Uma análise entre a energia, renda e emissões de CO2: evidências para o Brasil, 1962-2007

AutorThiago Costa Soares - João Eustáquio de Lima
CargoProfessor do departamento de Economia da UFJF/GV - Professor Titular de Econometria no Departamento de Economia Rural da UFV. Ph.D. em Economia Rural pela Michigan State University (USA), Pós-Doctor em Métodos Quantitativos, pela University
Páginas11-35
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h
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geotérmica
eólica
biomassa
ENERGIA
ENERGIA
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ENERGIA
SECUNDÁRIA
ELETRICIDADE
ENERGIA
RENOVÁVEL
ENERGIA
NÃO
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carvão
gás
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Κ+%.(%∀∋∀∋_&<2&∋7ΦΓΓϑ9∋,(∗
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.∀+%(∋∀∋−.∀6&∋%(∋ %∀∗(+%(∋+&∋ −∀.Ε&%&∋%∀∋ΦΓΗΞ∋(∋ΦΓΓα:∋Κ∋∃+(62&∋%∀1,∀∋
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−.(∗∀+0∃&+(%(1∋−&11(∋1∀.∋+∀3/∃3∀+0∃(%&:∋
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∃+#∀1,∃.∋+(∋∀≅−(+12&∋%(∋0(−(0∃%(%∀∋%∀∋3∀.(62&∋∀/Μ,.∃0(5∋−&∃1∋&∋1∀,&.∋%∀∗(+%(∋
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
Ukinc Xctkƒxgn Wpkfcfg Hqpvg"fg"fcfqu Rgtkqfkekfcfg"
qtkikpcn
ΡµΡ ∀.(62&∋%∀∋∀+∀.3∃(∋
∀/Μ,.∃0(∋7Υ∃%.8)/∃0(9

7οΥ9
Ν∃+∃1,Μ.∃&∋%∀∋Ν∃+(1∋
∀∋Ρ+∀.3∃(∋7ΝΝΡ9 Κ+)(/
;ς∆ ;.&%),&∋ς+,∀.+&∋
∆.),&
Ο(/&.∀1∋0&..∀+,∀1∋
7Πζ9 ∆(+0&∋Α∀+,.(/ Κ+)(/
ΑΒΧ
Ρ∗∃112&∋%∀∋!∃?≅∃%&∋
%∀∋Α(.θ&+∀/(%(1∋7ϕ,9 ∆(+0&∋Ν)+%∃(/ Κ+)(/

Κ∋3∀.(62&∋%∀∋∀+∀.3∃(∋∀/Μ,.∃0(∋.∀−.∀1∀+,(∋ &∋1∀,&.∋∀+∀.3Μ,∃0&∋ +(0∃&+(/∋
+∀1,∀∋∀1,)%&5∋#∃1,&∋Τ)∀∋(∋∗(∃&.∋−(.,∀∋%(∋−.&%)62&∋%&∋1∀,&.∋1∀∋.∀1)∗∀∋(∋∀11∀∋
,∃−&∋%∀∋∀+∀.3∃(:∋Κ∋#(.∃8#∀/∋Μ∋&.∃3∃+(/∗∀+,∀∋0&+1,.)Ε%(∋−∀/&∋Ν∃+∃1,Μ.∃&∋%∀∋
Ν∃+(1∋∀∋ Ρ+∀.3∃(∋∀∋ ∀1,8∋ %∃1−&+Ε#∀/∋+&∋ 1Ε,∃&∋%&∋ς+1,∃,),&∋ %∀∋;∀1Τ)∃1(∋Ρ0&Ζ
+∴∗∃0(∋Κ−/∃0(%(∋7ς;ΡΚ9:∋Β∋;ς∆∋4&∃∋0&+1∃%∀.(%&∋3!452∋%(∋.∀+%(∋+(0∃&+(/5∋
0&+4&.∗∀∋#∃1,&∋∀∗∋Ν&%∃(+&∋7ΦΓδε95∋Κ+%.(%∀∋∀∋_&<2&∋7ΦΓΓϑ95∋⊥0Υ∗∃%,∋∀∋
_∃∗(∋7ΧΙΙε9∋∀∋;(∃1∋7ΧΙΦΧ95∋∀∋.∀−.∀1∀+,(∋&∋(3.∀3(%&∋∗&+∀,8.∃&∋3∀.(%&∋−∀/(∋
−.&%)62&∋%∀∋1∋∀∋1∀.#∃6&1:∋;(.(∋.∀−.∀1∀+,(.∋(∋Τ)(/∃%(%∀∋%&∋∗∀∃&∋(∗
),∃/∃Θ&)Ζ1∀∋(1∋ ∀∗∃11>∀1∋%∀∋ ΑΒΧ5∋Τ)∀∋Μ∋ &∋−.∃+0∃−(/∋381∋ 0()1(%&.∋%&∋ ∀4∀∃,&∋
∀1,)4(:∋∋µ(∋−.?≅∃∗(∋1∀62&5∋(−.∀1∀+,(Ζ1∀∋&1∋.∀1)/,(%&1∋∀∋(+8/∃1∀1∋%&1∋%(%&1:
60" TGUWNVCFQU"G"CPèNKUG"FQU"FCFQU"
6030" Cpƒnkug"fguetkvkxc"fcu"xctkƒxgku

,&%(1∋(1∋#(.∃8#∀∃1∋(−.∀1∀+,(.(∗∋,∀+%[+0∃(∋0.∀10∀+,∀∋+&∋−∀.Ε&%&∋(+(/∃1(%&5∋
0&∗∋%∀1,(Τ)∀∋−(.(∋(∋−.&%)62&∋∀+∀.3Μ,∃0(∋Τ)∀5∋∀∗∋.∀/(62&∋(&∋(+&∋
()∗∀+,&)∋∗(∃1∋%∀∋ΦΗ∋#∀Θ∀15∋∀+Τ)(+,&∋Τ)∀∋(∋.∀+%(∋()∗∀+,&)∋Η5δε∋#∀Θ∀1∋∀∋(1∋
∀∗∃11>∀1∋%∀∋ΑΒΧ5∋Η5ϑϑ∋#∀Θ∀1:∋Ρ∗∋,∀.∗&1∋−∀.0∀+,)(∃15∋(∋−.&%)62&∋%∀∋∀+∀.3∃(∋

&1∋∃+#∀1,∃∗∀+,&1∋.∀(/∃Θ(%&1∋+&∋1∀,&.∋∀/Μ,.∃0&∋+(0∃&+(/∋(∋−(.,∃.∋%(∋%Μ0(%(∋%∀∋
ΦΓΗΙ∋∀∋&∋∃∗−(0,&∋Τ)∀∋(∋−.∃#(,∃Θ(62&∋,∀#∀∋1&<.>
∀∀
Vjkciq"Equvc"Uqctgu"̋"Lq«q"Gwuvƒswkq"fg"Nkoc
!−ς∗&)∋5−∋1=&
;&.∋&),.&∋/(%&5∋∗∀1∗&∋0&∗∋&1∋∃+#∀1,∃∗∀+,&1∋.∀(/∃Θ(%&15∋−&%∀Ζ1∀∋#∀.∃Ζ

%∀∋)∗∋4(,&.∋∀≅?3∀+&∋Τ)∀∋∃∗−(0,&)∋1&<.>
%∀∋0.∀10∃∗∀+,&∋−&1,∀.∃&.∗∀+,∀∋(∋∀11∀∋−∀.Ε&%&:∋Κ∋Τ)∀<. class="_ _3">&0&..∃%(∋
−&%∀∋1∀.∋(,.∃−.&3.(∗(∋+(0∃&+(/∋%∀∋.(0∃&+(∗∀+,&∋Τ)∀∋∀+,.&)∋∀∗∋
#∃3&.∋∀∗∋=)+Υ&∋%∀∋ΧΙΙΦ∋(∋4∀#∀.∀∃.&∋%∀∋ΧΙΙΧ5∋0)=&∋&<=∀,∃#&∋4&∃∋∀#∃,(.∋1&<.>
0(.3(1∋+&∋1∃1,∀∗(∋∀/Μ,.∃0&∋+(0∃&+(/:∋Κ∋0.∃1∀∋4&∃∋&0(1∃&+(%(∋−.∃+0∃−(/∗∀+,∀∋
−∀/(∋%∀14(#&.8#∀/∋0&+%∃62&∋Υ∃%.&/?3∃0(∋+(1∋.∀3∃>∀1∋⊥)%∀1,∀∋∀∋µ&.%∀1,∀∋ ∀∋
Ζ
,(+,&5∋−∀/&∋∗&%∀/&∋−.∀/∃∗∃+(.∋∀1,∃∗(%&∋∀+,.∀∋∀+∀.3∃(∋∀∋∗01125∋(∋Τ)∀<. class="_ _1">+2&∋

%(1∋#(.∃8#∀∃1∋1)−.(0∃,(%(1:∋

%∀∋ΑΒΧ5∋ΦΓΗΧΖΧΙΙϑ
"
0
500
1,000
1,500
2,000
1965 1970 1975 1980 1985 1990 1995 2000 2005
Energia PIB CO2

   
#(.∃8#∀∃1∋.∀+%(∋∀∋∀∗∃11>∀1:∋Κ∋,.(=∀,?.∃(∋%(1∋∀∗∃11>∀1∋∗(+,∀#∀Ζ1∀∋1∀∗∀/Υ(+,∀∋
(&∋;ς∆∋∀∋&∋0.∀10∃∗∀+,&∋%(1∋#(.∃8#∀∃15∋∀∗∋−∀.0∀+,)(/5∋4&∃∋(−.&≅∃∗(%(∗∀+,∀∋
αδΙβ∋+&∋−∀.Ε&%&∋%∀∋∃+,∀.∀11∀:∋Κ∋1∀3)∃.5∋%∀10.∀#∀Ζ1∀∋1&<. class="_ _0">∀0&Ζ
+&∗Μ,.∃0&:∋
∀#
!∀#∃#%&∋()∗∃∗%+,∗∃#∃∗%∗,−(#.∃,∗%/#∃∗∃∗∀())0∗)∃/∗∃1234∃∗5(/6%7(#)∃8#,#∃9∃:,#)(∋.∃;<=3>3??≅
!−ς∗&)∋5−∋1=&
6040" Tguwnvcfqu"gortkequ"fqu"oqfgnqu"XCT"g"XGEO
Κ1∋1Μ.∃∀1∋4&.(∗∋,.(+14&.∗(%(1∋∀∗∋/&3(.∃,∗&5∋−&∃15∋(11∃∗5∋−&%∀Ζ1∀∋∃+Ζ
,∀.−.∀,(.∋&1∋−(.Λ∗∀,.&1∋%&∋∗&%∀/&∋0&∗&∋∀/(1,∃0∃%(%∀1ε:∋µ2&∋&<1,(+,∀5∋∀11∀∋
−.&0∀%∃∗∀+,&∋∗(+,Μ∗∋(1∋0(.(0,∀.Ε1,∃0(1∋∃+∀.∀+,∀1∋]1∋1Μ.∃∀1∋,∀∗−&.(∃1∋+2&∋
(4∀,(+%&∋&∋.∀/(0∃&+(∗∀+,&∋&.∃3∃+(/∋∀+,.∀∋∀/(1:∋Β1∋.∀1)/,(%&1∋%&1∋,∀1,∀1∋%∀∋
.(∃Θ∋)+∃,8.∃(∋12&∋.∀−&.,(%&1∋−∀/(∋θ(

CFH"*pxgn+ RR"*pxgn+
Xctkƒxgn Nciuωv/uvcv Rtqd Dcpfωω v/uvcv Rtqd
ΡµΡ Ι Ι5Ιεδδ Ι5ΓΓΗ ε ΖΙ5εΞΗϑ Ι5ΓδΞΙ
;ς∆ Ι ΖΦ5ΙΦΦϑ Ι5ΓΞΧ Ξ ΖΦ5ΦΓΙΗ Ι5ΓΙΙε
ΑΒΧΦ ΖΦ5δΓδε Ι5ΗΞΓ Ξ ΖΦ5εΓΞΙ Ι5δΦϑ
CFH"*rtkogktc"fkhgtgp›c+ RR"*rtkogktc"fkhgtgp›c+
Xctkƒxgn Nciu v/uvcv Rtqd Dcpf v/uvcv Rtqd
ΡµΡ Ι Ζε5ΞδΞϑ Ι5ΙΙΗ Φ Ζε5ΧΓΗΧ Ι5ΙΙϑε
;ς∆ Ι Ζε5ΧϑΓε Ι5ΙΙδ Ι Ζε5ΧϑΓε Ι5ΙΙδ
ΑΒΧΙ Ζε5εΗεΗ Ι5ΙΙα Ι Ζε5εΗεΗ Ι5ΙΙα

   
Κ)∗∀+,(%&∋7Κ!η9∋∀∋;Υ∃//∃−1Ζ;∀..&+∋7;;9∋−(.(∋(#∀.∃3)(.∋(∋∀1,(∋
1Μ.∃∀15∋0&+1∃%∀.(+%&∋%∀1/&0(∗∀+,&∋∀∋,∀+%[+0∃(∋/∃+∀(.∋%∀,∀.∗∃+Ε1,∃0(∋∀∗∋+Ε#∀/∋
∀∗∋−.∃∗∀∃.(∋%∃4∀.∀+6(:∋η∃0(∋0/(.&5∋(∋−(.,∃.∋%(∋θ(∋Τ)∀∋(1∋#(.∃8#∀∃1∋+2&∋12&∋
∀1,(0∃&+8.∃(1∋∀∗∋+Ε#∀/∋∀5∋−&.,(+,&5∋4(ΘΖ1∀∋+∀0∀118.∃&∋%∃4∀.∀+0∃8Ζ/(1∋−(.(∋,&.+8
Ζ/(1∋∀1,8#∀∃1:∋Β1∋,∀1,∀1∋%∀∋.(∃Θ∋)+∃,8.∃(∋∀∗∋−.∃∗∀∃.(∋%∃4∀.∀+6(5∋0&∗∋0&+1,(+,∀∋
6∀&7∋%&∋

∀∋ν(++(+ΖΨ)∃++∋7νΨ9:∋Β1∋.∀1)/,(%&1∋−&%∀∗∋1∀.∋#∃1)(/∃Θ(%&1∋−∀/(∋θ(
]∋ Υ2∃<5&∋−)∗−∋∃,∗#%&∋)−∋,−;&,∗∃,∋⊥∋ ∗,−=∀&∋−
9_[∋−∋−7#))−)Ρ∋,−);−=∗#Ν∃7−
α∋ 6∃%)∋&Μ∗#5&)∋∃2∗&7∃∗#=∃7−
αα∋ [∃<5β#5∗∀∋)−Ε−=#&
∀∃
Vjkciq"Equvc"Uqctgu"̋"Lq«q"Gwuvƒswkq"fg"Nkoc
!−ς∗&)∋5−∋1=&
6∀&7
Nci CKE UKE 89
Ι ΖΗ5ΙαΦΞαΧ Ζα5δΙΙαδα Ζα5ΓΗΙΙΞΗ
Φ ΖΦΧ5ΞΓΓΙα ΖΦΦ5ϑϑΧΦΞω ΖΦΧ5ΦϑΙϑΗ
Χ ΖΦΧ5αδΓαΓ ΖΦΦ5αδΗαΞ ΖΦΧ5ΧΧεΞΞω
Ξ ΖΦΧ5ΗΦϑΦΗω ΖΦΦ5ΧΞϑΓε ΖΦΧ5ΦΦεΓΧ
ε ΖΦΧ5ΧΗαεα ΖΦΙ5αΦΙΙδ ΖΦΦ5ΗΧΗΧε
α ΖΦΧ5ΦΦΙαΧ ΖΓ5ΓϑΓΙΙδ ΖΦΦ5ΞΞεΞε
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ΚςΑ Ζε5Ιδϑδδε ΖΞ5δδΓαεΞ ΖΞ5αΦΦδΓΧ
⊥ςΑ ΖΞ5ϑΦΓΧΗΦ ΖΞ5αΧΙΓΧΙ ΖΞ5ΦεΞΧΗΓ
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!∀#∃#%&∋()∗∃∗%+,∗∃#∃∗%∗,−(#.∃,∗%/#∃∗∃∗∀())0∗)∃/∗∃1234∃∗5(/6%7(#)∃8#,#∃9∃:,#)(∋.∃;<=3>3??≅
!−ς∗&)∋5−∋1=&
;∀/&∋,∀1,∀∋_Ν5∋+2&∋1∀∋.∀=∀∃,(∋(∋Υ∃−?,∀1∀∋+)/(∋%∀∋()1[+0∃(∋%∀∋(),&0&..∀Ζ
/(62&∋1∀.∃(/∋(,Μ∋(∋Τ)∃+,(∋%∀4(1(3∀∗:∋Β∋0&..∀/&3.(∗(∋%&1∋.∀1Ε%)&1∋%&∋∗&%∀/&∋

Κ∋−.&%)62&∋%∀∋∀+∀.3∃(5∋+&∋0).,&∋−.(Θ&5∋Μ∋∀1,(,∃1,∃0(∗∀+,∀∋(4∀,(%(∋−&.∋
1)(∋%∀4(1(3∀∗:∋Ρ∗∋∗Μ%∃(5∋)∗(∋#(.∃(62&∋−&1∃,∃#(∋%∀∋ΦΙβ∋+&∋−∀.Ε&%&∋,∋,∀+Ζ
%∀∋(∋∀/∀#(.∋(∋#(.∃8#∀/∋∀∗∋ε5Φαβ∋∀∗∋,ψΦ:∋θ&%(#∃(5∋+2&∋Υ8∋∃+%Ε0∃&1∋%∀∋Τ)∀∋
&∋;ς∆∋ ∀∋(1∋∀∗∃11>∀1∋ %∀∋−&/)∀+,∀1∋ (4∀,∀∗∋(∋#(.∃8#∀/∋ +&∋0).,&∋−.(Θ&5∋ −&∃1∋
  
%∀∋∀+∀.3∃(∋−&11)∃∋ ∗(∃&.∋−.(Θ&∋%∀∋∗(,).(62&5∋−&.∋∀11∀∋∗&,∃#&5∋&∋3∀.+&∋

%∀10&∗−(11&1∋∀+,.∀∋(∋%∀∗(+%(∋∀∋&4∀.,(∋+&∋4),).&5∋0&∗&∋&0&..∀)∋+&∋−∀.Ε&%&∋
%∀∋.(0∃&+(∗∀+,&:∋Κ∋η∃3).(∋ε∋.∀11(/,(∋&1∋#(/&.∀1∋0(/0)/(%&1∋−(.(∋&1∋0&..∀/&Ζ
3.(∗(1∋∀1,∃∗(%&1∋(∋−(.,∃.∋%&∋ΟΡΑΝ:
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-.4
-.2
.0
.2
.4
1 2 3 4 5 6 7 8 9 10
Cor(LNENE R,LNENER(-i ))
-.4
-.2
.0
.2
.4
1 2 3 4 5 6 7 8 9 10
Cor(LNEN ER,LN P IB(-i ))
-.4
-.2
.0
.2
.4
1 2 3 4 5 6 7 8 9 10
Cor(LNEN ER,LNCO2(-i ))
-.4
-.2
.0
.2
.4
1 2 3 4 5 6 7 8 9 10
Cor(LNPIB,L NE NE R(-i ))
-.4
-.2
.0
.2
.4
1 2 3 4 5 6 7 8 9 10
Cor(LNPIB,L NP IB(- i))
-.4
-.2
.0
.2
.4
12345678910
Cor(LNP IB,LNCO 2( -i))
-.4
-.2
.0
.2
.4
1
2
3
4
5
6
7
8
9
10
Cor(LNCO2 ,LNENER(-i) )
-.4
-.2
.0
.2
.4
1 2 3 4 5 6 7 8 9 10
Cor(LNCO2 ,LN P IB(-i))
-.4
-.2
.0
.2
.4
1 2 3 4 5 6 7 8 9 10
Cor(LNCO2 ,LNCO2(-i))

∀(
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!−ς∗&)∋5−∋1=&
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−.(Θ&:∋Ρ∗∋1)∗(5∋)∗(∋#(.∃(62&∋−&1∃,∃#(∋%∀∋ΦΙβ∋()∗∀+,(∋0∀.0(∋%∀∋ε5αΗβ∋&∋
;ς∆∋+&∋−∀.Ε&%&∋−&1,∀.∃&.:∋⊥∀3)+%&∋&1∋.∀1)/,(%&1∋%&∋∗&%∀/&5∋∀11∀∋∃∗−(0,&∋Μ∋

%(∋∀+∀.3∃(5∋+&∋0).,&∋−.(Θ&5∋(4∀,(∋(1∋∀∗∃11>∀1∋%∀∋ΑΒΧ∋−&1∃,∃#(∗∀+,∀∋7ΦΙβ∋

∗∀1∗(∋−.&−&.62&∋∀≅−(+%∀∋(1∋∀∗∃11>∀1∋∀∗∋ε5εΗβ∋+&∋−∀.Ε&%&∋−&1,∀.∃&.:∋;&Ζ

+&∋0).,&∋−.(Θ&∋7)∗∋0Υ&Τ)∀∋%∀∋∗∀1∗(∋∗(3+∃,)%∀∋,∀+%∀∋(∋∀/∀#(.∋&1∋−&/)∀+,∀1∋
∀∗∋δ5εδβ∋%&∃1∋−∀.Ε&%&1∋]∋ 4.∀+,∀9:∋Κ∋θ( %∀0&∗−&1∃62&∋%&∋
∀..&∋%∀∋−.∀#∃12&∋%(1∋#(.∃8#∀∃1:∋
θ(
∀∗∃11>∀1∋%∀∋ΑΒΧ
!∀0&∗−&1∃62&∋%(∋#(.∃Λ+0∃(∋−(.(∋Ρ+∀.3∃(
∋;∀.Ε&%& Ρ;ω ΡµΡ ;ς∆ ΑΒΧ
∋Φ Ι5ΙΧΓ ΦΙΙ5ΙΙΙ Ι5ΙΙΙ Ι5ΙΙΙ
∋Χ Ι5Ιεα Γδ5αΦΓ Φ5ΞΞΙ Ι5ΦαΦ
∋Ξ Ι5Ιαδ Γδ5ϑδα Ι5δϑδ Ι5ΞΞϑ
∋ε Ι5ΙϑΧ Γδ5εΧε Φ5ΦεΦ Ι5εΞε
∋α Ι5Ιδϑ Γϑ5αϑϑ Φ5ΓεΗ Ι5εϑϑ
∋Η Ι5ΦΙε Γϑ5ΙδΙ Χ5εΦα Ι5αΙα
∋ϑ Ι5ΦΧΦ ΓΗ5ϑαΙ Χ5ϑΧΞ Ι5αΧϑ
∋δ Ι5ΦΞϑ ΓΗ5ΗΙΗ Χ5δεδ Ι5αεΗ
∋Γ Ι5ΦαΧ ΓΗ5αεΦ Χ5δΓΓ Ι5αΗΙ
∋ΦΙ Ι5ΦΗϑ ΓΗ5αΞΗ Χ5δΓΞ Ι5αϑΦ
∋!∀0&∗−&1∃62&∋%(∋#(.∃Λ+0∃(∋−(.(∋;ς∆
∋;∀.Ε&%& Ρ;ω ΡµΡ ;ς∆ ΑΒΧ
∋Φ Ι5ΙΞΧ εΓ5ΧΓδ αΙ5ϑΙΧ Ι5ΙΙΙ
∋Χ Ι5ΙαΞ ΗΓ5ΧΗΞ ΞΙ5ϑΦΗ Ι5ΙΧΦ
∋Ξ Ι5Ιϑϑ ϑδ5ΗΓϑ ΧΦ5ΧΞΙ Ι5ΙϑΞ
∋ε Ι5ΙΓϑ δΞ5ΓαΞ Φα5ΓΧδ Ι5ΦΦΓ
∋α Ι5ΦΦα δΗ5ϑαΞ ΦΞ5ΙΓδ Ι5ΦεΓ
∋Η Ι5ΦΧΓ δδ5αδΙ ΦΦ5ΧαΞ Ι5ΦΗΗ
∋ϑ Ι5ΦεΧ δΓ5ϑδΗ ΦΙ5ΙΞΓ Ι5Φϑα
∋δ Ι5ΦαΧ ΓΙ5ΗΗα Γ5ΦαΗ Ι5ΦϑΓ
∋Γ Ι5ΦΗΦ ΓΦ5ΞΦΦ δ5αΙΓ Ι5ΦδΦ
∋ΦΙ Ι5ΦΗδ ΓΦ5δΦΦ δ5ΙΙΓ Ι5ΦδΙ
∀)
!∀#∃#%&∋()∗∃∗%+,∗∃#∃∗%∗,−(#.∃,∗%/#∃∗∃∗∀())0∗)∃/∗∃1234∃∗5(/6%7(#)∃8#,#∃9∃:,#)(∋.∃;<=3>3??≅
!−ς∗&)∋5−∋1=&
∋!∀0&∗−&1∃62&∋%(∋#(.∃Λ+0∃(∋−(.(∋ΑΒΧ
∋;∀.Ε&%& Ρ;ω ΡµΡ ;ς∆ ΑΒΧ
∋Φ Ι5ΙΞδ Χδ5ΗΧϑ α5ΓΗϑ Ηα5εΙϑ
∋Χ Ι5ΙΗΧ εΞ5Χαα Χ5ΧϑΓ αε5εΗΗ
∋Ξ Ι5ΙδΓ αδ5εΧϑ Φ5ΧΦδ εΙ5Ξαε
∋ε Ι5ΦΦΦ Ηε5ΦΦΦ Φ5Φϑα Ξε5ϑΦε
∋α Ι5ΦΞΙ ΗΗ5ΞΓΞ Φ5εϑε ΞΧ5ΦΞΞ
∋Η Ι5Φεε ΗΗ5ΧΓΧ Χ5Ξϑα ΞΦ5ΞΞΞ
∋ϑ Ι5Φαα Ηα5Ξαδ Ξ5ΞΞΙ ΞΦ5ΞΦΦ
∋δ Ι5ΦΗα ΗΞ5δεΓ ε5εαδ ΞΦ5ΗΓΞ
∋Γ Ι5ΦϑΧ ΗΧ5ΦΓΞ α5αεΦ ΞΧ5ΧΗΗ
∋ΦΙ Ι5ΦϑΓ ΗΙ5εδϑ Η5αΓα ΞΧ5ΓΦδ


   

%(∋#(.∃(62&∋∀+∀.3Μ,∃0(∋(∃+%(∋Μ∋.∀/(0∃&+(%(∋(&1∋#(/&.∀1∋%∀4(1(%&1∋%∀11(∋#(Ζ
.∃8#∀/:∋;&.,(+,&5∋&∋−(+&.(∗(∋−&)0&∋&)∋Τ)(1∀∋+2&∋1∀∋(/,∀.(∋∀∗∋)∗(∋%Μ0(%(:∋
Κ∋.∀+%(5∋−&.∋1)(∋#∀Θ5∋(,.∃%(∋#(.∃(62&∋]∋−.?−.∃(∋.∀+%(5∋1∀+%&∋
εΓ5ΧΓβ∋∀≅−/∃0(%(∋ −∀/(∋∀+∀.3∃(:∋θ.(+10&..∃%(∋)∗(∋ %Μ0(%(5∋ (∋−(.,∃0∃−(62&∋
%(∋∀+∀.3∃(∋ −(.(∋∀≅−/∃0(.∋(∋ #(.∃(62&∋%&∋;ς∆∋ Μ∋ (∃+%(∋∗(∃&.∋7ΓΦ5δΦβ9:∋ Ρ∗∋
&),.(1∋−(/(#.(15∋+&∋0).,&∋−.(Θ&∋&∋0.∀10∃∗∀+,&∋∀0&+∴∗∃0&∋∀1,8∋∃+,∃∗(∗∀+Ζ
,∀∋.∀/(0∃&+(%&∋ ]∋0(−(0∃%(%∀∋%∀∋ −.&%)62&∋∀+∀.3Μ,∃0(∋+(0∃&+(/5∋∀+,.∀,(+,&5∋
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%∀∋)∗(∋%Μ0(%(5∋&∋Τ)∀∋.∀11(/,(∋(∋∃∗−&.,Λ+0∃(∋%∀∋∃+#∀1,∃∗∀+,&1∋−∀.∗(+∀+,∀1∋
+(∋∃+4.(∀1,.),).(∋∀+∀.3Μ,∃0(∋+(0∃&+(/5∋%(%&∋&∋,∀∗−&∋.∀/(,∃#(∗∀+,∀∋∗(∃&.∋%∀∋
∗(,).(62&∋%&∋1∀,&.:∋
φ8∋(1∋ ∀∗∃11>∀1∋%∀∋ ΑΒΧ5∋+&∋0).,&∋−.(Θ&5∋.∀1−&+%∀∗∋ (∋Ηα5εΦβ∋ %(∋#(Ζ
.∃(62&∋%(∋−.?−.∃(∋#(.∃8#∀/5∋ 1∀+%&∋Χδ5ΗΞβ∋ (,.∃]∋∀+∀.3∃(∋∀∋α5Γϑβ∋(&∋

)∗(∋%Μ0(%(∋Μ∋ (0.∀10∃%(∋ 7ΗΙ5εΓβ9∋ ∀∋ %∃∗∃+)∃∋ −(.(∋ΞΧ5ΓΧβ∋(∋∃∗−&.,Λ+0∃(∋
.∀/(,∃#(∋%(1∋∀∗∃11>∀1∋−(.(∋1∀∋(),&∀≅−/∃0(.:∋;&%∀Ζ1∀∋%∃Θ∀.∋Τ)∀5∋∗∀1∗&∋1∀+Ζ
%&∋0&+1∃%∀.(%&∋/∃∗−&∋&∋−.&0∀11&∋+(0∃&+(/∋%∀∋−.&%)62&∋∀+∀.3Μ,∃0(5∋+2&∋Υ8∋
∀#∃%[+0∃(1∋%∀∋Τ)∀∋(1∋∀∗∃11>∀1∋%∀∋−&/)∀+,∀1∋.∀%)Θ∃.2&∋+&∋/&+3&∋−.(Θ&∋0&∗∋
(∋(,)(/∋∀1,.),).(∋∀+∀.3Μ,∃0(∋%&∋∆.(1∃/:
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!−ς∗&)∋5−∋1=&
70" EQPUKFGTC~ËGU"HKPCKU
µ(1∋λ/,∃∗(1∋%Μ0(%(1∋ ,∀∗∋1∃%&∋0.∀10∀+,∀∋(∋−.∀&0)−(62&∋%(∋1&0∃∀%(%∀∋
0&∗∋(∋Τ)(/∃%(%∀∋%&∋∗∀∃&∋(∗∗)%(+6(1∋0/∃∗8,∃0(15∋%∀.∃#(%(1∋
∀∗∋1)(∋ ∗(∃&.∃(∋ %(1∋∀∗∃11>∀1∋%∀∋ −&/)∀+,∀15∋ 12&∋(−&+,(%(1∋0&∗&∋ )∗∋ %&1∋
∗(∃&.∀1∋&<1,80)/&1∋(&∋ 0.∀10∃∗∀+,&∋ ∀0&+∴∗∃0&∋ ∀∋ ]∋ Τ)(/∃%(%∀∋ %∀∋ #∃%(∋ %(∋
−&−)/(62&∋∗)+%∃(/:∋
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=(+∀∃.&∋%∀∋ΧΙΦΞ:∋
Ρ!ΡµνΒηΡΠ5∋Β:Ω∋∆ΚχΡΠ5∋µ:Ω∋ϕΠςΡ_ΡΠ5∋Ρ:Ω"θΥ∀∋∃∗−(0,∋ &4∋,∀0Υ+&Ζ

Νςµ!:∋Geqnqikecn"Geqpqokeu:∋ΧϑϑΖΧΓΧ:∋ΧΙΙα:
         
EGRG"Yqtmkpi"
Rcrgt∋µ&:∋Ηδ:∋ΧΙΙΓ:∋
Βχ_ΚΒ5∋!:∋;)∃0∋iqqfu
nkvgtcvwtg:∋χ+∃#∀.1∃,κ∋&4∋ο∃10&+1∃+ΖΝ(%∃1&+:∋Ν(∃:5∋ΧΙΙε:∋
ΠΡΡµΡ5∋ο:∋ν:∋Geqpqogvtke"Cpcn{uku:∋α∋Ρ%∃62&:∋;.∀+,∃0∀Ζν(//:∋ΦΙδΞ−:∋
ΧΙΙΞ:
##
!∀#∃#%&∋()∗∃∗%+,∗∃#∃∗%∗,−(#.∃,∗%/#∃∗∃∗∀())0∗)∃/∗∃1234∃∗5(/6%7(#)∃8#,#∃9∃:,#)(∋.∃;<=3>3??≅
!−ς∗&)∋5−∋1=&
Π;;Β5∋:∋⊥:∋Eqpvtcvqu"hwvwtqu"g"Kdqxgurcguvwfq"eqo"rtqegfkogpvq"
fg"cwvq/tgitguu«q"xgvqtkcn" guvtwvwtcn:∋Π∀1∀+Υ(∋∆Νη5∋+:ΦΗϑ5∋−:ϑΙΖδΦ5∋
ΧΙΙΗ:
χΡ⊥µΡΠςΡ5∋Π:∋C"hwvw tg"hqt"M{qvqA∋;(.∃1Ζφ&).%(+∋⊥0∃∀+0∀1∋Ρ0&+&∗∃Τ)∀1:∋

νΒ_ΑΒΝ∆Ρ5∋Π::∋Κ∋ ,Υ∀&.κ∋ &4∋ ,Υ∀∋ ,Υ∀&.κ∋ &4∋ −)∃0∋ 3&&%1:∋ Tgxkgy" qh"
Cwuvtkcp"Geqpqokeu∋ΦΙ5∋µγ:∋Φ∋ΦΖΧΧ∋−:∋ΦΓΓϑ:∋
ς;ΑΑ∋ 7ςµθΡΠΒΟΡΠµΝΡµθΚ_∋;ΚµΡ_∋Βµ∋Α_ςΝΚθΡ∋ΑνΚµΡ9:∋

ς;ΡΚ!ΚθΚ∋7ς+1,∃,),&∋%∀∋;∀1Τ)∃1(∋Ρ0&+∴∗∃0(∋Κ−/∃0(%(95∋ΧΙΦΧ:∋!∃1−&+Ε#∀/∋

ςΠηης5∋:5∋ΑΚ⊥θΡ_ΚΠ5∋ς:5∋⊥ςΨχΡςΠΚ5∋Ν:∋_:5∋_ςµνΚΠΡ⊥5∋η:∋Α:∋;.∀#∃12&∋
%(∋%∀∗(+%(∋−&.∋∀+∀.3∃(∋∀/Μ,.∃0(∋−(.(∋0/(11∀1∋%∀∋0&+1)∗&∋+(∋.∀3∃2&∋+&.%∀1,∀5∋
)1(+%&∋Β_⊥∋%∃+Λ∗∃0&∋∀∋∗)%(+6(∋%∀∋.∀3∃∗∀:"Geq pq ok c"Cr nkecfc5∋Π∃
;.∀,&5∋⊥;5∋#:∋ΦΞ5∋+:Φ5∋−:ΗΓΖΓδ5∋φ(+:5∋ΧΙΙΓ:∋
φΚΑΒ∆5∋φ:5∋ ηΠΡΡΝΚµ5∋ :5∋ ΠρςΡΠ5∋φ:5∋ ΝΒΠθΒµ5∋!:5∋ ⊥Ανχ_θ5∋
:5∋⊥θΚ⊥Ανχ⊥5∋ϕ:5∋⊥θΡµ!ςµΡΠ5∋φ:∋Uqetcvgu"u{uvgo"hqt"uejgfwn,
kpi"j{ftqgngevtke"igpgtcvkqp"wpfgt" wpegtvckpv{:∋Κ++(/1∋&4∋Β−∀.(,∃&+1∋
Π∀1∀(.0Υ∋ΓΓΖΦΞΞ∋−−:∋ΦΓΓα:∋
Uvcvc"oqfwng"*Ocvc+"vq"rtqxkfg"xctkqwu"hwpe,
vkqpu0                           

φΒνΚµ⊥Ρµ5∋⊥:∋Uvcvkuvkecn"cpcn{uku"qh"eqkpvgitcvkqp"xgevqtu:∋∋φ&).+(/∋&4∋
Ρ0&+&∗∃0∋!κ+(∗∃01∋(+%∋Α&+,.&/5∋#:∋ΦΧ5∋−:∋ΧΞεΖΧαε5∋ΦΓδδ:
ϕΡΝηΡΠθ5∋Α:Ω∋Guvkocvgf"Uwduvkvwvkqp"gncuvkekvkgu"qh"pguvgf"EGU"rtqfwe,
vkqp"hwpevkqp"crrtqcej"hqt"Igtocp{:∋Ρ+∀.3κ∋Ρ0&+&∗∃01:∋ΧεΓΖΧΗε:∋ΦΓΓδ:
#∃
Vjkciq"Equvc"Uqctgu"̋"Lq«q"Gwuvƒswkq"fg"Nkoc
!−ς∗&)∋5−∋1=&
_ςµΚΠΡ⊥5∋;:5∋ _Κ∆Κµ!ΡςΠΚ5∋ :∋ Gpgti{" GhÝekgpe{ Geqpqokeu" cpf"
∋&)>−?:∋φ&).+(/∋&4∋Ρ0&+&∗∃0∋⊥).#∀κ1:∋Ο&/:∋Χε5∋µ&:∋Ξ5∋−−:∋αϑΞΣαΓΧ:∋ΧΙΦΙ:


ΝΒ!ςΚµΒ5∋Ρ:∋Ν:∋Gncuvkekfcfg/tgpfc"g"rtg›q"fc"fgocpfc"fg"gpgtikc"
gnf‌ivtkec"pq"Dtcukn0" 
θ∀≅,&∋−(.(∋!∃10)112&5∋+:∋Ηδ5∋ΦΓδε:∋
ΝχϕνΡΠφΡΡ5∋Κ:5∋ Β⊥οΚΝς5∋Π:∋ Vt cf g" kp " Gpg ti {" Ug txk eg u
cpf"Kpfkc:∋ς+%∃(+∋0&)+0∃/∋4&.∋.∀1∀(.0Υ∋&+∋∃+,∀.+(,∃&+(/∋∀0&+&∗∃0∋.∀/(,∃&+1:∋

;Κς 5∋;:∋⊥:∋Ν: Fgocpfc"fg"gpgtikc"gnf‌ivtkec"pq"Dtcukn"pq"rgtqfq"r„u/tc,
ekqpcogpvq
%∀∋;?1Ζ.(%)(62&∋∀∗∋Ρ0&+&∗∃(∋Κ−/∃0(%(5∋χ+∃#∀.1∃%(%∀∋η∀%∀.(/∋%∀∋Ο∃6&1(5∋
Ο∃6&1(5∋ΧΙΦΧ:∋
⊥ΚΝχΡ_⊥Βµ5∋;:∋Κ:∋Fkcitcoocvke"Gzrqukvkqp" qh"c"Vjgqt{"qh"Rwdnke"
Gzrgpfkvwtg
ΞαΙΖΞαΗ:∋µ:5∋ΦΓαα:
⊥ΚΝχΡ_⊥Βµ5∋;:∋Κ:∋Vjg"Rwtg"Vjgqt{"qh"Rwdnke"Gzrgpfkvwtg:∋θΥ∀∋Π∀Ζ

⊥ΑνΝς!θ5∋Α:∋Κ:∋φ:5∋_ςΝΚ5∋Ν:∋Κ:∋ C"fgocpfc"rqt"gpgtikc"gnf‌ivtkec"pq"
Dtcukn:∋Π∀#∃1,(∋∆.(1∃/∀∃.(∋%∀∋Ρ0&+&∗∃(:∋Π∃&∋%∀∋φ(+∀∃.&5∋#:αδ5∋+:Φ5∋−:∋ΗϑΖΓΓ:∋
φ(+:5∋ΧΙΙε:∋
⊥ΡΠΠΚθΒ5∋Ρ:∋Htqpvgktcu"Rctcof‌ivtkecu"fg"GÝek‒pekc"rctc"q"Ugiogpvq"
fg"Vtcpuokuu«q"fg"Gpgtikc"Gnf‌ivtkec"pq"Dtcukn
−:∋!∃11∀.,(62&∋7∗∀1,.(%&9∋Σ∋;.&3.(∗(∋%∀∋;?1Ζ.(%)(62&∋∀∗∋Ρ0&+&∗∃(∋%&∋
⊥∀,&.∋;λ∃0&5∋χ+∃#∀.1∃%(%∀∋%∀∋∆.(1Ε/∃(5∋∆.(1Ε/∃(5∋ΧΙΙΗ:∋
#%
!∀#∃#%&∋()∗∃∗%+,∗∃#∃∗%∗,−(#.∃,∗%/#∃∗∃∗∀())0∗)∃/∗∃1234∃∗5(/6%7(#)∃8#,#∃9∃:,#)(∋.∃;<=3>3??≅
!−ς∗&)∋5−∋1=&
⊥ς_ΟΚ5∋⊥:5∋⊥ΒΚΠΡ⊥5∋ς:5∋;ςµνΒ5∋Α:∋Vjg"korcev"qh" tgpgycdng" gpgti{"
uqwtegu"qp"geqpqoke"itqyvj"cpf"EQ4"gokuukqpu"Î"c"UXCT"crrtqcej:∋

θΚµµχΠςΖ;ςΚµθΒ5∋Ν:∋Ρ:5∋!Ρ∋⊥ΒχΚ5∋Ν:∋Α:∋⊥:∋ΚΠΑΒΟΡΠ!Ρ5∋η:∋!:∋
Htqpvgktcu"fg"GÝek‒pekc"Guvqeƒuvkecu"rctc"cu"Gortgucu"fg"Fkuvtkdwk›«q"
fg"Gpgtikc"Gnf‌ivtkec"pq"DtcuknWoc"Cpƒnkug"fg"Fcfqu"fg"Rckpgn:∋Ρ1,)%&1

θςοΚΠς5∋Κ:∋ϕ:∋C"uvtwevwtcn"XCT"cp cn {u ku"qh"tgp gycdng"gpg ti {"eqpuwor,
vkqp."tgcn" IFR"cpf"EQ4"gokuukqpu Gxkfgpeg"htqo"Kpfkc:∋ Ρ0&+&∗∃01∋
∆)//∀,∃+5∋Ο&/:∋ΞΦ∋+&:Χ∋−−:∋ΦϑΓΞΖΦδΙΗ5∋ΧΙΦΦ:
ΟΚΠςΚµ5∋ν:Π:∋Oketqgeqpqoke"Cpcn{uku:∋Ξ∋Ρ%∃62&:∋µ(∋ς&.Τ)∀5∋ΡχΚ:∋
µ&.,&+∋∀∋Α&∗−(+κ:∋αΗΞ∋−−:∋ΦΓΓΧ
ΟςΡςΠΚ5∋φ:∋ ;:5∋!Ρ∋ΑΚ⊥θΠΒ5∋µ:∋φ:∋ χΡΠΠΚ5∋⊥:∋Ν:∋ C"gzrgtk‒pekc"fqu"
cpqu"3;;2"fc"kpf¿uvtkc"fg"gpgtikc"gnf‌ivtkec"dtcukngktcg"gz,
rcpu«q:∋Β<1∀.#(,&.∃&∋%∀∋/(∋∀0&+&∗Ε(∋_(,∃+&(∗∀.∃0(+(:∋µλ∗∀.&∋ΦαΧ5∋ΧΙΦΙ:

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