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jlyhq wkh rwkhu ?up*v ghflvlrq uxohv dqg djhqwv* ghflvlrq sur?ohv1
Wkh Qdvk htxloleulxp ri wkh hfrqrp| fdq eh dqdo|}hg e| edfnzdug lqgxfwlrq1
Htxloleulxp Wdvn Dvvljqphqwv= Lq Vwdjh 9 +wdvn dvvljqphqw vwdjh,/ vxssrvh wkdw d
qrq0hpsw| vhw ri wkh zrunhuv kdv dffhswhg ?up l*v zdjh r>hu1 Ghqrwh ßf +uhvshfwlyho|/ ßß,
(cid:240) (cid:240)
dv wkh vhw ri whvw vljqdov uhdol}hg e| froohjh +uhvshfwlyho|/ kljk vfkrro, dwwhqghhv zkr dffhsw
?up l*v r>hu1 Gh?qh ß (cid:236) ßQ ^ßß= Vlqfh lq wklv vwdjh/ wkh wdvn dvvljqphqw uxoh ri d ?up
(cid:240) (cid:240) (cid:240)
lv qr orqjhu vwudwhjlf/ zh fdq vlpso| dqdo|}h wkh rswlpdo wdvn dvvljqphqw uxoh iru ?up l
idflqj ß = Lw lv suryhg dv Ohppd 5 lq wkh dsshqgl{ wkdw wkh rswlpdo wdvn dvvljqphqw uxoh
(cid:240)
iru ?up l lv ri wkh irup=
+
4 li º Ł(cid:129)º(cid:230)
w +º>m, @ (cid:240) >m @k>f= +5,
(cid:240) 3 li º ?(cid:129)º(cid:230)
(cid:240)
Wklv fxw0r> surshuw| lv d frqvhtxhqfh ri wkh vwulfw POUS ri wkh whvw whfkqrorj|1
Htxloleulxp R>hu Dffhswdqfh Ghflvlrqv= Lq Vwdjh 8/ zkhq d zrunhu iurp hgxfdwlrq
q r
jurxs m zlwk whvw vljqdo º lv r>huhg d sdlu ri zdjh vfkhgxohv/ z(cid:230)+º,>z(cid:230)+º, / klv rswlpdo
(cid:129) 2
r>hu dffhswdqfh ghflvlrq/ dvvxplqj zlwkrxw orvv ri jhqhudolw| wkdw kh lsv d frlq zkhq kh
lv lqgl>huhqw/ lv=
;
A? 4 li z(cid:230)+º, Az(cid:230) +º,
(cid:240) (cid:240)(cid:226)
L(cid:230) +º,@ (cid:129) li z(cid:230)+º,@z(cid:230) +º, > zkhuh l9@l(cid:226)= +6,
(cid:240)(cid:247)Œ(cid:129)cŒ2: A= 32 li z(cid:230)(cid:240)+º, ?z(cid:230)(cid:240)(cid:226)+º,
(cid:240) (cid:240)(cid:226)
4;Qrwhwkdwwkhrqo|srvvleohr>htxloleulxpsdwk lq wkhprghodulvhvlqwkhwdvndvvljqphqwvwdjh/zklfk
lv qrw vwudwhjlf1 Lw fdq eh vkrzq wkdw dq| Qdvk htxloleulxp ri wkh prgho fdq eh surshuo| prgl?hg r> wkh
htxloleulxp sdwk lqwr d Shuihfw Ed|hvldq Htxloleulxp1 Khqfh xvlqj Shuihfw Ed|hvldq Qdvk lqvwhdg ri Qdvk
zloo qrw d>hfw dq| riwkh htxloleulxprxwfrph1
<
Wkh vhw ri whvw vljqdov uhdol}hge| ?up l*v zrunhuv zlwk hgxfdwlrqdo dwwdlqphqw m/ ß(cid:230)> lv wkh
vxssruw ri wkh ixqfwlrq L(cid:230) =
(cid:240)(cid:247)Œ cŒ :
(cid:129) 2
Htxloleulxp Zdjh Vfkhgxohv= Qrz zh frqvlghu wkh ?upv* zdjh r>hulqj ghflvlrqv lq
Vwdjh 7= Zh suryh dv Ohppd 4 lq wkh dsshqgl{ wkdw lq htxloleulxp wkh zdjh vfkhgxohv
r>huhg e| wkh wzr ?upv wr zrunhuv iurp hgxfdwlrq jurxs m duh doprvw hyhu|zkhuh htxdo/
wkdwlv/ z(cid:230)+º,@z(cid:230)+º,h{fhswsrvvleo|irudvhwrivljqdovzlwkphdvxuh }hur1 Wkh dujxphqw
(cid:129) 2
lv vlpsoh= Vxssrvh wr wkh frqwudu| rqh ?up r>huv d kljkhu zdjh wr dsrvlwlyh phdvxuh vhwri
zrunhuv iurp hgxfdwlrqjurxs m/ wkdw ?up frxogsur?wdeo| ghyldwh e| fxwwlqj wkh gl>huhqfh
lq kdoi/ wkhuhe| orzhulqj wkh zdjh eloo zkloh nhhslqj lwv zrun irufh xqfkdqjhg1 Wrjhwkhu
zlwk wkh r>hu dffhswdqfh uxoh +6,/ wklv lq sduwlfxodu lpsolhv wkdw wkh vhw ri whvw vljqdov iru
wkh wzr ?upv duh wkh vdph/ l1h1/ ß(cid:230) @ ß(cid:230)= Khqfh lq wkh htxloleulxp wdvn dvvljqphqw uxoh
(cid:129) 2
+5, lw pxvw eh wkdw (cid:129)º(cid:230) @ (cid:129)º(cid:230) ehfdxvh wkh wzr ?upv duh vroylqj wkh vdph sureohp1 Zulwh (cid:129)º(cid:230)
(cid:129) 2
dv wkh frpprq wkuhvkrog1
Qrzzhduelwudulo|?{ wkhhgxfdwlrqfkrlfhsur?oh M dqgvnloolqyhvwphqwghflvlrqsur?oh
h dqg dvn zkdw zdjh vfkhgxohv duh frpsdwleoh zlwkhtxloleulxp1 Zh zulwh z(cid:230)+ºmM>h, dv wkh
?upv*frpprqvhtxhqwldoo|udwlrqdozdjhvfkhgxohviroorzlqj+M>h,=Zulwh(cid:228)(cid:230) dvwkhiudfwlrq
ri txdol?hg zrunhuv lq hgxfdwlrq jurxs m lpsolhg e| +M>h,= Ghqrwh H(cid:230)^dmh+d>y, @h ‘ +uh0
^
vshfwlyho|/ H(cid:230)^dmh+d>y,@h ‘, dv wkh h{shfwhg lqqdwh delolw| lq h!flhqf| xqlwv ri d zrunhu
(cid:252)
iurp hgxfdwlrq jurxs m zkr fkrrvhv wr eh txdol?hg +uhvshfwlyho|/ xqtxdol?hg,1 Iru qrwd0
(cid:253) (cid:252)
wlrqdo vlpsolflw| zh zulwh i +º, @ (cid:228)(cid:230)i +º,. 4(cid:253)(cid:228)(cid:230) i +º, dv wkh suredelolw| ghqvlw| ri
Z(cid:230) ^ (cid:252)
whvwvljqdovlqhgxfdwlrqjurxsm zkhqlwviudfwlrqritxdol?hgzrunhuvlv (cid:228)(cid:230)=Lwfdqehvkrzq
wkdw lq htxloleulxp/ zlwk ªQ @ª dqg ªß @4>
+ (cid:253) (cid:252)
(cid:228)(cid:230)i +º, 4(cid:253)(cid:228)(cid:230) i +º,
z(cid:230)+ºmM>h, @pd{ ^ ª(cid:230)H(cid:230)^dmh+d>y,@h ‘. (cid:252) ª(cid:230)H(cid:230)^dmh+d>y,@h ‘>
i +º, ^ i +º, (cid:252)
Z(cid:230) Z(cid:230)
(cid:226)
(cid:228)(cid:230)i +º,
^ ª(cid:230)H(cid:230)^dmh+d>y, @h ‘{ = +7,
i +º, ^ ^
Z(cid:230)
Qrwhwkdw(cid:228)(cid:230) vhuyhvdvwkh?upv*sulrueholhiderxwdudqgrpo|gudzqzrunhuiurphgxfdwlrq
jurxs m ehlqj txdol?hg/ dqg (cid:228)(cid:230)i +º,@i +º, lv wkhlu srvwhulru eholhi wkdw wkh zrunhu lv
^ Z(cid:230)
txdol?hg zkhq d whvw vljqdo º lv uhdol}hg1 Lq wkh hyhqw wkdw wkh zrunhu lv txdol?hg/ klv
h{shfwhg surgxfwlylw| rq wkh vlpsoh wdvn lv ª(cid:230) wlphv wkh h{shfwhglqqdwh delolw| frqglwlrqdo
rq klv fkrrvlqj h > vlploduo| lq wkh hyhqw wkdw kh lv xqtxdol?hg/ klv h{shfwhg surgxfwlylw|
^
rq wkh vlpsoh wdvn lv ª(cid:230) wlphv wkh h{shfwhg lqqdwh delolw| frqglwlrqdo rq klv fkrrvlqj h =
(cid:252)
Klv h{shfwhg surgxfwlylw| rq wkh frpsoh{ wdvn lv wkh suredelolw| wkdw kh lv txdol?hg wlphv
wkh h{shfwhg h!flhqf| xqlwv frqglwlrqdo rq klv ehlqj txdol?hg wlphv { = Wkxv irupxod +7,
^
hvvhqwldoo| vwdwhv wkdw hdfk zrunhu lv sdlg klv h{shfwhg surgxfwlylw| lq klv pruh surgxfwlyh
wdvn1 Zh zloo khqfhiruwk zulwh H(cid:230)+dmh , dqg H(cid:230)+dmh , dv vkruw0kdqg iru H(cid:230)^dmh+d>y,@h ‘
^ (cid:252) ^
dqg H(cid:230)^dmh+d>y,@h ‘/ uhvshfwlyho|1
(cid:252)
Sursrvlwlrq 4 VxssrvhlqdQdvkhtxloleulxpdjhqwv*hgxfdwlrqfkrlfhdqgvnloolqyhvwphqw
ghflvlrq sur?ohv duh uhvshfwlyho| M dqg h= Wkhq wkh ?upv* zdjh r>huv pxvw eh jlyhq e| +7,
43
Description:that there exists a mapping to transform a multiMdimensional skill vector into a real number where wj i Z {P, Q} A. \е. We write W as the set of all feasible wage offers, i.e., W 1бwгw Z бh, cа " {P,Q} A \еа.17. Stage 5 (Offer Acceptance). The workers observe the wage schedules wь and wO an