7*2( *n*/*Ao<( to *n in5omee9e5t@! item T: %he 5<r.*t<re o3 the p*r*Io/* -e5re*(e(: Ho/-inA w =&#' 5on(t*nt! q8 in5re*(e( 7hen the Fo//o7er i( m*/e.o/ent ?w 9 0!hen5e q8 * 0@! *n- -e5re*(e( 7hen the Fo//o7er i( Iene.o/ent ?w * 0!hen5e q8 9 0@:
%he te5hni5*/ L<*/iE5*tion( 3or the pre3eren5e 5on.exit2 e9e5t *re not e(pe5i*//2re(tri5ti.e: ^n * (en(e! ce*-er 5hoi5e( q9 * 12 *re -omin*te-_ the2 pro-<5e 5hoi5e(et( 3or the Fo//o7er th*t *re (tri5t (<I(et( o3 tho(e pro-<5e- I2 q9 + 12: ?#oteth*t q9 = 12 i( the monopo/2 *( 7e// *( the Ct*5Be/IerA o<tp<t:@ %he 5on-itionw + 1 ?*/(o <(e- in the pre.io<( Vropo(ition@ (*2( th*t the Fo//o7er 7o</- not3*.or *n inei5ient *-.er(e tr*n(3erR *t the m*rAin he /o.e( hi( neiAhIor no moreth*n him(e/3: %he 5on-ition w( + w) " 0 (*2( th*t eL<*/ in5re*(e( in in5ome -onot p<(h pre3eren5e( to7*r-( m*/e.o/en5e ?*n- eL<*/ -e5re*(e( -o not p<(h to7*r-(Iene.o/en5e@: %he pre.io<( propo(ition <(e( *n e.en 7e*Ber 5on-ition! w( " 0:Cee the *ppen-ix 3or 3<rther -i(5<((ion o3 */tern*ti.e te5hni5*/ 5on-ition(:
TZ ! ! A#$
A p*r*metri5 ex*mp/e m*2 5/*ri32 the /oAi5: For Ai.en q9 ! [0; 24]! the Fo//o7er6(5hoi5e (et i( the p*r*Io/* f(m; y) : m = Mq1 ; y = Mq9;M = 24 ) q9 ) q1 ; q1 ![0; 24 ) q9]'! 7ith NTP = )*(+*;#
*)+*;#= "&!;"!";#
;": C<ppo(e th*t the Fo//o7er
h*( Exe- CoIIK$o<A/*( pre3eren5e( repre(ente- I2 u(m; y) = my-! (o &#' i(7m=y = 7q1 =q9: Co/.inA *#' = &#'! one oIt*in( q1 = Q(q917) = (24 )q9)=(2+ 7): #otinA th*t the (e/E(h Ie(t rep/2 i( q71 = Q(q910); one oIt*in( * 5/o(e-3orm expre((ion 3or the -e(ire- -e.i*tion! q8 = ) -
&#"- (24)q9): For Exe- 7 po(iti.e?Iene.o/ent pre3eren5e(@ or (m*//er th*n )2 ?(tronA/2 m*/e.o/ent pre3eren5e(@! the-e.i*tion i( neA*ti.e I<t in5re*(inA in the ce*-er6( o<tp<tR the oppo(ite i( tr<e 7hen7 i( neA*ti.e I<t /*rAer th*n )2 ?mo-er*te/2 m*/e.o/ent@: %hi( i( the 5omIine-imp*5t o3 the 5on.exit2 ?or (<I(tit<tion@ *n- (h*pe ?or in5ome@ e9e5t( note- *Io.e:h3 5o<r(e! re5ipro5it2 e9e5t( 7i// -e5re*(e 7 *n- hen5e in5re*(e q8:A -ire5t 7*2 to te(t Axiom ] i( to m*nip</*te the Er(t mo.er6( 5hoi5e 5o//e5tion
2 in the /*Ior*tor2 (o th*t * Exe- opport<nit2 (et i( more or /e(( Aenero<(: Forex*mp/e! (<ppo(e re(tri5tion( on the Ct*5Be/Ier ce*-er6( 5hoi5e (et m*Be * Ai.eno<tp<t 5hoi5e q& the mo(t Aenero<( ?(m*//e(t@ po((iI/e in one (it<*tion! *n- the(*me o<tp<t q& the /e*(t Aenero<( ?/*rAe(t@ po((iI/e in *nother (it<*tion: ^3 * Ai.enFo//o7er re*5t( -i9erent/2 in the t7o (it<*tion(! it m<(t Ie -<e to re5ipro5it2 e9e5t(!(in5e I2 ho/-inA q& 5on(t*nt 7e h*.e e/imin*te- the 5on.exit2 *n- (h*pe e9e5t(:%hi( i( the i-e* Iehin- the Ct*5Be/IerA miniKA*me intro-<5e- in the /*(t empiri5*/(e5tion:
Corollary \:n. Ct*5Be/IerA GiniKX*me: cet x; s; z ! (0; 24) Ie (<5h th*t x 9 s 9 z:C<ppo(e the Ct*5Be/IerA ce*-er h*( re(tri5te- o<tp<t 5hoi5e( q
"! fx; s' in *
(it<*tion ?*@ *n- q"! fz; s' in *nother (it<*tion ?I@: cet the ce*-er 5hoo(e s in
Ioth (it<*tion(: ^3 Fo//o7er6( pre3eren5e( (*ti(32 AxiomR thenWTP <(Mq1 ;Ms) +WTP =(Mq1 ;Ms) *n- Q<8(Mq1 ;Ms) " Q
=8(Mq1 ;Ms):
l:
;e IeAin i//<(tr*tion o3 empiri5*/ *pp/i5*tion( 7ith the ^n.e(tment A*me o3 ExK*mp/e ?b:`@: O(inA * -o<I/eKI/in- proto5o/! Cox ?Z[[`@ A*ther( -*t* 3rom * oneK(hotin.e(tment A*me ?%re*tment A@ 7ith bZ p*ir( o3 FG( *n- CG(: Cox */(o report(p*r*//e/ -*t* ?%re*tment C@ 7ith *nother bZ p*ir( in 7hi5h CG( *re p-i5t*tor(p7ith ex*5t/2 the (*me opport<nit2 (et( Ai.en to them I2 the experimenter: ^n Iothtre*tment(! the 5hoi5e( s *n- r *re re(tri5te- to inteAer .*/<e( I<t the 5on5/<(ion(o3 Vropo(ition ?\:l@ (ti// ho/-: Axiom C imme-i*te/2 imp/ie( th*t * CG 7ith *n2p*rti5</*r F. 7o</- h*.e more */tr<i(ti5 pre3eren5e( in %re*tment A th*n in %re*tKment C_ A1' !)# A1 $
'! 3or s k 0; 1; :::; 9: Vropo(ition ?\:l@ -e.e/op( the te(t*I/e
pre-i5tion( th*t the CG 7i// ret<rn more to the FG 7hen s i( /*rAer in %re*tmentA! *n- 3or * Ai.en s 7i// ret<rn more in %re*tment A th*n in %re*tment C:%o te(t the(e pre-i5tion(! 5on(tr<5t the -<mm2 .*ri*I/e D k T 3or %re*tment
C -*t*! (o D k [ 3or %re*tment A -*t*: ]eAre(( the CG 5hoi5e r on the *mo<nt(ent s *n- it( inter*5tion 7ith D! <(inA the ZK(i-e- %oIit pro5e-<re to *55o<nt 3orthe /imite- r*nAe o3 CG 5hoi5e( in the \` re/e.*nt oI(er.*tion( ?r ! [0; 3s]@:` %hee(tim*te- 5oei5ient 3or s i( [:\n ?6 (t*n-*r- error o3 [:ZZ@ 7ith oneK(i-e- pK.*/<e
`%he E.e oI(er.*tion( 3or e*5h tre*tment in 7hi5h ! & *re not <(e- in the e(tim*tion 3or t7ore*(on(_ ?*@ (in5e the CG opport<nit2 (et i( * (inA/eton! there i( nothinA 3or * theor2 *Io<t CG
]ESEAcE$ Ac%]O^CG Tb
o3 [:[[l! 5on(i(tent 7ith the Axiom ] pre-i5tion: %he e(tim*te- 5oei5ient 3orD 7 s i( K[:le ?60:32! p = 0:018@! 5on(i(tent 7ith the Axiom C pre-i5tion:;e 5onErm the Axiom C re(</t I2 -ire5t h2pothe(i( te(t( on the mo(t re/e.*nt
(<I(et o3 -*t*! 7here s = 5 ?7ith f oI(er.*tion( in e*5h tre*tment@ *n- s = 10?7ith Tb oI(er.*tion( in e*5h tre*tment@: %he G*nnK;hitne2 *n- tKte(t Ioth rePe5tthe n<// h2pothe(i( o3 no -i9eren5e Iet7een the *mo<nt( ret<rne- in 3*.or o3 the(tri5t Axiom C */tern*ti.e h2pothe(i( th*t ret<rn( *re /*rAer in %re*tment A: %heoneK(i-e- pK.*/<e( 3or the tKte(t ?re(pe5ti.e/2 the G*nnK;hitne2 te(t@ *re [:[Zf?[:[\n@ 3or the s = 5 -*t* *n- *re [:[` ?[:T[@ 3or the s = 10 -*t*:
f:
%he in.e(tment A*me -*t* *re 5on(i(tent 7ith the theor2 I<t the2 -o not permit5ri(p te(t( o3 re5ipro5it2 Ie5*<(e! *monA other /imit*tion(! ?*@ the opport<nit2 (et(*re /ine*r *n- hen5e 5*n6t re.e*/ m<5h *Io<t &#'! *n- ?I@ on/2 one 5hoi5e i(oI(er.e- per (<IPe5t! pre5/<-inA -ire5t oI(er.*tion o3 5h*nAe- pre3eren5e(: cimiKt*tion( ?*@ *n- ?I@ *re o.er5ome in the Ct*5Be/IerA -<opo/2 -*t* o3 H<5B! Gm//er!*n- #orm*nn ?Z[[T! hen5e3orth HG#@:%he HG# -*t* 5on(i(t o3 220 o<tp<t 5hoi5e( (q9; q1 ) I2 ZZ FG( ?or ce*-er(@
5hoo(inA q9 ! f3; 4; 5; : : : ; 15' r*n-om/2 rem*t5he- 3or T[ perio-( e*5h 7ith ZZCG( ?or Fo//o7er(@: A( note- in Ex*mp/e ?b:e@ *n- e/(e7here! the CG6( 5hoi5e q1 !f3; 4; 5; : : : ; 15' -etermine( p*2o9( (m; y) 7ithin *n opport<nit2 (et o3 -i(5retepoint( on * p*r*Io/i5 *r5: Cpe5iE5*//2! p*2o9( *re m =M q1 *n- y =M q9! 7hereM = 24 ) q9 ) q1 i( the proEt m*rAin: %he &#' 5*n Ie in3erre- *t * 5ho(enpoint (q9; q1 ) I2 the *#' *t th*t point! (24) 2q1 ) q9)=q9:]e5*// th*t Vropo(ition \:f pre-i5t( th*t the CG6( o<tp<t 5hoi5e re.e*/( * 5onK
(t*nt&#' i3 her pre3eren5e( *re /ine*r *n- <n*9e5te- I2 the FG6( o<tp<t 5hoi5eq9: %he 5orre(pon-inA -e.i*tion Q8 3rom her (e/E(h Ie(t rep/2 o<tp<t i( /ine*r/2-e5re*(inA in q9 i3 her pre3eren5e( *re Iene.o/ent: Con.exit2 *n- Axiom ] e9e5t(pro-<5e * re.e*/e-&#' th*t i( -e5re*(inA ?*n- Q8 th*t i( in5re*(inA@ in q9:%*I/e T report( te(t( o3 the(e pre-i5tion( on the HG# -*t*! omittinA the Zl -*t*
point( 7here the Vropo(ition6( h2pothe(i( q9 + 12 3*i/(:\ %o 5he5B 3or *(2mmetri5re(pon(e( to /*rAe *n- (m*// FG 5hoi5e( ?re/*ti.e to the Co<rnot 5hoi5e q9 = 8@! 7e-eEne the -<mm2 .*ri*I/e DP = 1 i3 q9 + 8: A// 5o/<mn( in the %*I/e report p*ne/reAre((ion( 7ith in-i.i-<*/ (<IPe5t Exe- e9e5t(: %he Er(t 5o/<mn! 7ith -epen-ent.*ri*I/e &#' 7 100! Erm/2 rePe5t( the h2pothe(i( o3 Iene.o/ent /ine*r *n- Exe-pre3eren5e(_ the 5oei5ient 3or q9 i( (iAniE5*nt/2 neA*ti.e! not po(iti.e: %he (e5on-5o/<mn! 7ith -epen-ent .*ri*I/e Q8! 5onErm( thi( re(</t: ;e in3er th*t j8 i(*n in5re*(inA 3<n5tion o3 FG o<tp<t q9! 5on(i(tent 7ith 5on.exit2 *n- re5ipro5it2:%he /*(t 5o/<mn report( th*t there i( * (tronAer re(pon(e to pAree-2p FG 5hoi5e(in ex5e(( o3 the Co<rnot o<tp<t n th*n to pAenero<(p FG 5hoi5e( Ie/o7 or eL<*/to o<tp<t n: Come (<pp/ement*r2 reAre((ion( *re note- in the Appen-ix! */(o5on(i(tent 7ith Vropo(ition \:f:
5hoi5e( to exp/*inR *n- ?I@ (in5e the /e3t ? k &@ *n- riAht ? ! '@ 5en(or( in the %oIit e(tim*tion*re eL<*/! the e(tim*tion */Aorithm 7o</- not Ie 7e// -eEne-:
\%he re(</t( *re (<I(t*nti*//2 <n5h*nAe- 7hen the -*t* point( 3or L () *re in5/<-e-:
T` ! ! A#$
Dep:V ariable WTP 7 100 Q8 Q8
q9 )5:436 1:11%>%%% 0:356 0:06%>%%% 0:246 0:08%>%%"
DP 7 q9 )0:106 0:05%>%"$
constant 28:876 11:01%>%%' )2:136 0:58%>%%% )0:816 0:87%>!()
V*ne/ ]eAre((ion( 7ith Exe- e9e5t(: $*t* 5on(i(t o3 Te`5hoi5e( I2 ZZ Fo//o7er( in HG# experiment 7hen q9 9 13: %he5oei5ient point e(tim*te( *re (ho7n 6 the (t*n-*r- error! 7ithoneK(i-e- pK.*/<e( in (<per(5ript(:
n:
%he HG# -*t* (ti// -o not permit te(t( o3 (ome o3 o<r mo(t -i(tin5ti.e preK-i5tion(: A// FG( ?ce*-er(@ h*.e the (*me 5hoi5e (et! e/imin*tinA .*ri*Ii/it2 th*t5o</- he/p (ep*r*te the 5on.exit2 e9e5t 3rom the re5ipro5it2 e9e5t: A/(o! -<e inp*rt to -i9erinA experien5e(! CG( m*2 h*.e -i9erent .ie7( on the Aenero(it2 o3* Ai.en o<tp<t 5hoi5e q9: ^n or-er to o.er5ome the(e /imit*tion( 7hi/e pre(er.inAthe ni5e L<*-r*ti5 (h*pe o3 the CG 5hoi5e (et(! 7e 5re*te- * ne7 .er(ion o3 theCt*5Be/IerA A*me th*t re(tri5t( FG( to Iin*r2 5hoi5e(:^n o<r Ct*5Be/IerA miniKA*me! e*5h (<IPe5t in the FG ro/e t7i5e 5hoo(e( q9 !
f6; 9' *n- t7i5e 5hoo(e( q9 ! f9; 12' 7itho<t 3ee-I*5B: E*5h (<IPe5t in the CGro/e i( then p*ire- (im</t*neo<(/2 7ith 3o<r -i9erent FG( *n- 5hoo(e( *n inteAer.*/<e o3 q1 ! f5; 6; :::; 11' 7ith no 3ee-I*5B: %he 5orre(pon-inA p*2o9( (m; y)*re 5/e*r/2 -i(p/*2e-: %he En*/ p*2o9 i( Ai.en I2 one o3 the 3o<r 5hoi5e(! (e/e5te-r*n-om/2 *t the en- o3 the (e((ion: %he =-o<I/e I/in-> pro5e-<re( *re -et*i/e- inthe in(tr<5tion( to (<IPe5t(! repro-<5e- *t the en- o3 the *ppen-ix:FiA<re ?T[@ (<mm*riJe( the -*t*: Gore Aenero<( ?(m*//er@ 5hoi5e( I2 the FG
(eem to Ie *((o5i*te- 7ith more */tr<i(ti5 or /e(( m*/e.o/ent ?(m*//er@ 5hoi5e( I2the CG! I<t it i( h*r- to te// 3rom the EA<re 7hether the e9e5t i( (iAniE5*nt:For ex*mp/e! there *re on/2 E.e oI(er.*tion( *t q9 = 6: Go(t import*nt/2! the(5*tterp/ot -oe(n6t (ho7 7hi5h o3 the Z` (<IPe5t( m*-e 7hi5h 5hoi5e(:%o in3er ho7 in-i.i-<*/ (<IPe5t( re(pon- to re5ipro5it2 5on5ern(! 7e t<rn *A*in
to p*ne/ reAre((ion( 7ith in-i.i-<*/ (<IPe5t Exe- e9e5t(: %he (e5on- 5o/<mn in%*I/e Z report( th*t! 5on(i(tent 7ith Coro//*r2 \:n! CG(6 *.er*Ae ;%V -e5re*(e-I2 */mo(t n 5ent( per -o//*r 7hen q9 = 9 7*( the /e(( Aenero<( 5hoi5e ?in-i5*te- I2D9 = 1@: %he (e5on- 5o/<mn report( the (*me -*t* in * -i9erent 7*2_ CG o<tp<t5hoi5e in5re*(e- I2 [:b` on *.er*Ae! (iAniE5*nt *t the p k [:[Tl /e.e/ ?oneK(i-e-@:Cin5e the opport<nit2 (et F* i( 5on(t*nt in the(e fZ -*t* point(! the re(</t 5*nnotIe -<e to 5on.exit2 or (h*pe e9e5t(R it m<(t Ie p<re re5ipro5it2: %he /*(t 5o/<mno3 %*I/e Z report( reAre((ion( 3or Q8 3or the entire -*t* (et! <(inA the *--ition*/-<mm2 .*ri*I/e( $l ?7hi5h t*Be( .*/<e T i3 L9 = 6; [ other7i(e@ *n- $TZ ?7hi5ht*Be( .*/<e T i3 L9 = 12; *n- [ other7i(e): %he (iAn( o3 *// 5oei5ient e(tim*te(*re 5on(i(tent 7ith Axiom ] *n- C! */tho<Ah ?(in5e it 5ome( 3rom on/2 \ nonKJerooI(er.*tion(@! the $l e(tim*te i( not (iAniE5*nt:
]ESEAcE$ Ac%]O^CG T\
;%V7T[[?L9ke@
j8?L9ke@
j8
nobs(gr) 72(24) 72(24) 96(24)D6 )0:246 0:35%>"&"
D9 )7:656 3:05%>%%+ 0:346 0:14%>%%+ 0:336 0:15%>%!)
D12 0:376 0:20%>%$(
constant )5:936 2:31%>%%( 0:276 0:10%>%%( 0:186 0:12%>%)+
V*ne/ ]eAre((ion( 7ith Exe- e9e5t( 3or Ct*5Be/IerAminiKA*me -*t*: Entrie( *re 5oei5ient e(tim*te( 6 (t*n-*r- error(7ith oneK(i-e- pK.*/<e( in (<per(5ript(:
e:
C/*((i5 5hoi5e theor2 ?e:A:! Hi5B(! TebeR C*m<e/(on! Te`f@ 5/*riEe- *n- <niEe-e*r/ier 7orB on ho7 pre3eren5e( *n- opport<nitie( *9e5t o<t5ome(: %he pre(entp*per *pp/ie( tho(e 5/*((i5 i-e*( to (o5i*/ pre3eren5e(: ;e 3o5<( on 7i//inAne(( top*2 ?;%V@! the re5ipro5*/ o3 the m*rAin*/ r*te o3 (<I(tit<tion Iet7een o7n in5ome*n- other(6 in5ome: ^n5re*(inA ;%V */onA in-i9eren5e 5<r.e( i( (imp/2 5on.exit2!*n- 5on.ex (o5i*/ pre3eren5e( pro.i-e * <niEe- *55o<nt o3 (e.er*/ (o5i*/ moti.e(pre.io<(/2 5on(i-ere- (ep*r*te/2! (<5h *( ei5ien52! m*ximin! *n- ineL<*/it2 *.erK(ion:%he (*me 5/*((i5 i-e*( */(o permit * <niEe- -eEnition o3 re5ipro5it2: ;e (*2 th*t
one (et o3 pre3eren5e( i( more */tr<i(ti5 th*n ?GA%@ *nother i3 it h*( * /*rAer ;%V*t e.er2 point: ;e 3orm*/iJe re5ipro5it2 *( * GA%K(hi3t in pre3eren5e( 3o//o7inAmore Aenero<( Ieh*.ior I2 other(: %he -eEnition( *pp/2 to m*/e.o/ent ?;%V 9 [@*( 7e// *( Iene.o/ent ?;%V * [@ pre3eren5e(! *n- *<tom*ti5*//2 5omIine po(iti.e*n- neA*ti.e re5ipro5it2Con.exit2 *n- re5ipro5it2 *re L<ite -i9erent 3orm*//2 *n- 5on5ept<*//2! I<t 7e
(ho7 th*t empiri5*/ 7orB h*( * n*t<r*/ ten-en52 to 5on3o<n- the t7o notion(: %heproI/em i( (imp/2 th*t more Aenero<( Ieh*.ior I2 * Er(t mo.er ten-( to p<(h the(e5on- mo.er6( opport<nitie( >(o<the*(t!> to7*r-( /*rAer in5ome 3or the Er(t mo.er*n- (m*//er in5ome 3or the (e5on- mo.er: Con.exit2 t2pi5*//2 imp/ie( Are*ter ;%V*( one p<(he( (o<the*(t! e.en 7hen there i( no GA%K(hi3t in pre3eren5e(:Ce.er*/ theoreti5*/ propo(ition( -e.e/op the oI(er.*I/e 5on(eL<en5e( o3 5on.exit2
*n- re5ipro5it2: ;e (ho7 th*t more norther/2 5hoi5e( on the e*(tern Io<n-*r2 o3*n opport<nit2 (et re.e*/ more */tr<i(ti5 ?or /e(( m*/e.o/ent@ pre3eren5e(: For Exe-pre3eren5e(! 5hoi5e( in *n opport<nit2 (et re.e*/ Io<n-( on pre3eren5e( th*t 7etr*n(/*te into Io<n-( on 5hoi5e( in ne7 opport<nit2 (et(: %he /*(t t7o theoreti5*/propo(ition( -eri.e te(t*I/e pre-i5tion( 3or the 7e//KBno7n ^n.e(tment A*me *n-the Ct*5Be/IerA -<opo/2 A*me:Fin*//2! to i//<(tr*te the theor2! 7e ex*mine t7o exi(tinA -*t* (et( *n- one
ne7 -*t* (et: Exi(tinA in.e(tment A*me -*t* *re 5on(i(tent 7ith 5on.exit2 *n-re5ipro5it2! *n- 5onErm th*t peop/e re(pon- more (tronA/2 to *5t( o3 5ommi((ionth*n to -e3*</t 5hoi5e(: Exi(tinA Ct*5Be/IerA -*t* 5onErm re5ipro5it2t5on.exit2e9e5t( *n- (<AAe(t * (tronAer neA*ti.e re(pon(e to Aree-2 Ieh*.ior th*n the po(iti.ere(pon(e to Aenero<( Ieh*.ior: %he ne7 Ct*5Be/IerA miniKA*me -*t* *//o7 <(
Tl ! ! A#$
to (ep*r*te 5on.exit2 3rom re5ipro5it2 e9e5t(! *n- 5onErm th*t re5ipro5it2 h*(* (iAniE5*nt imp*5t:%heoreti5*/ 5/*riE5*tion (et( the (t*Ae 3or 3<rther empiri5*/ 7orB: hne 5*n no7
reEne e*r/ier empiri5*/ (t<-ie( th*t ex*mine */tr<i(m *n- re5ipro5it2: C<5h 7orB(ho</- (he- /iAht on the extent to 7hi5h t2pi5*/ h<m*n pre3eren5e( -ep*rt 3rom(e/E(hne((! *n- to 7h*t extent the2 *re */tere- I2 experien5inA Aenero<( or (e/E(hIeh*.ior:F<rther theoreti5*/ 7orB i( */(o in or-er: ^n p*rti5</*r! Axiom C in.oBe( the
(t*t<( L<o to -i(tinA<i(h Iet7een *5t( o3 5ommi((ion *n- omi((ion! *n- Iet7eenAenero<( *n- Aree-2 *5t(: d<t 7h*t -oe( it t*Be 3or * 5hoi5e to Ie5ome Aener*//2re5oAniJe- *( the (t*t<( L<o! *n- 7h*t i3 *n *5t h*( IeneE5i*/ (hort r<n imp*5tI<t i( h*rm3</ in the /onA r<nU An(7er( to the(e *n- other L<e(tion( *7*it 3<rthertheoreti5*/ -e.e/opment:
A:
A:T: !,960/A, /.B17, C,.C/0/A/0D 6.E F1710F,0/B 8G,H,G,.B,C 3
%,776 $313 Preferences are homothetic on #"# iC&#' is constant along everyray R* = f(t; td) : t * 0' * #"#:
Proof. d2 -eEnition! pre3eren5e( *re homotheti5 i9 the2 5*n Ie repre(ente- I2 *<ti/it2 3<n5tion u(m; y) 7ho(e r*tio o3 p*rti*/ -eri.*ti.e( u(=u) -epen-( on/2 onthe r*tio m=y! not on m *n- y (ep*r*te/2: d<t the r*tio d = m=y i( 5on(t*nt onthe r*2 R* I2 5on(tr<5tion: !
A:Z: !,960/A, BIGA60IG, 6.E F1710F,0/B 8G,H,G,.B,C3
%,776 $323 If preferences are homothetic then mK(m; dm) is constant along theray R*.
Proof. ^t i( 7e// Bno7n th*t homotheti5 pre3eren5e( 5*n Ie repre(ente- I2 * <ti/it23<n5tion u(m; y) th*t i( homoAeno<( o3 -eAree 1! *n- th*t Er(t ?(e5on-@ p*rti*/-eri.*ti.e( o3 homoAeneo<( 3<n5tion( o3 -eAree T *re homoAeneo<( o3 -eAree [ ?KT@?e:A: S*ri*n! TeeZ! p:`nZ@: ^t then 3o//o7( -ire5t/2 3rom eL<*tion ?Z:T@ th*tmK(m;md) = K(1; d)! -m * 0: !
A:b: JIGA60IG, C/K. 1H B1.A,5 1881G0I./0D C,03
%,776 $333 A compact connected subset F * #"# 8ith non-empty interior isconvex if and only if K " 0 at every regular point F ! EF .
Proof. r]o5B*3e//*r! Tef[s !
]ESEAcE$ Ac%]O^CG Tf
A:`: *06BL,9M,GK N1991O,GPC 1881G0I./0D C,03 Q'R 6.E JIGA60IG,%he Fo//o7er6( opport<nit2 (et F (q
") ?7ith Fo//o7er 3ree -i(po(*/@ h*( e*(tern
Io<n-*r2 S(q") = f(m; y) : m = (24)q
")q
#)q
#; y = (24)q
")q
#)q
"; q
#! [0; 24)
q"]': A/onA thi( Io<n-*r2 Q'R = )*(+*;#
*)+*;#= "&!;"!";#
;"= (24 ) 2q
#)=q
") 1:
%h<( Q'R .*rie( (mooth/2 3rom neA*ti.e to po(iti.e .*/<e( *( q#p*((e( thro<Ah
q7#= 12 ) !
"q" ! the (e/E(h Ie(t re(pon(e: %he nee- to p*2 *t 5orner( (0; 0) *n-(0; (24)q
")q
") re(pe5ti.e/2 t*Be( .*/<e( 3rom ()(; 1)24=q
"] *n- [24=q
")1;+():
^n(ertinA the S(q") expre(ion( into ??Z:T@! one .eriEe( th*t 5<r.*t<re */onA the
e*(tern Io<n-*r2 i( K(m; y) = 2q!!"
%(2q1 + q9 ) 24)
"+ q"9
i!$+": A( <(<*/! 5<rK
.*t<re i( not -eEne- *t the t7o 5orner(:
+S'T1GE,G/.K;e (ho7 th*t F (q&
") !"# F (q
") 3or *// q
"* q&
"! (0; 24):
Case 1: q"+ q&
"+ 24: Con(i-er " : #"# )% #"# (: t: R(m) =
'"&!;"
"
"&!;"
("m *n-
S(y) =;""("&!;"
")
;"("&!;")
y: Cin5e q&"9 q
"7e h*.e
R"(m) =
)24) q&
"
24) q"
*"* 1;
*n- toAether 7ith q&"+ 24) q
"imp/2
(q") q&
")24 * (q
") q&
")(q
"+ q&
") = q9 ) q&""
*n- there3ore!
S"(y) =q&"(24) q&
")
q"(24) q
")! (0; 1):
F<rthermore! "F (q") 8 F (q&
") (in5e 3or *// P ! "F (q
"); P ! F (q&
") *( 3o//o7(:
P ! "F (q") imp/ie( 9q
#! [0; 24) q
"] (:t:
P9 =
)24) q&
"
24) q"
*"(24) q
") q
#)q
#=
)24) q&
")24) q&
"
24) q"
q#
*24) q&
"
24) q"
q#; *n-
P1 =q&"
+24) q&
"
,
q"(24) q
")(24) q
") q
#)q
"=
)24) q&
")24) q&
"
24) q"
q#
*q&"
*n- there3ore P ! F (q&") 3or Fo//o7er6( o<tp<t 5hoi5e
"&!;""
"&!;"q#! [0; 24) q&
"]:
Case 2: q"+ q&
"* 24: ^n thi( 5*(e F (q
") * F (q&
") *n- there3ore F (q&
") !"#
F (q"):
A:\: RG181C/0/1. 5313 C<ppo(e th*t either pre3eren5e( A or the opport<nit2 (etF *re (tri5t/2 5on.ex! *n- /et F Ie the A)5ho(en point in F: %hen F ! E2F :
Proof. C<ppo(e th*t F = (m; y) =! E2F : %hen I2 -eEnition o3 E2F there exi(t(z * m (<5h th*t M = (z; y) ! F : Vo(iti.e monotoni5it2 in o7n p*2o9 imp/ie( th*tM i( (tri5t/2 pre3erre- to F! 5ontr*-i5tinA the h2pothe(i( th*t F i( the AKpre3erre-point in F : !
Tn ! ! A#$
A:l: RG181C/0/1. 5323 'F,1G,0/B69 8G,E/B0/1.C H1G -5,E 1881G0I./0D C,03C<ppo(e th*t either pre3eren5e( A *n- /! or the opport<nit2 (et F ! *re (tri5t/25on.ex: cetF# *n- F$ Ie the point( in F 5ho(en 7hen pre3eren5e( *re re(pe5ti.e/2A *n- /: %hen
?T@ / !)# A imp/ie( d3B " d3$ :?Z@ ^3 F ! E2F /ie( on * r*2 7ith (/ope Iet7een d3$ *n- d3B ! then there *re
pre3eren5e( $ 7ith / !)# $ !)# A (<5h th*t F i( the $K5ho(en pointin F:
?b@ %here *re *-mi((iI/e pre3eren5e( 3or 7hi5h S1 i( the 5ho(en point! *n- otherpre3eren5e( 3or 7hi5h * point *rIitr*ri/2 5/o(e to N1 i( the 5ho(en point inF :
Proof. Fir(t! note th*t 3or homotheti5 *n- (tri5t 5on.ex pre3eren5e( J ! -Y; Z !E2F; d' 9 d6 i9&#'% (Y ) *&#'% (Z): $enote P the point o3 the in-i9eren5e5<r.e thro<Ah Y 7hi5h i( in the (*me r*2 7ith Z; i:e: d6 = d? ; *n- 7rite
?A:T@ &#'% (Y ) *&#'% (P ) =&#'% (Z)
7here the ineL<*/it2 3o//o7( 3rom (tri5t 5on.exit2 o3 J pre3eren5e( 7here*( theeL<*/it2 3rom homotheti5it2 o3 J pre3eren5e(:Part 1. C<ppo(e th*t / !)# A: %hen d3B " d3$ *( 3o//o7(: ^3 it 7ere
d3B 9 d3$ then F#; F$ ! E2F 3rom Vropo(ition \:T *n- ?A:T@ imp/2
*#'(F$) =&#'$(F$) "&#'#(F$) "&#'#(F#) = *#'(F#)
" *#'(F$)
7here the eL<*/itie( 3o//o7 3rom the optim*/it2 o3 F% ! 3or J pre3eren5e(! J = A;/Rthe /*(t ineL<*/it2 3o//o7( 3rom the po(iti.e 5<r.*t<re o3 E2F ! the Er(t ineL<*/it23o//o7( 3rom 3o//o7( 3rom / MAT A 7here*( the (e5on- 3o//o7( 3rom ?A:T@: A5ontr*-i5tion i( re*5he- i3 either o3 pre3eren5e( A; / or the opport<nit2 (et F i((tri5t/2 5on.ex (in5e then either the (e5on- or the /*(t ineL<*/it2 i( (tri5t:Part 2. Let F Ie Ai.en (<5h th*t d3(
9 d3 9 d3): cet w< *n- w= -enote
5ontin<o<(&#' 3<n5tion( 3or A *n- / pre3eren5e(: ^3 w=(F) = w<(F) then F i(the 5ho(en point 3or Ioth A *n- / pre3eren5e(: ^3 w=(F) * w<(F) then 5on(i-er(ome pre3eren5e( $ (<5h th*t! 3or *// Y ! w@(Y ) = kw=(Y ) + (1) k)w<(Y ) 7here
k =NTP (F)) w<(F)w=(F)) w<(F)
:
%here exi(t( * VK<ti/it2 3<n5tion 7ith 7? (Y ) (in5e the /*tter i( 5ontin<o<( ?H<re7i5J!Te\n! pp: fKT[R (ee */(o H<r7i5J *n- OJ*7*! TefT@: /!)# $ !)# A ?on point(7here /!)# A) 3o//o7( 3rom k Iet7een 0 *n- 1 ?imp/ie- I2 d3(
9 d3 9 d3)):F
i( $K5ho(en (in5e (tr*iAht3or7*r-/2! w? (F) = NTP (F)Part 3. cine*r pre3eren5e( 7ith w AoinA to )( ?u() h*.e the 5ho(en point
*rIitr*ri/2 5/o(e to S1 ?N1 ): !
A:f: RG181C/0/1. 5343 'F,1G,0/B69 8G,E/B0/1.C H1G E/U,G,.0 1881G0I./0DC,03 cet *n *Aent 7ith (tri5t/2 5on.ex *n- homotheti5 pre3eren5e( A 5hoo(e F *n-W 3rom (ome opport<nit2 (et( F *n- G; re(pe5ti.e/2: cet Y = tF ! EG Ie themo(t -i(t*nt point 3rom the oriAin on the r*2 thro<Ah F in the opport<nit2 (et G!*n- /et Z ! E2G (o/.e *#'%1 (F) = *#'%0(Z): %hen! 3or pre3eren5e( A;
]ESEAcE$ Ac%]O^CG Te
?T@ i3 F ! G then W ! F 4 or W = F;?Z@ d5 + d3 i9 *#'%1 (F) + *#'%0(Y )! *n-?b@ d5 " d6 i9 d6 + d3 :
Proof.Part 1. Ct*n-*r- re.e*/e- pre3eren5e( theor2:Part 2. d5 " d3 i( eL<i.*/ent 7ith KaL *#'%0(Y ) + *#'%0(W ) I2 5on.exit2
o3 G *n- 5on(tr<5tion o3 Y R *n- KbL &#'(W ) +&#'(Y ) 3rom ?A:T@: hn theother h*n-! I2 5on(tr<5tion o3 Y *n- homotheti5it2 KcL &#'(,) =&#'(-)!*n- KdL &#'(-) = *#'%1 (-);*#'%0(W ) = &#'(W ) (in5e F;W *re themo(t pre3erre- point( in re(pe5ti.e/2! F;G: *#'%0(Y ) + *#'%1 (-) 3o//o7( 3rom?*@K?-@ *n- tr*n(iti.it2:Part 3: d5 * d6 i9 d6 9 d3 : ]e3errinA to ?A:T@! &#'(Y ) 9 &#'(Z) i9
(d3 =)d) * d6 *n-
&#'(Y ) =&#'(F) = *#'%1 (F) = *#'%0(Z) + *#'%0(W ) =&#'(W )
9&#'(Z)
7here the Er(t *n- the thir- eL<*/itie( *re tr<e I2 5on(tr<5tion o3 Y *n- Z! the(e5on- *n- the 3o<rth eL<*/itie( 3o//o7 3rom the optim*/it2 o3 F *n- W ! 7here*(the Er(t *n- the /*(t ineL<*/itie( *re! 3or 5on.ex opport<nit2 (et( *n- pre3eren5e(!eL<i.*/ent 7ith d5 * d6 : !
A:n: RG181C/0/1. 5363 ).A,C07,.0 S67,3 cet the FG in the ^n.e(tment A*me5hoo(e F. *( the CG6( opport<nit2 (et! *n- /et r(s) Ie the CG6( re(pon(e: A/(o/et the (*me CG Ie Ai.en the (*me opport<nit2 (et F. in * -i5t*tor A*me! *n- /etr7(s) Ie hi( re(pon(e there: A((<me th*t&#' + 1 *n-&#'( " 0: %hen_
?T@ 5on.exit2 imp/ie( th*t r7(s) i( in5re*(inA in s;?Z@ Axiom R imp/ie( th*t r(s) i( in5re*(inA in s;?b@ Axiom S imp/ie( th*t r(s) " r7(s) 3or s = [! T! Z! :::! T[:
Proof. Parts 1 and 2. %o (tre*m/ine not*tion! /et w(s) =WTP (m(s); y(s))! 7herem(s) = 10+3s)r(s) *n- y(s) = 10)s+r(s): d2 h2pothe(i(! w + 1 *n- ?*@ w( " 0:d2 cemm* A:` Ie/o7! (tri5t 5on.exit2 imp/ie( th*t w(w)w) * 0: ^t 3o//o7( th*t?I@ w( ) w) * 0: Cin5e Q'RkT! * 5on(t*nt! */onA the e*(tern Io<n-*r2 o3 theopport<nit2 (et! the Er(t or-er 5on-ition 3or optim*/it2 reL<ire( w(s) */(o to rem*in5on(t*nt: %here3ore
0 =dw
ds= w(
dm
ds+ w)
dy
ds= [(3) dr=ds)w( + ()1 + dr=ds)w)]= 2[w(] + (1) dr=ds) [w( ) w)] :
%he Ir*5Bete- expre((ion( *re po(iti.e I2 ?*@ *n- ?I@ *Io.e! (o 7e m<(t h*.edr=ds * 1 3or 5hoi5e( not *t the 5orner: For 5orner 5hoi5e( *n- 7e*B 5on.exit2! the*rA<ment *//o7( on/2 to 5on5/<-e th*t r(s) i( non-e5re*(inA:V*rt b: Fo//o7( -ire5t/2 3rom Axiom *: !
%,776 $343 Strict convexity implies that w(w ) w) * 0:
Z[ ! ! A#$
Proof. C<I(tit<te
w =u)u(; w( =
u)(u( ) u((u)u"(
; w) =u))u( ) u()u)
u"(
in the 3orm</* 3or KA to Aet
KA =(w) ) w(w)(1 + w")$+"
9 0
!
A:e: RG181C/0/1. 5373 *06BL,9M,GK &I1819D S67,3 ^n the (t*n-*r- Ct*5Be/KIerA A*me o3 ex*mp/e b:e! /et Q8(q9) = q1 ) q71 Ie the -e.i*tion o3 the Fo//o7er6(o<tp<t 5hoi5e q1 3rom the (e/E(h Ie(t rep/2 q71 = 12)
!"q9 7hen the ce*-er 5hoo(e(
o<tp<t q9: hne h*(dQ8dq9
= )1
2w )
dw
dq9q9
7here w =&#'(Mq1 ;Mq9):
?T@ ^3 Fo//o7er6( pre3eren5e( A *re Exe- *n- /ine*r then&#' o3 the optim*/point i( 5on(t*nt 7ith re(pe5t to q9 *n- *:%
*;"i( po(iti.e i3 *n- on/2 i3
pre3eren5e( *t the point *re m*/e.o/ent:?Z@ ^3 Fo//o7er6( pre3eren5e( A *re Exe- *n- 5on.ex! then&#' i( -e5re*(inA in
q9 *n-*:%
*;"5ont*in( *n *--ition*/ term th*t i( po(iti.e pro.i-inA q9 + 12!
w + 1! w( " 0 *n- w( + w) " 0:?b@ ^3 Fo//o7er6( pre3eren5e( (*ti(32 Axiom ! (tri5t/2! then&#' i( -e5re*(inA
in q9 *n-*:&
%
*;"5ont*in( *n *--ition*/ po(iti.e term:
?`@ ^3 Fo//o7er6( pre3eren5e( (*ti(32 Axiom * (tri5t/2 then&#' i( -e5re*(inAin q9 *n-
*:'%
*;"h*( *n *--ition*/ po(iti.e ?neA*ti.e@ term i3 the (t*t<( L<o
i( (m*//er ?/*rAer@ th*n q9:
Proof. %he FOC i( (w(q1 ; q9) =)WTP (Mq1 ;Mq9) = NTP ="&!";#;"
) 1! 7hi5h5*n Ie re7ritten *(
?A:Z@ q1 = 12)w(q1 ; q9) + 1
2q9
*n- there3ore Q8 (*ti(Ee(
?A:b@ Q8 = )w(q1 ; q9)
2q9
R6G0 13 Linear preferences ^3 Fo//o7er6( pre3eren5e( *re Exe- *n- /ine*r 7ithWTP = w then -i9erenti*tion o3 ?A:b@ 7ith re(pe5t to q9 Ai.e(
dQ8dq9
= )w
2
R6G0 2:Convex Preferences ^3 Fo//o7er6( pre3eren5e( *re Exe- *n- 5on.ex then
dQ8dq9
= )w(q1 ; q9)
2)q92
dw(q1 ; q9)
dq9
]ESEAcE$ Ac%]O^CG ZT
;e (h*// (ho7 th*t *A,;# B;"-*;"i( neA*ti.e: ^n-ee-
dw(q1 ; q9)
dq9= w(
dm
dq9+ w)
dy
dq9
= w((()1)dq1dq9
)q1 +Mdq1dq9
) + w)(()1)dq1dq9
)q9 +M)
7hi5h *3ter (<I(tit<tinA M = 24 ) q9 ) q1 ; q1 = 12 ) A,;# B;"-#!" q9 *n-
*;#*;"
=
)A,;# B;"-#!" ) *A,;# B;"-
*;"q9 *n- (o/.inA 3or
*A,;# B;"-*;"
7e Aet
dw(q1 ; q9)
dq9=B
A
7hereA = 2 + [w(w ) w)] q"9
*n-B = 24(w) ) w() + q9(1) w)(w( ) w) + ww( ) w)):
A( in the proo3 o3 the pre.io<( propo(ition *n- cemm* ?A:`@! 7e h*.e w))w( + 0-<e to 5on.exit2! w + 1 *n- w( " 0:C<ppo(e q9 + 12: %hen 2q9 + 24 *n- w) ) w( + 0 imp/2
B 9 )+w"w( ) 2ww) + w(
,q9
^3 w ! [0; 1] then the expre((ion in Ir*5Bet( i( nonKneA*ti.e ?7rite it *( w(ww( )w) + w(=w ) w)) 7hi5h i( /*rAer th*n 2w(ww( ) w)) " 0@: ^3 ho7e.er w 9 0then the term in Ir*5Bet( i( po(iti.e (in5e w") ) w"( + 0: %o (ee thi(! re5*// th*tw) + w( " 0 *n- w) ) w( + 0:R6G0 33 Axiom R ECect. cet wC(q1 ; q9) -enote WTP 3or 5h*nAe- pre3eren5e(
*( in Axiom R: %hen
QC8 = )wC(q1 ; q9)
2q9
3or *// q9; *n-
dQC8dq9
= )wC(q1 ; q9)
2)q92
dwC(q1 ; q9)
dq9
= )w(q1 ; q9)
2)wC(q1 ; q9)) w(q1 ; q9)
2)q92
dwC(q1 ; q9)
dq9
From Axiom R the (e5on- term i( po(iti.e *n- (imi/*r/2 *( in p*rt Z the thir-term i( po(iti.e i3 in-<5e- pre3eren5e( *re Iene.o/ent ?wC " 0) or m*/e.o/ent 7ithwC) + w
C( " 0:
R6G0 4: Axiom S ECect.cet w.(q1 ; q9) -enote WTP 3or 5h*nAe- pre3eren5e( *( in Axiom S %hen
Q.8 = )w.(q1 ; q9)
2q9
i( (m*//er ?/*rAer@ th*n QC8 i3 the (t*t<( L<o i( (m*//er ?/*rAer@ th*n q9! *n-
dQ.8dq9
= )w.(q1 ; q9)
2)q92
dw.(q1 ; q9)
dq9
h*( *n *--ition*/ po(iti.e ?neA*ti.e@ term i3 the (t*t<( L<o i( (m*//er ?/*rAer@ th*nq9: !
ZZ ! ! A#$
A:T[: $90,G.60/A, !,KG,CC/1.C3 %he /*(t proo3 (<AAe(t( */tern*ti.e (pe5iE5*Ktion( 3or the HG# reAre((ion(: cet a = w(w ) w)! b = w) ) w( *n- c =(1 ) w) (w( ) w) + ww( ) w)) : ]e5*// 3rom the proo3 th*t a " 0; b + 0 *n-c " 0 3or *// q9 ! *n-
dw(q1 ; q9)
dq9=
24b
2 + aq"9+
c
2 + aq"9q9;
dQ8dq9
= )w(q1 ; q9)
2)
12b
2 + aq"9q9 )
c
2(2 + aq"9)q"9
%he Er(t or-er %*2/or exp*n(ion Q8(q9) : C + *:%
*;"q9 then (<AAe(t( EttinA Q8
to * 5<Ii5 expre((ion in q9!
Q8 = :% + :!q9 + :"q"9 + :$q
$9 + u" + `":Vre-i5tion( *re_ :" * 0; :$ 9 0:
?A:`@
%he pre-i5te- 5oei5ient (iAn( then *re :" * 0; :$ 9 0; 5on(i(tent 7ith the re(</t(reporte- in t*I/e ?b@ Ie/o7: ciBe7i(e! *A
*;": =! + ="q9 (<AAe(t( the L<*-r*ti5
(pe5iE5*tion WTP = :% + :!q9 + :"q"9 + u" + `": %he pre-i5tion( :" * 0; :! 9 0
*re 5on(i(tent 7ith the re(</t( I<t *re not (iAniE5*nt in thi( (pe5iE5*tion: A//o7KinA *(2mmetri5 re(pon(e( to ce*-er 5hoi5e( more or /e(( Aenero<( th*n Co<rnotpro-<5e( more (iAniE5*nt e(tim*te(! *( reporte- in the /*(t 5o/<mn:
Dep:V ariable Q8 WTP 7 100 WTP 7 100
q9 )2:136 0:93%>%!$ )6:076 5:24%>!"& )3:986 5:19%>"""
DP 7 q9 2:626 0:92%>%%$
q"9 0:296 0:11%>%%' 0:086 0:27%>$+' 0:096 0:26%>$)'
q$9 )0:016 0:004%>%%'
constant 4:416 2:63%>%&+ 28:266 24:87%>!"* 0:396 26:29%>&*&
V*ne/ ]eAre((ion( 7ith Exe- e9e5t(: $*t* 5on(i(t o3 ZZ[5hoi5e( I2 ZZ Fo//o7er( in HG# experiment: hneK(i-e- pK.*/<e(*re reporte- *n- 6 re3er( to (t*n-*r- error:
d:
V,9B17,%hi( i( *n experiment *Io<t -e5i(ionKm*BinA: vo< 7i// Ie p*i- * o\ p*rti5ip*tion3ee p/<( *n *--ition*/ po(iti.e or Jero *mo<nt o3 mone2 -etermine- I2 the -e5i(ion(th*t 2o< *n- the other p*rti5ip*nt( m*Be! *( exp/*ine- Ie/o7: V*2ment i( in 5*(h*t the en- o3 the experiment: A re(e*r5h 3o<n-*tion h*( pro.i-e- the 3<n-( 3or thi(experiment:
Q1 '69L/.K $991O,E#o7 th*t the experiment h*( IeA<n! 7e *(B th*t 2o< -o not t*/B: ^3 2o< h*.e *L<e(tion! p/e*(e r*i(e 2o<r h*n- *n- *n experimenter 7i// *ppro*5h 2o< *n- *n(7er2o<r L<e(tion in pri.*te:
]ESEAcE$ Ac%]O^CG Zb
$ +1./01G 6.E 'O1 SG1I8CA monitor 7i// Ie (e/e5te- r*n-om/2 3rom *monA tho(e o3 2o< 7ho 5*me here to-*2:%he re(t o3 2o< h*.e Ieen -i.i-e- r*n-om/2 into t7o Aro<p(! 5*//e- the Fir(t Go.erXro<p *n- the Ce5on- Go.er Xro<p:
J1789,0, RG/A6BD%he experiment i( (tr<5t<re- (o th*t no one a not e.en the experimenter(! themonitor! *n- the other (<IPe5t( a 7i// e.er Bno7 2o<r per(on*/ -e5i(ion in theexperiment: vo< 5o//e5t 2o<r 5*(h p*2ment 3rom * (t*9 per(on in the E5onomi5($ep*rtment oi5e 7ho h*( no other ro/e in the experiment: vo<r p*2ment i( in* (e*/e- en.e/ope 7ith * 5o-e /etter ?A! d! C! et5@: vo<r pri.*52 i( A<*r*ntee-Ie5*<(e neither 2o<r n*me nor 2o<r (t<-ent ^$ n<mIer 7i// *ppe*r on *n2 -e5i(ionre5or-(: %he on/2 i-enti32inA m*rB on the -e5i(ion 3orm( 7i// Ie * 5o-e /etterBno7n on/2 to 2o<: vo< 7i// (ho7 2o<r 5o-e /etter to the (t*9 per(on *n- noIo-2e/(e 7i// (ee it: %he experimenter( 7i// not Ie in the -ep*rtment oi5e 7hen 2o<5o//e5t 2o< 5*(h p*2ment: %hi( pro5e-<re i( <(e- to prote5t 2o<r pri.*52:
'F, )E,6 1H 0F, S67,%he A*me in.o/.e( t7o p/*2er(! 5*//e- the Fir(t Go.er ?FG@ *n- the Ce5on- Go.er?CG@! in the ro/e( o3 pro-<5er( o3 *n i-enti5*/ Aoo-: E*5h -e5i-e( ho7 m<5h to proK-<5e: %he proEt 3or e*5h p/*2er i( the n<mIer o3 <nit( he -e5i-e( to pro-<5e time(pri5e! net o3 5o(t: %he pri5e o3 the Aoo- -e5re*(e( *( tot*/ pro-<5tion in5re*(e(: ^32o< *n- the other p/*2er pro-<5e too m<5h! 2o< 7i// -ri.e -o7n the pri5e *n- 2o<rproEt(: h3 5o<r(e! i3 2o< -on6t pro-<5e m<5h 2o< 7on6t h*.e m*n2 <nit( to (e//:%o (imp/i32 2o<r t*(B! the proEt( 7i// Ie 5*/5</*te- 3or 2o< *n- (ho7n in *n e*(2KtoKre*- t*I/e: vo<r 5*(h p*2ment 7i// in5/<-e the proEt 2o< e*rn in one ro<n- o3the A*me: %he ro<n- 7i// Ie (e/e5te- r*n-om/2 *t the en- o3 the experiment:
S67, &,06/9CE*5h ro<n- the FG 5hoo(e( Iet7een t7o po((iI/e *mo<nt( to pro-<5e! *( (ho7n in* t*I/e 7ith t7o ro7(: %he CG (ee( the 5hoi5e o3 the FG! *n- then -e5i-e( *monA(e.en po((iI/e *mo<nt( to pro-<5e! *( (ho7n in (e.en 5o/<mn( o3 the (*me t*I/e:%he t*I/e (ho7( the proEt( 3or Ioth p/*2er(: %he FG6( proEt i( (ho7n in it*/i5( inthe /o7er /e3t 5orner o3 e*5h Iox! *n- the CG6( proEt i( (ho7n in Io/- in the <pperriAht 5orner: For ex*mp/e! in %*I/e T Ie/o7! i3 FG 5hoo(e( h<tp<tkl *n- CG then5hoo(e( h<tp<tk`! then FG6( proEt i( n` *n- CG6( proEt i( \l:
'6M9, 11 *+PC JF1/B, 1H WI08I0 XI6.0/0DY4 5 6 7 8 9 10 11
FG6( h<tp<tkl +&')
(+)'
("("
))((
)%+%
'&+!
&++%
&"((
FG6( h<tp<tke **&&
*%'%
+!'&
("')
)$')
'&'&
&''%
$)&&
&/U,G,.0 *IM[,B0 R6/GC /. "A,GD &,B/C/1.E*5h Fir(t Go.er *n- e*5h Ce5on- Go.er 7i// m*Be 3o<r -e5i(ion(: d<t the p*irinAo3 Fir(t Go.er( 7ith Ce5on- Go.er( 7i// Ie -i9erent in e.er2 -e5i(ion: %hi( me*n(th*t 2o< 7i// inter*5t 7ith * $^FFE]E#% per(on in the other Aro<p in e.er2-e5i(ion th*t 2o< m*Be:
Z` ! ! A#$
"58,G/7,.0 RG1B,EIG,C 6.E 0F, +1./01GAt the IeAinninA o3 the experiment! the monitor 7i// 7*/B thro<Ah the room 5*rr2KinA * Iox 5ont*ininA <nm*rBe-! /*rAe m*ni/* en.e/ope(: E*5h (<IPe5t in the Fir(tGo.er Xro<p 7i// t*Be one o3 the(e en.e/ope( 3rom the Iox: %hi( en.e/ope 7i//5ont*in the experiment -e5i(ion 3orm( *n- * 5o-e /etter:A3ter the Fir(t Go.er( h*.e m*-e their -e5i(ion(! the2 ret<rn the experiment -e5iK(ion 3orm( to their /*rAe m*ni/* en.e/ope( *n- then 7*/B to the 3ront o3 the room*n- -epo(it the en.e/ope( in the Iox on the t*I/e: ^t i( .er2 import*nt th*t the Fir(tGo.er( -o #h% ret<rn their 5o-e /etter( to the /*rAe m*ni/* en.e/ope(! Ie5*<(ethe2 7i// nee- them to 5o//e5t their p*2o9(:A3ter *// Fir(t Go.er( h*.e -epo(ite- their en.e/ope( in the Iox! the Gonitor 7i//t*Be the Iox to *nother room in 7hi5h the experimenter( 7i// (ort the -e5i(ion3orm( *n- p/*5e them in the 5orre5t /*rAe m*ni/* en.e/ope( 3or the Ce5on- Go.er(:%he experimenter( 7i// */(o p<t 5o-e /etter( in the en.e/ope( 3or the Ce5on- Go.er(:#ext! the Gonitor 7i// 7*/B thro<Ah the room 5*rr2inA * Iox 5ont*ininA <nm*rBe-!/*rAe m*ni/* en.e/ope(: E*5h (<IPe5t in the Ce5on- Go.er Xro<p 7i// t*Be one o3the(e en.e/ope( 3rom the Iox: %hi( en.e/ope 7i// 5ont*in the experiment -e5i(ion3orm( *n- * 5o-e /etter:A3ter the Ce5on- Go.er( h*.e m*-e their -e5i(ion(! the2 ret<rn the experiment-e5i(ion 3orm( to their /*rAe m*ni/* en.e/ope( *n- then 7*/B to the 3ront o3 theroom *n- -epo(it the en.e/ope( in the Iox on the t*I/e: ^t i( .er2 import*nt th*tthe Ce5on- Go.er( -o #h% ret<rn their 5o-e /etter( in the /*rAe m*ni/* en.e/ope(Ie5*<(e the2 7i// nee- them to 5o//e5t their p*2o9(:A3ter *// Ce5on- Go.er( h*.e -epo(ite- their en.e/ope( in the Iox! the Gonitor 7i//t*Be the Iox to *nother room in 7hi5h the experimenter( 7i// re5or- the proEt(*n- 5*(h p*2ment( -etermine- I2 the (<IPe5t(6 -e5i(ion(:
$ !199 1H 6 &/, &,0,G7/.,C VF/BF &,B/C/1. R6DC +1.,DA/tho<Ah 2o< 7i// m*Be 3o<r -e5i(ion(! on/2 one 7i// p*2 5*(h: ;hi5h o3 the(e-e5i(ion( 7i// p*2 5*(h 7i// Ie -etermine- I2 ro//inA * (ixK(i-e- -ie: %he experiKmenter 7i// ro// the -ie in 3ront o3 2o< *n- the monitor 7i// *nno<n5e 7hi5h o3 then<mIere- (i-e( h*( en-e- <p on top: %he Er(t n<mIer 3rom T to ` th*t en-( <pon top 7i// -etermine the p*Ae n<mIer o3 the -e5i(ion th*t p*2( 5*(h:%he monitor6( 5*(h p*2ment 7i// Ie the *.er*Ae o3 *// Fir(t Go.er( *n- Ce5on-Go.er( p*2ment(:
\, J6G,HI9de 5*re3</ in re5or-inA 2o<r -e5i(ion(: ^3 * Fir(t Go.er 3orAet( to 5ir5/e one o3 thero7( in the t*I/e! or 5ir5/e( Ioth ro7( on the (*me -e5i(ion p*Ae! then it 7i// Ieimpo((iI/e to *(5ert*in 7h*t -e5i(ion the Fir(t Go.er m*-e: ^n th*t 5*(e! the Fir(tGo.er 7i// Aet p*i- [ *n- the Ce5on- Go.er 7i// Aet p*i- l[ i3 th*t -e5i(ion p*Ae i((e/e5te- 3or p*2o9 I2 the ro// o3 the -ie: ^3 * Ce5on- Go.er -oe(n6t 5ir5/e * 5o/<mn!then it 7i// Ie impo((iI/e to *(5ert*in 7h*t -e5i(ion the Ce5on- Go.er m*-e: ^nth*t 5*(e! the Ce5on- Go.er 7i// Aet p*i- [ *n- the Fir(t Go.er 7i// Aet p*i- l[ i3th*t -e5i(ion p*Ae i( (e/e5te- 3or p*2o9 I2 the ro// o3 the -ie:
R6D !60,CFor e*5h point o3 proEt 2o< e*rn! the experimenter 7i// p<t * Exe- n<mIer o3 -o//*r(in 2o<r en.e/ope: %hi( Exe- n<mIer i( 5*//e- the p*2 r*te *n- i( 7ritten on the
]ESEAcE$ Ac%]O^CG Z\
Io*r- *t the 3ront o3 the room: %o-*26( p*2 r*te i( o[:Z\! 7hi5h me*n( th*t e.er2p*rti5ip*nt e*rn( Z\ 5ent( 3or e*5h proEt point (ho7n in the t*I/e:
NG,]I,.09D $CL,E XI,C0/1.C
jT_ Ex*5t/2 ho7 *re proEt( 5*/5</*te- in the %*I/e(UA_ Vri5e i( b[ min<( the (<m o3 FG o<tp<t *n- CG o<tp<t: G*rAin*/ 5o(t i( l:VroEt i( o<tp<t time( ?pri5e min<( m*rAin*/ 5o(t@: d<t 2o< -on6t h*.e to 7orr2*Io<t -oinA the 5*/5</*tionR the %*I/e( -o it 3or 2o<:
jZ_ ;ho 7i// Bno7 7h*t -e5i(ion( ^ m*BeUA_ #oIo-2 e/(e Ie(i-e( 2o<R th*t i( the point o3 the pri.*te en.e/ope( et5: %heexperimenter( *re on/2 intere(te- in Bno7inA the -i(triI<tion o3 5hoi5e( 3or FG(*n- CG(! not in the pri.*te -e5i(ion( o3 in-i.i-<*/ p*rti5ip*nt(:
jb_ ^( thi( (ome p(25ho/oA2 experiment 7ith *n *Aen-* 2o< h*.en6t to/- <(UA_ #o: ^t i( *n e5onomi5( experiment: ^3 7e -o *n2thinA -e5epti.e! or -on6t p*22o< 5*(h *( -e(5riIe-! then 2o< 5*n 5omp/*in to the 5*mp<( H<m*n C<IPe5t(Committee *n- 7e 7i// Ie in (erio<( tro<I/e: %he(e in(tr<5tion( *re on the /e.e/*n- o<r intere(t i( in (eeinA the -i(triI<tion o3 5hoi5e( m*-e in 5omp/ete pri.*52:
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80
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120
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er P
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0.2 (1)
0.8 (4)
0.48 (14)
0.24 (7)
0.17 (5)
0.10 (3)
0.37(16)
0.37 (16)
0.12 (5)
0.14 (6)
0.16 (3)
0.58 (11)
0.21 (4)
0.05 (1)
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