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- 8. ! ! !!!!!!>$?$2$ ! b! 10 y, output per 9 worker 8 y=f (k) 7 D C 6 B 5 4 3 A 2 1 0 0 1 2 3 4 5 6 7 8 9 10 k, capital per worker ! 7-?.A$!!K! !!!!!!!!!!!!!!!!!<,!-,'A$/)$!-,!$!&A*4!6*-,(!<!(*!9!0$B!(*!/!A$0/(-3$02!0/A?$!-,'A$/)$!-,!#!&A*4! I=b!.,-()!*&!*.(6.(!6$A!8*A;$A!(*!P=G!.,-()!*&!*.(6.(!6$A!8*A;$A=!<,!$[./0!/4*.,(!*&! -,'A$/)$!-,!'/6-(/0!&A*4!6*-,(!5!(*!V!0$B!(*!/!4.'#!0$))$A!-,'A$/)$!-,!#!&A*4!T=P!.,-()! *&!2!(*!a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e5*,3$A?$,'$f!#26*(#$)-)! U90/,'#/AB!IJJcH!IKIW=!!
- 10. ! ! !!!!!!>$?$2$ KJ! ! y y=f(k) y3 C y2 B i3=s f(k3) y1 A i2=s f(k2) i1=s f(k1) k1 k2 k3 k ! 7-?.A$!o!I!!!! F#$,!4*A$!*&!(#$!*.(6.(!-)!)/3$B!A/(#$A!(#/,!'*,).4$BH!-(!8-00!-,'A$/)$!(#$!)/3-,?! A/($H!8#-'#!8-00!-,!(.A,!-,'A$/)$!-,3$)(4$,(=!<)!-,3$)(4$,(!-,'A$/)$)!4$/,)!'/6-(/0! /''.4.0/($)H!8#-'#!-,'A$/)$)!'/6-(/0!6$A!8*A;$A!A$).0(-,?!-,!/,!-,'A$/)$!-,!*.(6.(! 6$A!8*A;$A!/)!8$00=!+,!(#-)!'/)$H!(#$!-,3$)(4$,(!'.A3$!8-00!)#-&(!.68/AB)H!-,'A$/)-,?! (#$!B-)(/,'$!D$(8$$,!)/3-,?)!/,B!B$6A$'-/(-*,H!8#-0$!(#$!*.(6.(!6$A!8*A;$A!8-00! 4*3$!A-?#(8/AB!/0*,?!(#$!'.A3$=!<)!(#$!*.(6.(!6$A!8*A;$A!-,'A$/)$)H!-(!0$/B)!(*! #-?#$A!)/3-,?)!A/($H!8#-'#!A$)(/A()!(#$!'2'0$=!+,!&-?.A$!IH!/,!-,'A$/)$!-,!-,3$)(4$,(! )#-&()!(#$!'.A3$!&A*4!-K!(*!-I!D$'/.)$!*&!(#$!-,'A$/)$!-,!$!)(*';H!&A*4!;K!(*!;IH!(#/(!-)! ?*-,?!(*8/AB)!)/3-,?!A/(#$A!(#/,!'*,).46(-*,=!"#$!)#-&(!&A*4!-K!(*!-I!-)! /''*46/,-$B!D2!/!A-?#(8/AB!4*3$4$,(!/0*,?!(#$!#!'.A3$!&A*4!6*-,(!<!(*!9=!"#-)!
- 27. ! ! !!!!!!>$?$2$ Ia! ! /,B!ZVE!B$&0/(*A!U+,&0/(-*,W=!M(#$A!'*,(A*0!3/A-/D0$)!/A$!/BB$B!6A*?A$))-3$02!(*!($)(! (#$!A*D.)(,$))!*&!(#$!D$,'#4/A;!4*B$0=!"#$)$!/A$!w,-(!0/D*A!'*)()H!E.D0-'! $Y6$,B-(.A$)!/)!y!*&!ZVEH!d/AB!-,&A/)(A.'(.A$!UQ*/B)WH!/,B!Q$/0!$Y'#/,?$!A/($)! UQ%QW=!! /01&.! 2! /! 345167-89! 4:;<.=9! >:?@A9! 1)BC?.&;)9! D?E;:! 7;'.9! 8FEC&%! *"GA)@&.F:A'9! H;?@'9! H*H9!8;C&.&%?C!:&'$9!IF'&)A''!7C&J?.AK! "#$!'A-(-'/0!3/A-/D0$)!*&!(#$!A$?A$))-*,!$[./(-*,!/A$!6*0-(-'/0!A-);!/,B! D.)-,$))!'0-4/($=!E/)(!)(.B-$)!#/3$!)#*8,!(#/(!D$(($A!D.)-,$))!'0-4/($H!8#-'#!-)!/0)*! ;,*8,!/)!e)*&(f!-,&A/)(A.'(.A$H!-)!_4*A$!-46*A(/,(!-,!/((A/'(-,?!7V+!(#/,!#/AB! -,&A/)(A.'(.A$!).'#!/)!A*/B)`=!+,!/BB-(-*,H!9.))$!/,B!d$&$;$A!)(/($!(#/(!6*0-(-'/0!A-);! -)!A$0/($B!(*!(#$!A-);!(#/(!/!)*3$A$-?,!#*)(!?*3$A,4$,(!8-00!.,$Y6$'($B02!'#/,?$! e(#$!A.0$)!*&!(#$!?/4$f!.,B$A!8#-'#!D.)-,$))$)!*6$A/($!U9.))$!/,B!d$&$;$A!IJJaH! GcbW=!<''*AB-,?!(*!i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iA-&/C'#,$-B$A!/,B!:/($-!IJKJH!PTW=! <!)$A-$)!*&!)($68-)$!4.0(-60$!A$?A$))-*,!/,/02)$)H!'*,)-)(-,?!*&!B-&&$A$,(! 3/A-/D0$)H!-)!'*,B.'($B!-,!*AB$A!(*!&-,B!*.(!8#-'#!/A$!(#$!4*)(!-46*A(/,(!3/A-/D0$)! /4*,?!(#$!*8,$A)#-6)6$'-&-'H!-,($A,/0-]/(-*,)6$'-&-'H!/,Bj*A!0*'/(-*,)6$'-&-'!
- 28. ! ! !!!!!!>$?$2$ Ib! ! 3/A-/D0$)!-,!B$($A4-,-,?!-,3$)(4$,(!&0*8)=!+,!*AB$A!(*!A$0/($!-(!8-(#!(#$!(#$*A$(-'/0! &A/4$8*A;!*&!(#$!A$)$/A'#![.$)(-*,H!8#-'#!$Y/4-,$)!(#$!A*0$!*&!-,)(-(.(-*,)!-,! B$($A4-,-,?!7V+H!(#$!B-)'.))-*,!8-00!&*'.)!*,!*,$!3/A-/,(!*&!(#$!A$?A$))-*,!4*B$0=!+(! -)!/!&-Y$B!$&&$'()!4*B$0!(#/(!/,/02]$)!(#$!-46/'(!*&!6*0-(-'/0!A-);!*,!7V+=!"#$!$[./(-*,! -)!/)!&*00*8)^! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!UmW! UmW! UzW! UW!! L,!7V+&.!h!! J!m!! K!L,!ZN+j5<E&.!m!! I!L,!ZA*8(#&.!m!! G!L,!"A/B$&.!m!! S!L,!+,&0/(-*,&.!m!! P! L,!E.D0-'!%Y6$,B-(.A$)&.!m!! T!L,!E*0-(-'/0!Q-);&.!m!! a!9.)-,$))!50-4/($&.!m!$&.!!! ! +,!(#$!$[./(-*,!(#/(!-)!D$-,?!$)(-4/($BH!(#$!/.(#*A)!)(/($!(#$!$Y6$'($B!)-?,)! &*A!(#$!D$,'#4/A;!3/A-/D0$)H!D.(!,*(!&*A!(#$!/BB$B!'*,(A*0!3/A-/D0$H!_E.D0-'! %Y6$,B-(.A$)`H!/,B!(#$!#26*(#$)-)!3/A-/D0$)=!d*8$3$AH!D2!A$02-,?!*,!(#$*A2H!-(!'/,!D$! -,&$AA$B!(#/(!(#$!$Y6$'($B!)-?,!*&!6*0-(-'/0!A-);!8-00!D$!,$?/(-3$!B.$!(*!(#$!&/'(!(#/(!-(! -)!/!'#/A/'($A-)(-'!*&!_D/B`!-,)(-(.(-*,)H!8#-'#!8-00!#*0B!D/';!7V+!-,&0*8)=!"#$!6.D0-'! $Y6$,B-(.A$)!3/A-/D0$!-)!$Y6$'($B!(*!#/3$!/!6*)-(-3$!)-?,!D$'/.)$!*&!(#$!/)).46(-*,! (#/(!-,'A$/)$B!$Y6$,B-(.A$)!-,!6.D0-'!-,&A/)(A.'(.A$!8-00!'*,(A-D.($!(*!D$(($A!(#$! -,)(-(.(-*,)!-,!/!?-3$,!'*.,(A2=!L/)(02H!(#$!6/6$A!0**)$02!B$&-,$)!D.)-,$))!'0-4/($!D2! B$)'A-D-,?!-(!/)!_D.)-,$))!*6$A/(-,?!'*,B-(-*,)`=!d*8$3$AH!-(!-)!)-4-0/A!(*!(#$!-! 3/A-/D0$!-,!C$'(-*,!G!*&!(#$!(#$*A2!'#/6($AH!8#-'#!-)!B$&-,$B!/)!&/3*A/D0$!'*,B-(-*,)! -,!/,!$'*,*42H!).'#!/)!-,)(-(.(-*,/0![./0-(2H!-,($A$)(!A/($)H!(A/B$!*6$,,$))H!ZVEH!/,B! $B.'/(-*,!*&!8*A;&*A'$H!(#/(!&/'-0-(/($!'/6-(/0!&0*8)=!"#.)H!D.)-,$))!'0-4/($!-)! $Y6$'($B!(*!#/3$!/!6*)-(-3$!)-?,!D$'/.)$!-(!6A*4*($)!'/6-(/0!-,&0*8=!!! ! "#$!/A(-'0$!.)$)!B/(/!&A*4!GG!B$3$0*6-,?!/,B!(A/,)-(-*,!'*.,(A-$)!&A*4!KccT! o!IJJb!/,B!)*.A'$)!*&!B/(/!/A$!&A*4!(#$!F*A0B!9/,;!B/(/D/)$H!+,($A,/(-*,/0!L/D*A! MA?/,-]/(-*,H!+7CH!/,B!F*A0B8-B$!Z*3$A,/,'$!+,B-'/(*A)=!
- 29. ! ! !!!!!!>$?$2$ Ic! ! Q$).0()! ! V$6$,B$,(!R/A-/D0$^!L,!7V+!-,!y/?$!ZVE!&*A!'*.,(A2!&! +,B$6$,B$,(! R/A-/D0$)! 5*,)(/,(! 5*$&&-'-$,()!!! Q*D.)(!C(/,B/AB!%AA*A)! KT=Pc!sss! K=cK! L,!ZN+j5<E! J=GP!ss! J=KP! L,!ZA*8(#!UyW! !J=JG! J=JG! L,!"A/B$! S=ST!sss! J=Gb! L,!+,&0/(-*,! !J=Ja!ss! J=JG! L,!E.D0-'! J=K!sss! J=JS! J=Kc!ss! J=K!! %Y6$,B-(.A$)! L,!E*0-(-'/0!Q-);! 9.)-,$))!50-4/($! J=Kb! QI ! N.4D$A!*&! MD)$A3/(-*,)! d/.)4/,!"$)(! J=Ia! SIc! UEA*D!q!5#-IW! UJ=JJW! 9A$.)'#E/?/,! ($)(! UEA*D!q!5#-IW! J=IK! IbI=bS! GI=JP! UJ=JJW! H*(#!o!()(/(-)(-'^!ss!-,B-'/($)!)-?,-&-'/,'$!/(!(#$!Py!0$3$0X!sss!-,B-'/($)!)-?,-&-'/,'$! /(!(#$!Ky!0$3$0!! C*.A'$^!iA-&/C'#,$-B$AH!d/Bv-0/H!/,B!+.0-/,/!:/($-=!e9.)-,$))!50-4/($H!E*0-(-'/0!Q-);! /,B!7V+!-,!V$3$0*6-,?!5*.,(A-$)^!%3-B$,'$!&A*4!E/,$0!V/(/=f!1).A:)?.&;)?C! L;F:)?C!;B!*%;);J&%'!?)@!/&)?)%A!I=!N*=!P!UIJKJW^!TG=!! 7*A!(#$!4*)(!6/A(H!(#$!D$,'#4/A;!'*,(A*0!3/A-/D0$)!#/3$!(#$!$Y6$'($B!)-?,)H! $Y'$6(!&*A!(#$!_ZA*8(#`!3/A-/D0$!8#*)$!'*$&&-'-$,(!(.A,$B!*.(!(*!D$!,$?/(-3$H!D.(!-)! )(/(-)(-'/002!-,)-?,-&-'/,(=!"#$!/.(#*A)!#26*(#$)-]$B!(#/(!(#$!_"A/B$`!3/A-/D0$!'*.0B! $-(#$A!#/3$!/!6*)-(-3$!*A!,$?/(-3$!)-?,H!8#-'#!B-)/?A$$B!8-(#!/!6/A(!*&!(#$!(#$*A2! )$'(-*,!)(/(-,?!(#/(!4*A$!(A/B$!*6$,,$))!6A*4*($)!B*4$)(-'!)/3-,?)!(*!0$/3$H!D.(!-(!
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