Local and national REDD income under alternative PES designs: theory and illustration from Sumatra

HAL Id: hal-01072351

https://hal.archives-ouvertes.fr/hal-01072351

Submitted on 6 Jun 2020

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Local and national REDD income under alternative PES designs: theory and illustration from Sumatra

Solenn Leplay, Jonah Bush, Philippe Delacote, Sophie Thoyer

To cite this version:

Solenn Leplay, Jonah Bush, Philippe Delacote, Sophie Thoyer. Local and national REDD income under alternative PES designs: theory and illustration from Sumatra. International Conference:

Environment and Natural Resources Management in Developing and Transition Economies, Centre

d’Études et de Recherches sur le Développement International - Clermont Auvergne (CERDI). FRA.,

Nov 2010, Clermont-Ferrand, France. 32 p. �hal-01072351�

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R.!$/ ;*:#"$#* 4*8 S# 'NQT4*+!**&H+9 ABCCDI 4*8 ;*:#"$#* ABCCFI -+,54 # '.# +7# 4""

>0UU 4 -.&'#-'! # '+ 4 ,!"'&Q"#7#" @01 $-.#,#P V'.# -+ # &8#4 +6 >0UU &$ '+ - #4'# 4 ,!"'&Q

"#7#" A:"+24"Q*4'&+*4"Q"+-4"I $3$'#, +6 543,#*'$ 6+ #*7& +*,#*'4" $# 7&-#$ A@01I '.4' ?&"" #8!-#

#,&$$&+*$ 4*8 &*- #4$# 6+ #$' -4 2+* $'+-H$W A;*:#"$#*/ BCCFI( R.# &*'# *4'&+*4" >0UU ,#-.4Q

*&$, &$ -"#4 "3 8#$&:*#8 4$ 4 @01 $-.#,#/ 2#-4!$# 8#7#"+5#8 -+!*' &#$ A2!3# $I 543 :+7# *,#*'$

&* ' +5&-4" 6+ #$'$ -+!*' &#$ A$#""# $I 6+ 4 :"+24" 5!2"&- :++8 $!55"&#8 A47+&8#8 #,&$$&+*$ 6 +, 8#6+ #$'4'&+* 4*8 8#: 484'&+*I( R.#*/ &* ,+$' -4$#$/ >0UU &*-+,# &$ !$#8 23 ' +5&-4" -+!*' 3 :+7# *,#*'$ A2!3# $I '+ 543 "4*8 !$# $ A$#""# $I 6+ +*Q'.#Q: +!*8 #,&$$&+*$ #8!-'&+*$ '. +!:.

"#$$ 8#6+ #$'4'&+* 4*8 8#: 484'&+* 4-'&7&'&#$( G6 -+! $#/ $!-. @01X>0UU $-.#,# #J!& #$ '+

,+*&'+ -+,5"&4*-# 23 #-&5&#*' -+!*' &#$( )' *#-#$$&'4'#$ 4--#$$ '+ #"&42"# 8#6+ #$'4'&+* 84'4/

?.&-. -4* 2# 5 +7&8#8 23 $4'#""&'# &,4:#/ 5# &+8&- +*Q$&'# -.#-H$ 4*8 -#*' 4" 84'424$# 8#7#"Q +5,#*' A84'4 +* 6+ #$' -+7# / $+&" -4 2+*/ ' ## .#4"'./ &""#:4" 4-'&7&'&#$/ &*6 4$' !-'! #$ 8#7#"+5Q ,#*'(((I A;*:#"$#*/ BCCFI( Y+$' 8#7#"+5&*: -+!*' &#$ 4 # -! #*'"3 &* 4 #48&*#$$ 5.4$#/ 2!&"8&*:

'.#& ,+*&'+ &*:/ #5+ '&*: 4*8 7# &<-4'&+* AY>ZI -454-&'&#$/ 4*8 $' #*:'.#*&*: &*$'&'!'&+*$ A #Q 8!-'&+* +6 -+ !5'&+*/ -"4 &<-4'&+* +6 "4*8 !$# &:.'$ 4*8 5 +5# '3 &:.'$(((I A;*:#"$#*/ BCCFI(

)* '.# =+5#*.4:#* 4--+ 8 #$'42"&$.#8 4' '.# =G@ [\ &* BCCF/ ]1/ ;!$' 4"&4/ L 4*-#/ ^454*/

_+ ?43 4*8 '.# ]T 5 +,&$#8 ]1U `(\ 2&""&+* 6+ 64$'Q$'4 ' 6!*8$ '+ #,5+?# >0UU( )* '.#

,+*'.$ 6+""+?&*: =+5#*.4:#* '.&$ <:! # .4$ : +?* '+ ]1U a(\ 2&""&+*( )* +! 4 '&-"#/ ?# ,4H#

'.# 4$$!,5'&+* '.4' ' +5&-4" -+!*' &#$ .47# 2##* 42"# '+ 54$$ '.# #48&*#$$ 5.4$# $!--#$$6!""3 4*8 .47# '.# -454-&'3 '+ &,5"#,#*' #b-&#*' @01 $-.#,#$ '+ #8!-# '.#& 8#6+ #$'4'&+*( R.&$

c

!"#$ %&"% %&!$! '()#%*+!$ "*! ",-! %( !$%+ "%! "#. *!/(*% '"*,(# ! +$$+(#$ "% #"%+(#"- -!0!-1 "$

$!% )/ +# %&! 2344 5((. /*"'%+'! "#. 6)+."#'! 723441 899:1 899;< =(* *!/(*%+#6 "% +#%!*#"%+(#"- -!0!-> ?! "$$) ! %&!*!=(*! %&"% %&!@ "*! !#%!*+#6 %&! + /-! !#%"%+(# /&"$!A %&! ,"$!-+#! &"$

,!!# #!6(%+"%!. "#. B()%&!*# '()#%*+!$C 6(0!*# !#%$ "*! +#0+%!. %( '&(($! %&!+* %"*6!% +# %!* $ (= .!=(*!$%"%+(# *!.)'%+(#$ "#. %( + /-! !#% .( !$%+' /(-+'+!$ "'%+(#$ +# (*.!* %( "'&+!0! %&!$!

%"*6!%$> ?! =(')$ &!*! (# %&! '&(+'! '(#'!*#+#6 3DB>

!"#$%&'(&#)' *+,)-.$/- )-0 ,/'$%1 /,($/-. (/ #*0&%* 0*2 3/#*.()($/-4 ) 5&'($2'*6*' 789 .%:*5*

E&+$ $!'%+(# /*(0+.!$ " $%"%+' (.!- (= .!=(*!$%"%+(# .!'+$+(#$ ,@ ="* !*$1 F&+'& +$ %&!# )$!. %(

+.!#%+=@ (/%+ "- 3DB /(-+'@ (/%+(#$ ,@ B()%&!*# 6(0!*# !#%$> 2% +$ ,"$!. (# $+ /-! "$$) /%+(#$

F&+'& &!-/ )$ %( '"/%)*! (#! (= %&! + /(*%"#% =!"%)*!$ (= 3DB $'&! !$A %&! $%*)'%)*! (= ="* !*$C (//(*%)#+%@ '($%$>

!"#$%&'%"(& )*+(,-#., #, ( /%-#,)--0(-0%-%(& 1)2.")-'('#.,

?! '(#$+.!* " /(/)-"%+(# (= "6!#%$ (= .!=(*!$%"%+(# i 1 '"--!. ="* !*$ +# %&! *!$% (= %&! /"/!*1 /*"'%+'+#6 "6*+')-%)*! +# =*(#%+!* =(*!$% -"#.> D"'& ="* !* i "@ #!!. %( !G%!#. &+$ ="* !. -"#.1 '&(($+#6 &(F )'& =(*!$% &! F+-- '(#0!*% %( "6*+')-%)*!> ?! "$$) ! %&"% ="* !*$ "*! *+$H #!)%*"->

E&+$ '&(+'! %"H!$ %&! =(* (= " /*(I% "G+ +J+#6 /*(,-! A

max

Π

= max

L

λ

f (L (λ

)) − ω L (λ

) 7K<

f +$ %&! "6*+')-%)*"- *!0!#)! =)#'%+(# (= "..+%+(#"- .!=(*!$%!. -"#. L (λ

)1 +% +$ %F+'! .+L!*M

!#%+",-! "#. N)"$+ '(#'"0! f

> 0 "#. f

≤ 0 > λ

+$ "# !O'+!#'@ ="'%(* '&"*"'%!*+J+#6 !"'&

="* !* i (λ

> 0)> 2% !#'( /"$$!$ ,(%& %&! /*(.)'%+0+%@ (= .!=(*!$%!. -"#. 7F&+'& .!/!#.$ (#

+%$ $-(/!1 !-!0"%+(#1 (* N)"-+%@ (= $(+-<1 "#. %&! #!% *!%"+- /*+'! %&"% "6*+')-%)*"- /*(.)'%+(# '"#

=!%'& 7F&+'& "@ .!/!#. =*( %&! .+$%"#'! %( "+# *(".$<> ?! "$$) ! %&"% %&! $!% (= ="* !*$

i +$ .+$%*+,)%!. )#+=(* -@ "-(#6 λ

∈

λ; λ > ω +$ %&! )#+% '($% (= -"#. '(#0!*$+(#> ?! "$$) !1 F+%&()% -($$ (= 6!#!*"-+%@1 %&"% %&+$ '($% +$ '(#$%"#% "'*($$ -"#.$ "% =*(#%+!* "*!">

P

O

i L

(λ

)

dΠ

dL = 0 ⇐⇒ λ

f

(L (λ

)) − ω = 0 ⇐⇒ f

(L (λ

)) = ω λ

f

L

(λ

) = (f

)

ω λi

λ

=

L

(λ

) = 0

λ > λ

L

(λ

) > 0 λ

λ

< λ

L

(λ

) < L

(λ

)

L

L

= ´

λ

L

(λ) dλ

!" #$%% &'!"(") * +,-.!/0,1.! .-*2&3"- ., *4,56 6"3,-"&.*.5,2

!"# $%&'("!) "&*+$%, %-.*"(+/ ($0 .-1&%-0$!$(&+ /-$0 ! 2 33 $%!+01-% T 1%&4 .-5-)&'-. "&*+6

$%(-07 8#("# (0 '%&'&%$(&+!) $& !5&(.-. "!%9&+ -4(00(&+0: ;+ '%!"$("-7 $#- 2 33 $%!+01-% (0

"!)"*)!$-. &+ $#- 9!0(0 &1 !5&(.-. .-1&%-0$!$(&+ A 7 4*)$(')(-. 9, $#- !5-%!/- "!%9&+ <*!+$($, 0$&%-. (+ &+- #-"$!%- &1 1&%-0$: =#-%- !%- &+6/&(+/ .-9!$-0 &+ $#- 8!, $#- %-1-%-+"- )-5-) >!)0&

"!))-. 9!0-)(+-? 0#&*). 9- 0-$ (+ &%.-% $& 4-!0*%- $#- %-.*"$(&+: @- 4!A- $#- !00*4'$(&+ (+ $#(0 '!'-% $#!$ $#- 9!0-)(+- "#&0-+ (0 $#- 9*0(+-006!06*0*!) >BCD? .-1&%-0$!$(&+ )-5-)7 (:-: $#- .-1&%6 -0$!$(&+ )-5-) 9-1&%- 2 33 (0 0-$ (+ ')!"- >C+/-)0-+7 EFFG?: ;+ &*% 4&.-)7 $#- +!$(&+!) 9!0-)(+- (0 $#*0 $#- $&$!) BCD .-1&%-0$!$(&+7 L

= ´

λ

L

(λ) dλ: =#(0 9!0-)(+- (0 "&4'!%-. $& $#-

&90-%5-. .-1&%-0$!$(&+ *+.-% $#- H I "&+$%!"$7 L

= ´

λ

L

(λ) dλ7 -!"# 1!%4-% i .-1&%-0$(+/

L

(λ

) *+.-% $#- H I "&+$%!"$: =#- J&%$#6I&*$# $%!+01-% (0 T 7 "!)"*)!$-. !0K

T = t A = t (L

− L

)

t (0 $#- (+$-%+!$(&+!) $%!+01-% %!$- 1&% 0!5-. -4(00(&+0: ;$ %-L-"$0 $#- 5!)*- &1 !5&(.-. .-1&%6 -0$!$(&+ (+ $-%40 &1 %-.*"-. -4(00(&+0 &1 "!%9&+: t = P × EF 8#-%- P (0 -($#-% $#- (+$-%+!$(&+!)

"!%9&+ '%("-7 MN-. 9, $#- 4!%A-$ (1 1&%-0$ "!%9&+ (0 (+$%&.*"-. (+ $#- (+$-%+!$(&+!) "!%9&+ 4!%6 A-$7 &% !+ -N&/-+&*0 5!)*- "#&0-+ 9, J&%$#-%+ "&*+$%(-0O !+. EF (0 $#- !5-%!/- "!%9&+ -4(00(&+0 1!"$&%7 8#("# "&+5-%$0 .-1&%-0$!$(&+ (+$& "!%9&+ -4(00(&+0: ;+ $#- %-0$ &1 $#- '!'-%7 8- 8&+P$

$!A- (+$& !""&*+$ .(Q-%-+"-0 &1 "!%9&+ .-+0($, (+ 1&%-0$K $#-%-1&%-7 8- !00*4- $#!$ t (0 $#- 0!4- 1&% !)) $,'-0 &1 1&%-0$0 : @- !)0& !00*4- $#!$ $#- )-5-) &1 .-1&%-0$!$(&+ "!+ 9- &90-%5-. 8($#6

&*$ *+"-%$!(+($, $#!+A0 $& $#- 4&+($&%(+/7 %-'&%$(+/ !+. 5-%(M"!$(&+ "!'!"($(-0 &1 $#- $%&'("!)

"&*+$%(-07 !0 .-0"%(9-. !9&5-:

!" 2*.5,2*7 7"4"7) 8$0 &'!"("&

!"#$%&' (!)%&'*%'#+, !-#.*/0 1%2.,.!', #! 2"&3 1%4!&%,#/#.!'

C00*4- $#!$ ! I&*$#-%+ "&*+$%, -+5(0!/-0 $& 0-$ *' ! H I 0"#-4- $& %-.*"- .-1&%-0$!$(&+7 (+ &%.-% $& R&(+ $#- (+$-%+!$(&+!) 2 33 0"#-4- !+. $& /-$ $#- $%!+01-% T .-0"%(9-. !9&5-

! "#$%!% &$'"(")! *+,% !- "%!$.+!" !/$% 0+1!-( &"2")&$)3 -) !/" 1+2+1$!, -0 ."+%4(".")!5 ("2-(!$)3 +)&

6"($71+!$-) -0 "+1/ 1-4)!(,5 2("%")!"& $) !/" 899 3--& 2(+1!$1" +)& 34$&+)1" : 8995 ;<<=5 ;<<>?

G

!"# $"!%&'!( )"*(%!+',- .' )"(,+/'! %0" %12', " 3"*%&'!( 4"5'!(#'(%,6 7 89'('5":'(%; 4"5<

'!(#'(% #7=+#+>+(4 ,")+7: 0': 7!'? #'7,*!'/ &'!' 91 %"%7: 74!+)*:%*!7: 2!"@% 2:*, +()"#' !"#

+(%'!(7%+"(7: ABCC %!7(, '!,D 7(/ 7 89*/4'%<#7=+#+>+(4; 4"5'!(#'(% #7=+#+>+(4 %&' /+E'!'()' 9'%0''( +(%'!(7%+"(7: ABCC %!7(, '!, 7(/ 271#'(%, #7/' %" 7!#'!, *(/'! FB3 ,)&'#', - G&+, 89*/4'%<#7=+#+>+(4; %12' )7( )72%*!' %&' '7%*!', " 7 )"!!*2% 4"5'!(#'(%? 07(%+(4 %" /+5'!%

2*9:+) #"('1 %" %&' 9'('@% " 7 2":+%+)7: ':+%'? 9*% +% )7( 7:," /',)!+9' 7 4"5'!(#'(% 07(%+(4 %"

+(5',% ABCC +()"#' +( H'1 ,')%"!, I "! '/*)7%+"(? &'7:%&? +( !7,%!*)%*!'? "! '5'( 74!+)*:%*!'J- K:: :+('7! )"#9+(7%+"(, " %&',' %0" '=%!'#' %12', /',)!+9' %&' !7(4' " 4"5'!(#'(%7: 9'&75+"!,

%&7% )"*:/ 9' "9,'!5'/- L'%M, ("%' U %&' *%+:+%1 *()%+"( " %&' 4"5'!(#'(%- G&' 4"5'!(#'(%

#7=+#+>', +%, *%+:+%1 U *(/'! %&' 9*/4'% )"(,%!7+(% %&7% %"%7: FB3 271#'(%, )7(("% '=)''/

ABCC %!7(, '!,6

max U = T + α (Π

+ Π

) + (1 − α) ( − E) INJ s.t. T ≥ E

0&'!' T +, %&' ABCC %!7(, '! !"# $"!%&'!( )"*(%!+', %" %&' 3"*%&'!( 4"5'!(#'(% /',)!+9'/

79"5'? Π

+, %&' %"%7: 74!+)*:%*!7: 2!"@% " 7:: 7!#'!, 27!%+)+27%+(4 +( %&' (7%+"(7: FB3 ,)&'#'?

7(/ Π

+, %&' %"%7: 74!+)*:%*!7: 2!"@% " 7:: 7!#'!, 0&" /" ("% 27!%+)+27%' +( %&' FB3 ,)&'#' 7(/ 2*!,*' %&'+! OKP 74!+)*:%*!7: 7)%+5+%+',- E +, %&' %"%7: 9*/4'%7!1 )",% " %&' /"#',%+) FB3 ,)&'#'? )"!!',2"(/+(4 %" %&' 271#'(% !"# %&' 3"*%&'!( 4"5'!(#'(% %" 7!#'!, 27!%+)+27%+(4

%" %&' FB3- α /',)!+9', %&' %12' " 4"5'!(#'(%6 + α = 1? %&' 4"5'!(#'(% +, 9'('5":'(% 7(/

#7=+#+,', %"%7: 0': 7!' #'7,*!'/ &'!' 7, %&' ,*# " +(%'!(7%+"(7: %!7(, '!, 2:*, 2!"@%, 4'('!7%'/

91 74!+)*:%*!7: 7)%+5+%+',

D 7(/ + α = 0? +% +, 9*/4'% #7=+#+>+(4- G0" FB3 ,)&'#' 7!' )"(,+/'!'/ +( %&' "::"0+(4 ,')%+"(6

QJ G&' 8"22"!%*(+%1 )",%; )"#2'(,7%+"( ,)&'#' +( 0&+)& '7)& 27!%+)+27%+(4 7!#'! +, '=<

7)%:1 )"#2'(,7%'/ "! &+, "22"!%*(+%1 )",% " !'/*)+(4 /' "!',%7%+"(- R( %&+, ,)&'#'? 0' 7,,*#'

!" #$%&'$()*+$!,- ./ 0! ,!+ )!,#$0/" +1/ &!+/,+$*' &!#$+$2/ 3//04*)5 /6/)+# !, +1/ 4708/+ !3 +*9 "/2/,7/ 3"!%

*8"$)7'+7"/:;/ *'#! *##7%/ +1*+ 8!2/",%/,+# 0! ,!+ +*5/ $,+! *))!7,+ $, +1/$" 7+$'$+< 37,)+$!, +1/ /,2$"!,%/,+*' 0/8"*0*+$!, *##!)$*+/0 .$+1 0/3!"/#+*+$!,:

!

=>? &*<%/,+# +! 3*"%/"# *"/ ,!+ $,)'70/0 4/)*7#/ +1/< *"/ )!,#$0/"/0 0!%/#+$) +"*,#3/"#@ +1/< *"/ 0/07)+/0 3"!% +1/ &74'$) 4708/+ *,0 *00/0 +! 3*"%/"# #7"&'7#: A3 ./ *##7%/ +1*+ =>? 1*2/ ,! +"*,#*)+$!, )!#+#- +1/, +1/#/ &*<%/,+# *"/ ,/7+"*' $, +/"%# !3 +!+*' 0!%/#+$) ./'3*"/:

QS

!" #"$ %&%#" %'( )"$*+$, "$+ $+-.%$+/ 0 "1" + /+)0$+, " %0' 0 2+$0 34+ 4%55 /%,&.,, !%, &!0%&+

).$ !+$67 8!+ ,+ %'( .# 0) ,.&! ,&!+*+ $+-.%$+, !" !+ ,&!+*+ *"'"(+$ 3 !+$+") +$ !+ (09:

+$'*+' 6 "&-.%$+, " (00/ ;'045+/(+ 0) %'/%9%/."5 )"$*+$<, "($%&.5 .$"5 #$0= ,7

>6 8!+ =?+/:#$%&+ ,&!+*+ %' 4!%&! )"$*+$, "$+ "55 0@+$+/ !+ ,"*+ =?+/ #"A*+' #+$ !+& "$+

0) "90%/+/ /+)0$+, " %0' 3&0*#"$+/ 0 !+%$ BCD /+)0$+, " %0'67 D'/+$ !%, ,&!+*+E )"$*+$,

&!00,+ !+ 5+9+5 0) "90%/+/ /+)0$+, " %0' !+A 4"' 0 "&!%+9+7 8!%, %, 1",+/ 0' !+ ",,.*# %0' !" #.15%& ". !0$% %+, &"' 01,+$9+ %'/%9%/."5 /+)0$+, " %0' 5+9+5,E 10 ! .'/+$ BCD "'/ .'/+$

&0' $"& 7

8!+,+ 40 ,&!+*+, !+$+)0$+ /0 '0 $+-.%$+ !+ ,"*+ %')0$*" %0' "'/ *0'% 0$%'( &0, ,7 F%'&+ ,.&! &0, , "$+ %*#0,,%15+ 0 +, %*" +E 4+ ",,.*+ %' " =$, %', "'&+ !" !+A "$+ +-."5 0 2+$0 %' 10 ! &",+,7 C *0$+ /+ "%5+/ /%,&.,,%0' 4%55 1+ #$09%/+/ %' !+ &0'&5./%'( ,+& %0'7 C'0 !+$ ,%*#5%)A%'( ",,.*# %0' %, !" !+$+ %, '+% !+$ #$%&+ +@+& )++/1"&; '0$ 5+";"(+7 G' 0 !+$ 40$/,E !+ $+/.& %0' 0) /+)0$+, " %0' 1A "(+' , H0%'%'( " IJF ,&!+*+ /0+, '0 #$09%/+

"//% %0'"5 %'&+' %9+, 0 '0' &0' $"& %'( )"$*+$, 0 %'&$+",+ !+%$ BCD /+)0$+, " %0' 5+9+5,7

!" #$$#%&'()&* +#,& +#-$"(,.&)#( ,+!"-"

G' !+ 0##0$ .'% A &0, &0*#+'," %0' 3KL6 ,&!+*+E 4+ ",,.*+ !" !+ (09+$'*+' &"' 01,+$9+

%'/%9%/."5 "*0.' , 0) /+)0$+, +/ "$+", .'/+$ BCDE ", 4+55 ", 0##0$ .'% A &0, ,7 8!+ (09+$'*+' 0@+$, " &0*#+'," %0' +-."5 0 !+ )0$+(0'+ $+9+'.+E %) !+ "(+' , 0) /+)0$+, " %0' "&&+# 0 "1" + /+)0$+, " %0' 0 0 3 L

(λ

) = 0 %) i H0%', !+ ,&!+*+67 G'/++/E %) !+ &0*#+'," %0' %, #+$)+& 5A

*+",.$+/E )"$*+$, "$+ %'/%@+$+' 1+ 4++' #"$ %&%#" %'( %' !+ ,&!+*+ %' +?&!"'(+ )0$ !+ )0$+(0'+

$+9+'.+E 0$ #.$,.%'( !+%$ "($%&.5 .$"5 "& %9% %+,7 G %, !+$+)0$+ !+ (09+$'*+' 4!%&! ,+5+& , )"$*+$,E 1",+/ 0' !+%$ 0##0$ .'% A &0, ,7 8!+ ,&!+*+ %, %55., $" +/ 1A M%(.$+ >N %' !+ BCD ,&+'"$%0E )"$*+$, λE λ

"'/ λ ¯ /+)0$+, $+,#+& %9+5A KBE KO "'/ KJ7 C,,.*+ !" )"$*+$, λ "'/

λ

"$+ ,+5+& +/ 0 #"$ %&%#" + %' !+ KL ,&!+*+7 M"$*+$ λ $+/.&+, /+)0$+, " %0' 0 2+$0 "'/ (+ ,

#"%/ KCBE )"$*+$ λ

"5,0 , 0#, /+)0$+, " %0' "'/ (+ , " &0*#+'," %0' KLO7 M"$*+$ ¯ λ %, '0

%'9% +/ 0 H0%' !+ ,&!+*+N !+ ;++#, /+)0$+, %'( KJ7

8!+ (09+$'*+' &!00,+, !+ 0 "5 5+9+5 0) /+)0$+, " %0' 4!%&! *"?%*%2+, % , . %5% A "'/ !+'

%'9% +, )"$*+$, 0 H0%' !+ ,&!+*+E , "$ %'( 4% ! !+ 504+, 0##0$ .'% A &0, )"$*+$E .# 0 !+

P*"$(%'"5 )"$*+$Q λ ˆ E 4!0,+ &0' $%1. %0' 0 !+ ,&!+*+ +'"15+, 0 $+"&! !+ /+,%$+/ 5+9+5 0) 0 "5

RR

Marginal profit of deforestation

Deforested area

A

O B C

D E

λ ˆ

λ ∈ [λ, λ] ˆ L

(λ

) = 0

λ ∈ [ˆ λ, λ] L

(λ

)

max

U = max

ˆλ^B

t ˆ

λ

L

(λ)dλ + ˆ

ˆλ^B

Π

(L (λ))dλ

s.t. t ˆ

λ

L

(λ)dλ ≥ ˆ

λ

Π

(L (λ))dλ

max

U = max

λˆ^M

t ˆ

λ

L

(λ)dλ − ˆ

λ

Π

(L (λ))dλ

s.t. t ˆ

λ

L

(λ)dλ ≥ ˆ

λ

Π

(L (λ))dλ

! "#$ !#%&'( %!! )*#) )*! )+, -#.&-&/#)&,$ 01,2'!-% #1! !34&5#'!$)6 7$8!!89 &$"1!#%&$: ˆ λ

*#% !.#")'( )*! ,00,%&)! &-0#") ,$ ´

λˆ

Π

(L (λ))dλ )*#$ ,$ ´

λ

Π

(L (λ))dλ6 ;*&% &% 84! ), )*! 4$&<,1- 8&%)1&24)&,$ #%%4-0)&,$ ,< )*! λ%6 ;*!1!<,1!9 )*! -#1:&$#' #:!$) <,1 )*! 2!$!5,'!$)

"#%!9 &8!$)&=!8 2( ˆ λ

9 &% )*! %#-! #% <,1 )*! 248:!) -#.&-&/&$: "#%! ˆ λ = ˆ λ

= ˆ λ

> &) &% )*!

#:!$) +*,%! #5!1#:! ,00,1)4$&)( ",%) ,< #5,&8!8 8!<,1!%)#)&,$ &% !34#' ), t9 t =

L^BAU(ˆλ)

6

;*&% 1!%4')9 +*&"* &% ,$'( 5#'&8 <,1 )*! ?@ %"*!-!9 &% !#%&'( 4$8!1%),,8> )*! &$)!1!%)% ,< )*!

2!$!5,'!$) :,5!1$-!$) A+*&"* -#&$)#&$% #:1&"4')41#' #")&5&)( ,< *&:* 01,=) <#1-!1%B ",$5!1:!

+&)* )*! &$)!1!%)% ,< )*! 248:!)C-#.&-&/&$: :,5!1$-!$) A+*&"* %!'!")% )*! ',+!%) ",%) <#1-!1%

), '&-&) DEF !.0!$8&)41!%B6 G,1!,5!19 )*! 248:!)#1( ",$%)1#&$) &-0,%!% )*#) )*! -&$&-4- H,1)*CF,4)* )1#$%<!1 1#)! t 2! #) '!#%) !34#' ), )*! #5!1#:! ,00,1)4$&)( ",%) ,< λ> &$ )*&% "#%!

λ &% )*! ,$'( <#1-!1 I,&$&$: )*! %"*!-! #$8 t

=

(

)

L^BAU(λ)

6 J,1 -,1! 8!)#&'% #2,4) 1!%4')%9

%!! K00!$8&. L6

!" #$"%&'()*" +*!","

7$ )*! =.!8C01&"! %"*!-!9 )*! :,5!1$-!$) ,M!1% # =.!8C01&"! K 0!1 4$&) ,< #5,&8!8 8!<,1!%)#)&,$6 E#"* <#1-!1 i I,&$&$: )*! %"*!-! "*,,%!% )*! '!5!' ,< 8!<,1!%)#)&,$ L

(λ

) *! +#$)% ), ",--&) ),9 &$ ,18!1 ), -#.&-&/! *&% &$",-! R

(λ

)6 ;*! :,5!1$-!$) "*,,%!% )*! ),)#' 8!<,1!%)#)&,$

'!5!'9 +*&"* -#.&-&/!% &)% 4)&'&)(> &) %!)% )*! ,0)&-#' K 0!1 *!")#1! ,< #5,&8!8 8!<,1!%)#)&,$

",11!%0,$8&$: ), )*! 8!%&1!8 ),)#' 8!<,1!%)#)&,$6 J&:41! N &''4%)1#)!% )*! =.!8C01&"! %"*!-!>

<#1-!1% λ, ˘ λ, λ I,&$ )*! %"*!-!6 J#1-!1% λ #$8 ˘ λ 1!84"! 8!<,1!%)#)&,$ ), /!1, #$8 :!) 0#&8 1!%0!")&5!'( ?KO@ #$8 ?KPE6 J#1-!1 λ 1!84"!% 8!<,1!%)#)&,$ <1,- ?7 ), ?Q #$8 :!)% 0#&8 JRQ76

;*! <#1-!1S% -#.&-&/#)&,$ 01,:1#- &%>

max

R

= λ

f (L (λ

)) − ω L

(λ

) + K !

L

(λ

) − L

(λ

) ATB s.t. L

(λ

) > L

(λ

) #$8 R

(λ

) > Π

(L

)

UN

!" #$%&'($)"$ *(+),&,(+ ,%- dR

dL = 0 ⇐⇒ f

(L

(λ

)) = ω + K

λ

./0

1,+*"

≥

2+) f

,% 2 )"*$"2%,+3 45+*&,(+6 L

(λ

) = f

(

i

) ≤ L

(λ

) ,% 27829%

:"$,#");

!" <"+":(7"+& 3(:"$+="+&>% =2?,=,@2&,(+ A$(<7"= 8$,&"%-

max

U ! K

= max

K^B

t ˆ

λ

! L

(λ) − L

!

λ, K

dλ +

ˆ

λ

Π

! λ, K

dλ .B0 s.t. t ≥ K

C+) &!" <5)3"& =2?,=,@,+3 3(:"$+="+&>% A$(3$2= 8$,&"%-

max

U ! K

= max

K^M

! t − K

ˆ

λ

! L

(λ) − L

!

λ, K

dλ .D0

s.t. t ≥ K

E" *2+ %"" 4$(= "F52&,(+ B 2+) D !(8 <(&! &9A"% (4 3(:"$+="+& =29 ),G"$ 8!"+ ,=A7"="+&' ,+3 2 HI %*!"="; !" #?") A$,*" K

,+J5"+*"% A(%,&,:"79 &!" <"+":(7"+& 3(:"$+="+&>% 5&,7,&9

&$(53! !,3!"$ A29="+&% &( 42$="$%6 8!"$"2% &!" #?")'A$,*" K

$")5*"% &!" <5)3"&'=2?,=,@,+3 3(:"$+="+&>% 5&,7,&9;

K+ ($)"$ &( *27*572&" &(&27 2:(,)") )"4($"%&2&,(+ 2+) &(&27 IL1 <5)3"&6 8" +"") &( ),%&,+35,%!

<"&8""+ ),G"$"+& 7":"7% (4 K-

M2%" N- ,4 K < λ f

(0) − ω ⇒ L

(λ

) = f

ω+K1

λi

, ∀ λ ∈ λ; λ

6 277 42$="$% %,3+ &!"

*(+&$2*& 2+) $")5*" A2$&,2779 &!",$ )"4($"%&2&,(+; (&27 )"4($"%&2&,(+ ,% L

= ´

λ

L

(λ) dλ ; M2%" O - ,4 λ f

(0) − ω ≤ K < λ f

(0) − ω ⇒



 



 



L

(λ

) = 0 4($ ∀ λ ∈ h λ; ˘ λ i L

(λ

) = f

ω+K2

λi

4($ ∀ λ ∈ h

˘ λ; λ i 6 277 23"+&% P(,+ &!" IL1 %*!"="; E" )"#+" λ ˘ =

- 42$="$% 8,&! λ ∈ h

λ; ˘ λ i

%&(A )"4($"%&2&,(+ 27&(3"&!"$6 8!"$"2% 42$="$% 8,&! λ ∈ h

λ; ˘ λ i

%&(A )"4($"%&,(+ (+79 A2$&,2779;

(&27 +2&,(+27 7":"7 (4 )"4($"%&2&,(+ ,% L

= ´

λ˘

L

(λ) dλ;

NQ

K

K

Deforested area

A B

O C E

D F G

H I

K ≥ λ f

(0) − ω ⇒ L

(λ

) = 0 ∀ λ ∈ λ; λ

K = λ f

(0) − ω

t ≥ K

!! "#$%&#' ( )#) *$# +%" ,,&%- .,) /&-/ ( )# $%&#) 0 .1 &2+2 2+0 "+)#.#& % 3 45 )(/+6+7 8/+%

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*+#9++% #/+ 6 )# !" >#.*,+ $%&#) 0 2+0 "+)#.#& % 0 .-+%#) 2+0 "+)#&%- #/+ ,+.)# 345 )(/+6+3 .%2 #/+ ,+.)# !" >#.*,+ $%&#) 0 2+0 "+)#.#& % *' .,, .-+%#) 3:; )(/+6+7 ?.)&(.,,'< &# "+@$&"+) # ( 6!."+ #/+ 1+".,, !! "#$%&#' ( )# 0 #/+ .-+%#)< 9&#/ #/+ )#++!%+)) 0 #/+&" 6."-&%., !" >#

($"1+7

8 /.1+ . *+##+" $%2+")#.%2&%- 0 #/+ #".2+ =< #.A+ #/+ +B#"+6+ (.)+ 0 . ) (&+#' 9&#/ %,'

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6."-&%., !" ># ($"1+7 I-+%# i /.) . )6.,,+" !! "#$%&#' ( )# 3 4?5 &) )6.,,+" #/.% 4J: 3 .%2 . K.##+" 6."-&%., !" ># ($"1+ #/.% .-+%# j7 I))$6+ #/.# #/+ - 1+"%6+%# ."*&#".",' )+,+(# .-+%#

i .%2 %,' .-+%# i 0 " #/+ 45 )(/+6+7 H% #/&) (.)+< .1 &2+2 2+0 "+)#.#& % &) 4?< .%2 #/+ # #., ( )# 0 #/+ ! ,&(' &) 4?57 L 9 ( %)&2+" #/.# #/+ - 1+"%6+%# &6!,+6+%#) . >B+2M!"&(+ )(/+6+

9&#/ .% ."*&#"."' >B+2 !"&(+ 0 K 7 H% #/&) (.)+< .1 &2+2 2+0 "+)#.#& % 9&,, *+ I? N OJ< 0 " .

# #., ( )# 0 I?LP N OJQR7 H# &) +.)' # )++ -".!/&(.,,' #/.# #/&) 45 )(/+6+ !+"0 "6) *+##+"

&% #+"6) 0 .1 &2+2 2+0 "+)#.#& % 3 4? &) ,."-+" #/.% I? N OJ3< 9/&,+ &# ( )#) ,+)) #/.% #/+

>B+2M!"&(+ )(/+6+ 0 " #/+ -&1+% K 3 4?5 S I?LP N OJQR7 8/+ 45 )(/+6+ /.) . 6 "+

+T(&+%# $#( 6+ #/.% #/+ >B+2M!"&(+ )(/+6+ &% (.)+ E7

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*$# /+ /.) . )#++!+" 6."-&%., !" ># ($"1+7 H0 .% !! "#$%&#' ( )# )(/+6+ &) )+#< .%2 %,' i

!."#&(&!.#+)< #/+ ( )# 0 #/+ ! ,&(' &) #/$) 4?5 0 " .% .1 &2+2 2+0 "+)#.#& % 0 4?7 H% ( %#".)#<

&0 . >B+2M!"&(+ )(/+6+ &) )+# 9&#/ .% =+"+2 !"&(+ K < .-+%# i "+2$(+) /&) 2+0 "+)#.#& % *' .%

.6 $%# I?< 9/&,+ .-+%# j "+2$(+) &#) 2+0 "+)#.#& % *' .% .6 $%# OJ7 8/+ # #., ( )# 0 #/+

! ,&(' &) #/+% I?LP N OJQR7 U A&%- -".!/&(.,,'< &# &) +.)' # )++ #/.# 9&#/ #/+ >B+2M!"&(+

)(/+6+< .1 &2+2 2+0 "+)#.#& % &) ,."-+"< .%2 #/+ ( )# 0 #/+ ! ,&(' &) )6.,,+" #/.% $%2+" .% 45 )(/+6+7 8/+ >B+2M!"&(+ )(/+6+ 1+"M!.') #/+ .-+%#) 9/+% ( 6!."+2 # #/+&" !! "#$%&#' ( )#) C#/+ !.'6+%# &% +B(+)) &) ?LP N JQRG< *$# &# &) )#&,, ,+)) +B!+%)&1+ #/.% !.'&%- #/+ >"#) $%&#) 0 2+0 "+)#.#& % 0 #/+ .-+%# 9&#/ #/+ , 9+)# !! "#$%&#' ( )#7

41+".,,< #/&) ,&##,+ +B+6!,+ )/ 9) #/.# 9+ (.% +B!+(# #/+ >B+2M!"&(+ )(/+6+ # *+ 6 "+

EV

!"#$% &' ()*+,$!-). )/ 01% 2 ,.3 4( -51%*%- 6!01 06) ,"%.0-

Case 1:

OC scheme > FP scheme

B K

A M N C

O F

D E

G H Marginal profit of

deforestation

L Agent j

Agent i

Marginal profit of deforestation

L K

O A B

C

Case 2:

FP scheme > OC scheme

M N

D E

F

G H

Agent j Agent i

%75!%.08 !9%9 +%$/)$*!." :%00%$ !. 0%$*- )/ ,;)!3%3 3%/)$%-0,0!). ,0 , <)6%$ 5)-08 01,. 01% 4(

-51%*%= 61%. 01% *,$"!.,< :%.%>0 5#$;%- )/ 01% <)6 )++)$0#.!0? 5)-0 ,"%.0- ,$% -0%%+%$ 01,.

01% *,$"!.,< :%.%>0 5#$;%- )/ 01% 1!"1 )++)$0#.!0? 5)-0- ,"%.0-9 @. 5).0$,-0= 01% 4( -51%*% !-

%A+%50%3 0) :% *)$% %75!%.0 01,. 01% >A%3B+$!5% -51%*% 61%. 01% *,$"!.,< :%.%>0 5#$;%- )/

01% 1!"1 )++)$0#.!0? 5)-0 ,"%.0- ,$% -0%%+%$ 01,. 01% ).% )/ 01% <)6 )++)$0#.!0? 5)-0- ,"%.0-9 C. #0)+!,. )+0!). 6)#<3 :% 0) 5)*+%.-,0% %,51 /,$*%$ %A,50<? 01% -1,$% )/ )++)$0#.!0? 5)-0- ,<<)6!." 0) $%,51 01% 3%-!$%3 <%;%< )/ ,;)!3%3 3%/)$%-0,0!).= %A5<#3!." 01% 1!"1%$ )++)$0#.!0?

5)-0- +%$ 1%50,$%9 D)6%;%$= .%")0!,0!." , -+%5!>5 5).0$,50 6!01 %,51 /,$*%$ %."%.3%$- 0)) 1!"1 0$,.-,50!).- 5)-0- 9

!"#$%&'(") "* +,- (./0#0( *"& 1/0 12" 3'40&0)1 15$0( "*

6"70&)#0)1(8 )9#0&'.%: ('#9:%1'")(

!"#$%&'"# ()*+#%* ,&%- " .+"/("%&' 0+!'%&1!

E!01)#0 ,. ,.,<?0!5,< %A+$%--!). )/ f (L

)= $%-#<0- !. 0%$*- )/ 0)0,< ,;)!3%3 3%/)$%-0,0!).= 6%</,$%=

,.3 :#3"%0,$? 5)-0- ,;,!<,:<% !. ,++%.3!A F= 5,..)0 :% 5)*+,$%39 @. 01% /)<<)6!."= 6% ,--#*%

01,0 f (L

) !- , G#,3$,0!5 /#.50!).' f (L

) =

L

+ bL

+ c = 6!01 a < 0, ,.3 b, c > 09 H1#-

IJ

f

(L

) = aL

+ b !" #$%&' a ()* +,& )+&&-&' +,& . '/(! # 01'2& ()* %,(0,* ) .&!+($!&" 3$2&*

() 0'10( # &#&.&!+ "&+&'.(!(!/ +,& $1+0$.& $4 +,& +%$ )0,&.&)5 6,& 789 "&4$'&)+ +($! ' +& 4$' 4 '.&' i () +,1) L

(λ

) =

i

−

* !" ,() -'$:+ () Π

(λ

) = −

+

c −

λ

+

5 6$ 3& 0$!)()+&!+ %(+, )&0+($! ;* %& '&)+'(0+ - ' .&+&' 2 #1&) (! $'"&' +$ #(.(+ $1' ! #<)() +$ -$-1# +($! $4 4 '.&') , 2(!/ )+'(0+ -$)(+(2& 2 #1&) $4 789 "&4$'&)+ +($!= L

> 0 ⇒

< λ

!" Π

(λ

) > 0 ⇒ −

+

c −

λ

> −

5 9!"&' +,& >? )0,&.&* +,& 3&!&2$#&!+ !" +,& 31"/&+@. A(.(B(!/ /$2&'!.&!+) "$-+ +,&

) .& + '/&+ /'$1- $4 - '+(0(- +(!/ 4 '.&')5 6,& . '/(! # /&!+ )-#(++(!/ +,& 4 '.&')C -$-1# +($! (!+$ +%$ /'$1-) () λ ˆ =

λ ˆ = b (ω + t) + √

t

b

+ 2acω

+ 4acωt b

− 2ac

D(+, t

b

+ 2acω

+ 4acωt > 05

9!"&' +,& :A&"@-'(0& )0,&.&* 4 '.&') . A(.(B& +,&(' (!0$.&* 0,$$)(!/ +,&(' #&2&# $4 "&4$'@

&)+ +($! L

(λ

)5 D& :!" +, + L

(λ

) =

ω+K λi

− b

5 82$("&" "&4$'&)+ +($! 3< 4 '.&' i () L

− L

= −

> 0 !" ,() (!0$.& 1!"&' +,& )0,&.& (!0'& )&)= R

− Π

=

−

> 05

8) !$+(0&" 3&4$'&* /&!+) '& 3&++&' $E %,&! +,& FG )0,&.& () (!+'$"10&"5 H$'&$2&'* !$+& +, + +,& (!0'& )& (! (!0$.& () # '/&' 4$' 4 '.&') %(+, #$% -'$"10+(2(+<=

< 05 I$+& #)$

+, + +,& (!0$.& (!0'& )& () # '/&' %,&! +,& . '/(! # -'$:+ 01'2&) '& #&)) )+&&-5

J!"(2("1 # "&4$'&)+ +($! #&2&# (!0'& )&) %,&! +,& &K0(&!0< 4 0+$' λ

(!0'& )&) $' +,& #&2&#

$4 :A&"@-'(0& K "&0'& )&)5 I$+& ,$%&2&' +, + 2$("&" "&4$'&)+ +($! (!0'& )&) ) K (!0'& )&)5 H$'&$2&'* +,&'& () '&(!4$'0&.&!+ &E&0+=

2 i

∂λi∂K

= −

i

> 0 L +,& . '/(! # &E&0+ $! +,&

#&2&# $4 "&4$'&)+ +($! $4 +,& :A&"@-'(0& (!0'& )& () ,(/,&' %,&! +,& -'$"10+(2(+< 4 0+$' () ,(/,&'5 6,&'&4$'&* %,&! K (!0'& )&)* +,& '&"10+($! $4 +,& #&2&# "&4$'&)+ +($! () /'& +&' 4$' ,(/,&' λ

5 J+

() #)$ (.-$'+ !+ +$ !$+& +, + 2$("&" "&4$'&)+ +($! (!0'& )&) ) +,& . '/(! # -'$:+ 01'2&) '&

#&)) )+&&-&'* %,(0, 0$!:'.) +,& ! #<)() /(2&! (! +,& -'&2($1) )&0+($!5

8) #'& "< "&.$!)+' +&" (! )&0+($! M5;* %& . < 4 0& +,'&& "(E&'&!+ 0 )&) "&-&!"(!/ $! +,&

$-+(. # 2 #1& $4 K 0,$)&! 3< & 0, +<-& $4 /$2&'!.&!+5 J! 0 )& N* %,&'& ## 4 '.&') - '+(0(- +&

NO

! "# $%#&'()*+# ,+"#-# ./ 0!.!&1 , !(, &#2!)#, 3 *!0 34 !5# "#)6 "# .#0#7!4#0 5!7#)0-#0 )#&*, )*./ #, "# ! 34 3-!/0 !2 8!) "'9!/ " :;<< )30,2#) ")!/5" "# $%#&'()*+# ,+"#-#

(K = t)= >"*4# "# ./&5# '-3%*-*?*05 5!7#)0-#0 )#&*, )*./ #, !041 "342 !2 "# *0 #)03 *!034 :;<< )30,2#) !

K =

@ A0 +3,# B6 >"#)# ,!-# 23)-#), 3)# #0+!/)35#& ! , !( &#2!)#, 3 *!0 34 !5# "#) 30& ! "#), +!0 *0/# (3) *3441 >* " 35)*+/4 /)34 3+ *7* 16 ># !.,#)7# "3 K

30& K

3)# &*, *0+ 2)!- #3+" ! "#)6 ./ >* "!/ 0/-#)*+34 30341,*, ># +300! &# #)-*0# "# 734/# !2 "# $%#&'()*+# +"!,#0 .1 #3+" 5!7#)0-#0 C,## 3((#0&*% D 2!) -!)# &# 3*4,E@ A0 +3,# D6 >"#)#

344 23)-#), , !( &#2!)#, 3 *!0 34 !5# "#)6 ># +!0,*&#) "3 "# 9!/ "#)0 5!7#)0-#0 +"!!,#, "#

4!>#, $%#&'()*+# ,+"#-# (!,,*.4#6 *@#@ "# -3)5*034 !((!) /0* 1 +!, !2 "# 43, /0* !2 &#2!)#, #&

3)#3 !2 λF K

= K

= λ b − ω@

!"#$%" &' (#)!*+,-$ "+)#$-%+&("

A0 !)&#) ! *44/, )3 # "# &*G#)#0 1(#, !2 (!4*+1 )#,(!0,#, ># +30 !. 3*06 ># +"!!,# >! +!0' )3, #& ,# , !2 (3)3-# #),6 ()#,#0 #& *0 3.4# H@

I3)3-# #) 3 . + ω λ λ Π(λ) Π(λE L

T

Π(λ) L^BAUT

9*-/43 *!0 H 'JD JD JK DL DL MLL !"# "# $$$ %&% #$$ "# $$$

'()*+,-(./ 0# 1&$ 1# !$$ 2 2# &$ "% $$$ % " !3 & $

4,5+6 17 8,9,)6-69 :,+*6; (/ -<6 -=. ;()*+,-(./;

4<6 -=. ;6-; .> ?,9,)6-69; @;()*+,-(./; 1 ,/A B +6,A -. 6C*(:,+6/- -.-,+ A6>.96;-,-(./ */A69 -<6 DEF ;G6/,9(. @,9.*/A %#$BH I(J< ?9.K- >,9)69; ,96 ,+;. C*(-6 ;()(+,9 (/ -<6 -=. ;()*+,-(./;

@-<6 <(J<6;- A6>.96;-,-(./ ?9.K- (; "#$$$ */A69 ;()*+,-(./ 1 ,/A "%$$$ */A69 ;()*+,-(./ BL

=<696,; -<6 >,9)(/J ?.?*+,-(./ (/ ;()*+,-(./ 1 A(;?+,M; , )*G< =(A69 9,/J6 .> .??.9-*/(-M G.;-; ?69 */(- .> A6>.96;-,-6A ,96, @-<6 .??.9-*/(-M G.;- ?69 */(- .> A6>.96;-6A ,96, (; 56-=66/

#$$ ,/A "#$$$ */A69 ;()*+,-(./ 1L ,/A 56-=66/ !3 ,/A & $ */A69 ;()*+,-(./ B -<,/ -<6

?.?*+,-(./ .> ;()*+,-(./ H 4<6 ,J9(G*+-*9,+ ?9.A*G-(:(-M >,G-.9 (; )*+-(?+(6A 5M 2$ 56-=66/

-<6 +6,;- ?9.A*G-(:6 ,/A -<6 ).;- ?9.A*G-(:6 >,9)69 (/ ;()*+,-(./ 1L (- (; ./+M )*+-(?+(6A 5M 1 (/ ;()*+,-(./ H N/ ;()*+,-(./ 1L -<6 ),9J(/,+ .??.9-*/(-M G.;- G*9:6 (; ;-66?69 -<,/ (/

;()*+,-(./ H 4<6/ -=. G<,9,G-69(;-(G; A(O69 56-=66/ 5.-< ;()*+,-(./;7 ;()*+,-(./ 1 ?96;6/-;

).96 <6-69.J6/.*; ,:69,J6 .???.9-*/(-M G.;-; ,/A ;-66?69 ),9J(/,+ ?9.K- G*9:6;L G.)?,96A -.

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t2 t1

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t Benevolent state under fixed price scheme

Budget maximizing state under FP scheme

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