Herramientas para combatir la evasión fiscal - un experimento económico
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(8) '-*"1$)&2'*:"."#=$*)"#*&I8$/*$*7G*;-#*)8*+$#("M*.*")*/$*($)$*&%+-)&(&1$*OK8"*I8$#:$* +#-+-#,&2'* ,-'* "/* &'I#")-* :",/$#$:-Q* F* 9M* /$* %8/($* K8"* )"* ,-.#$* $* /-)* "1$)-#")* O'2(")"*K8"*")($*)-/-*"6&)("*)&*H$F*"1$)&2'QG** * T-* -.)($'("M* "/* ")K8"%$* (#&.8($#&-* '-* )"* #"/"I$* $* 8'$* -./&I$,&2'G* 0'%$#,$:-* :"'(#-* :"/* $%+/&-* ,-',"+(-* :"* ,&8:$:$'=$M* ,8F-)* $(#&.8(-)* )"* #"/$,&-'$'* fg* ,-'* ,&"#($* #",&+#-,&:$:* :"* :"#",H-)* F* :"."#")* +$#$* ,-'* O8'$Q* ,-%8'&:$:* :"* +"#("'"',&$h* O>&'M* ?@@VM* +G* ZQ* /-)* &':&1&:8-)* -.(&"'"'* ($%.&N'* 8'* ."'"C&,&-*:"*)8*,-'(#&.8,&2'M*+/$)%$:-*"'*/$*&'1"#)&2'*)-,&$/*F*+#-1&)&2'*:"*.&"'")* +J./&,-)*+-#*+$#("*:"/*I-.&"#'-VG*0)(-)*)"*%$'&C&")($'*"'*/-)*+$#E%"(#-)*#")($'(")* :"* OAQ* F* O?Q* :-':"* 5* )"#=$* /$* #"+#")"'($,&2'* :"* /$* #"'($.&/&:$:* )-,&$/* :"/* +$I-* &':&1&:8$/*O8.Q*F*:"*/$*,-'(#&.8,&2'*:"/*#")(-*:"*/$*,&8:$:$'=$*O8:;.QG*B$*&'(8&,&2'*:"* ")* )"',&//$i* &',/8)-* $'("* "/* &',8%+/&%&"'(-* +-#* +$#("* :"* 8'* &':&1&:8-M* N)("* $8'* ,8"'($*,-'*/&.#"*$,,")-*$*/$*&'C#$")(#8,(8#$*+J./&,$*O&G"G*+$#K8")M*.&./&-(",$)M*"(,GQG* * o8":$#=$* +"':&"'("M* "'* ")("* +#&%"#* ")K8"%$M* ")($./","#* /$* #"/$,&2'* "'(#"* OAQ*F*O?QG*B$*$8:&(-#=$*C&),$/*)-.#"*8'*&':&1&:8-*"'*+$#(&,8/$#*)"*+#")"'($*,-'*8'$* +#-.$.&/&:$:* <M* K8"* :"+"':"* :"* /$* +-/=(&,$* F* /$* "C&,&"',&$* O:"* C-#%$* ,#",&"'("Q* "'* /$)* ")(#$("I&$)* :"* ,-'(#-/* :"* /$* $8(-#&:$:* :"* #",$8:-G* * ;-#* "':"M* /$* C8',&2'* $* %$6&%&P$#* K8":$#=$* ,-')(#8&:$* "'* /$* ",8$,&2'* O]QM* :-':"* E(π )* #"+#")"'($* "/* &'I#")-*C&'$/*:"/*&':&1&:8-*/8"I-*:"/*+$I-G* * E(π ) = qU(a) + (1 − q)U(n) *****************************O]Q*. * 0 < q < 1*. * B$*,-':&,&-'")*:"*+#&%"#*F*)"I8':-*-#:"'M*#")+",(&1$%"'("M*)-'4* *. ∂E(π ) = qU'(ts − t + Mt) + (1 − q)U'(n)(ts − t) * ∂D ******************************************************** V*L"IJ'*/$*("-#=$*",-'2%&,$M*8'-*:"*/-)*%",$'&)%-)*+$#$*,-##"I&#*C$//$)*:"/*%"#,$:-*,-')&)("*"'*/$*. &'("#1"',&2'* :&#",($* :"/* 0)($:-* %":&$'("* /$* +#-1&)&2'* :"* .&"'")* +J./&,-)G* 9&,H-)* .&"'")M* :-($:-)* ,-'* /$* ,$+$,&:$:* :"* ("'"#* "6("#'$/&:$:")* +-)&(&1$)* )-.#"* /$* )-,&":$:* OI"'"#$#* .&"'")($#QM* )-'* C&'$',&$:-)M*"'*I#$'*+$#("M*,-'*"/*#",$8:-*(#&.8($#&-G**. *. V*.
(9) *. ∂ 2 E(π ) = qU''(ts − t + Mt) 2 + (1 − q)U''(n)(ts − t) 2 ∂D 2 * * >/*)8+-'"#*K8"*/-)*$I"'(")*)-'*$1"#)-)*$/*#&")I-WM*")*:",&#**=>?"@$A$=>?+@$B$CM* /$*,-':&,&2'*)"*)"I8':-*-#:"'*:"* E(π ) *")*'"I$(&1$M*I$#$'(&P$':-*,-'*,-',$1&:$:`** ")* :",&#M* )"* ,8"'($* ,-'* 8'$* C8',&2'* %E6&%&P$./"`G* 9&,H-* )8+8")(-* )"* "',8"'(#$* $1$/$:-* +-#* /$* "1&:"',&$* "6+"#&%"'($/* \* 1"#M* +-#* "S"%+/-M* 0,n"/* b* q#-))%$'* O?@@VQ* \* "* &',/8)-* +#")"'("* "'* ")(8:&-)* #"/$,&-'$:-)* $* /$* #$,&-'$/&:$:* :"/* )",(-#* "%+#")$#&$/*"'*D-/-%.&$*OD$&,":-M*?@@^QG** * B$* +#"I8'($* K8"* )&I8"* ")4* d,8E/* "/* %-'(-* O8Q* 2+(&%-* K8"* :",/$#$* 8'* &':&1&:8-* %$6&%&P$:-#* :"* ."'"C&,&-)e* ;$#$* #")-/1"#/$* H$.#=$* K8"* "'C#"'($#* /$* 8(&/&:$:* ")+"#$:$* :"/* ,8%+/&%&"'(-M* =?(@M* ,-'* /$* 8(&/&:$:* ")+"#$:$* :"* /$* "1$)&2'M* =?-@G* * UE( p) = Y − Dt + Dts + D−1ts *******************************OZQ*************. ********************************** UE(e) = q(Y + D−1ts − MtY ) + (1 − q)(Y + D−1ts) ***************OkQA@*. * >/* 8(&/&P$#* /$)* "6+#")&-'")* OZQ* F* OkQ* +$#$* ,-%+#$#* /$* 8(&/&:$:* ")+"#$:$* "'* ,$:$*,$)-M*)"*("':#=$*K8"*)$(&)C$,"#*/$*,-':&,&2'*O^Q*+$#$*K8"*"/*&':&1&:8-*-+("*+-#* "/* ,8%+/&%&"'(-G* >/I".#$&,$%"'("* ")(-* )"* (#$:8,"* "'* "/* ,8%+/&%&"'(-* :"* /$* :")&I8$/:$:*O^$Q4* * UE( p) > UE(e) ***************************************************************O^Q*. * Dt − Dts < qMtY *************************************************************O^$Q*****************************************. ******************************************************** W*B$*%":&:$*$.)-/8($*:"*$1"#)&2'*$/*#&")I-*:"*>##-r`;#$((*1?D@$)"*:"C&'"*,-%-4*. r(w) = _. U''(x) U'(x) G*. L&*")("*1$/-#*")*+-)&(&1-*"/*&':&1&:8-*")*$1"#)-*$/*#&")I-G*L&*")*'"I$(&1-*-,8##"*/-*,-'(#$#&-G*;-#*"':"M* )&* "/* '8%"#$:-#* ")* '"I$(&1-* F* "/* :"'-%&'$:-#* +-)&(&1-* F* %$F-#* K8"* ,"#-* \* ,-',$1&:$:* \* "/* &':&1&:8-*)"#E*$1"#)-*$/*#&")I-G** A@**9$:$*/$*"1$)&2'*C&),$/M*"'*")("*,$)-*9(s@*. *. W*.
(10) *********************************************************** D(1 − s) < qMY *****************************************************************O^.Q*. * D$."* $'-($#M* )&'* "%.$#I-M* K8"* )&* 7s8M* )"IJ'* /-* ")(&+8/$#=$* /$* -./&I$,&2'* /"I$/M*"'(-',")*)"*,8%+/&#=$*/$*,-':&,&2'*O^,QG** * 1 − s < qM ***********************************************************O^,Q*. * >* +$#(&#* :"* :&,H$* "6+#")&2'M* /$* ")(E(&,$* ,-%+$#$(&1$* +"#%&("* "6(#$"#* /$)* ,-',/8)&-'")* .E)&,$)* K8"* #")+$/:$'* /$* &'(8&,&2'* :"/* %-:"/-G* 9"* 8'* /$:-M* "/* ,8%+/&%&"'(-* ")* ,#",&"'("* ($'(-* "'* /$* +#-.$.&/&:$:* :"* )$',&2'* OKQ* ,-%-* "'* "/* %-'(-*:"*/$*%8/($*O"/*,8$/*,#","*,-'*/$*($)$*jQG*>*)8*1"PM*/$*"1$)&2'*$8%"'($*,-'*/$* ,$=:$*:"*5i*)&*/-)*&':&1&:8-)*+"#,&."'*8'$*%"'-#*#"'($.&/&:$:*O)-,&$/Q*$)-,&$:$*$*)8* ,-'(#&.8,&2'*("':#E'*%"'-#")*$/&,&"'(")*$/*+$I-G** *. @8=8'-;&10)&C)'D'"%;20;&"#'' * 0/* %-:"/-* :"* $,(-#* #$,&-'$/* '-* ,-'("%+/$* "/"%"'(-)* $)-,&$:-)* $* 1$/-#")M* )"'(&%&"'(-)*Ft-*"%-,&-'")*"'*/$)*:",&)&-'")*&':&1&:8$/")G*L&'*"%.$#I-M*,-%-*)"* :&),8(&2M* "6&)("* "1&:"',&$* "%+=#&,$* +$#$* )-)("'"#* /-* ,-'(#$#&-G* jE)* $8'M* )"IJ'* D-#&,"//&*"(*$/G*O?@A@QM*H$F*&',/8)-*#$P-'")*+$#$*+"')$#*K8"*/$*%&)%$*#$,&-'$/&:$:* &',/8F"* ")("* (&+-* :"* ,-%+-'"'(")G* 0'* +$/$.#$)* :"* /-)* $8(-#")* fg* '8")(#-)* #")8/($:-)* $+-#($'* $* /$* /&("#$(8#$* :"* /$* '"8#-,&"',&$* :"%-)(#$':-* K8"* /$* #$,&-'$/&:$:*'-*:"."*)"#*-+8")($*$*/$)*"%-,&-'")h*O+G*?Z?QG* * !"#"$"%&'()*+(,+$ * D-%-* /-)* :&),8("* 7-.* O?@@kM* +G* AkQM* "/* $'E/&)&)* :"* 1$#&-)* ,$)-)* &'("#'$,&-'$/")* :"%8")(#$* K8"* /$* /"I&(&%&:$:* :"/* I-.&"#'-* \* F* +-#* ($'(-M* "/* $,$(-* :"*/$*/"F`M*I8$#:$*8'*1=',8/-*%E)*")(#",H-*O"'*"/*/$#I-*+/$P-Q*,-'*)8*#"/$,&2'*C#"'("* $/* ,&8:$:$'-* O,"#,$'=$M* ,-'C&$'P$Q* K8"* ,-'* /$* "C&,&"',&$* %&)%$* :"* )8* I")(&2'* +J./&,$G* * 0'* ")("* %&)%-* )"'(&:-M* )8I&"#"* q$#,=$* u&//"I$)* O?@@WQM* /$)* #"/$,&-'")* :"*. *. A@*.
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p) = Y − Dt + Dts + D−1ts − θ[ E(I) P − E(I) R ]*************************OXQ* *. 0 ≤ θ ≤ 1* * ************* U(e) = q(Y + D−1ts − MtY ) + (1 − q)(Y + D−1ts) *****************************OVQ* * 0'* /$* ",8$,&2'* OXQ* )"* :$* +$)-* $* /$* "6&)("',&$* :"* 8'* +$#E%"(#-* :"* :"),-'C&$'P$* θ M* "/* ,8$/* -),&/$* "'(#"* @* F* AAAM* * F* K8"* )"* ,-':&,&-'$* $* /$* :&C"#"',&$ E(I) P − E(I) R i* "/* 1$/-#* ")+"#$:-* :"* /$* &'1"#)&2'* +J./&,$* OEM* (#$)* "/* #",$8:-*. (#&.8($#&-Q*K8"*"/*&':&1&:8-*,#""*K8"*"/*0)($:-*")($*"'*,$+$,&:$:*:"*H$,"#*OF*+-#* +/$'"$:$Q* F* /$* K8"* ,#""* K8"* #"$/%"'("* H$,"* OG* +-#* #"$/QM* #")+",(&1$%"'("G* L&* /$* :&C"#"',&$*")*$/($M*"//-*)"*(#$:8,"*"'*:"),-'C&$'P$*F*1&,"1"#)$G** *. Dt − Dts + θ[ E(I) P − E(I) R ] < qMtY ********************************************OWQ* * 0'*")("*,$)-M*#"(-%$':-*/$*,-':&,&2'*O^QM*)"*:"."*)$(&)C$,"#*OWQ*\*#")8/($:-* :"* OXQ* F* OVQ* `* +$#$* K8"* "/* &':&1&:8-* -+("* +-#* "/* ,8%+/&%&"'(-G* 0'* ")("* ,$)-M* )"* %$'(&"'"'* /$)* +#":&,,&-'")* :"/* %-:"/-* :"/* $,(-#* #$,&-'$/M* &'(#-:8,&"':-M* )&'* "%.$#I-M*"/*"C",(-*,#",&"'("*:"*/$*:"),-'C&$'P$*)-.#"*"/*$/&,&"'("*$*/$*"1$)&2'G** * ******************************************************** AA*. L"* $.#"* /$* +-)&.&/&:$:* $* K8"* "/* &':&1&:8-* :"),-'C="* +/"'$%"'("* "'* "/* 0)($:-* OsAQ* -* ,-'C="* +/"'$%"'("*"'*"/*%&)%-*Os@QG*. *. AA*.
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n"/M* L,H%$:"#M* D8#(&)M* L,$#'&"#M* b* >%")M* ?@@kQG* c$/* :&C"#"',&$M* +#")"'("*"'*$8(-#")*,-%-*R-r/")*b*q&'(&)*O?@@ZQ*F*v&%%"#/&'I*O?@@]Q*$+8'($*$* ,-',/8&#*K8"*%&"'($)*K8"*/$*+"'$*O)H$%"Q*H$,"*+$#("*:"/*,$#E,("#*:"*/$)*+"#)-'$)M* /$*,8/+$*OI8&/(Q*")*#")8/($:-*:"*/$*$,,&2'*&':&1&:8$/G*0'*-(#$)*+$/$.#$)M*/$)*+"#)-'$)* "6+"#&%"'($'*/$*+#&%"#$*,8$':-*)8*,-':8,($*")*"6+8")($*$*/$*/8P*+J./&,$*\*$)=*'-* )"* $##"+&"'($'* :"* /$* %&)%$* `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p) = Y − Dt + Dts + D−1ts **********************************************************OA@Q*. * ************* U(e) = q(Y + D−1ts − MtY − λ (Y − D) + (1 − q)(Y + D−1ts − λ (Y − D)) ******OAAQ****************** * ********************************************************************************************************************** 0 ≤ λ ≤ 1* *. 0'*")("*,$)-M*/$*1$#&$,&2'*:"/*%-:"/-*)"*&'(#-:8,"*"'*/$*",8$,&2'*:"*"1$)&2'G*. 0/*+$#E%"(#-*:"*,8/+$* λ M*$C",($#E*'"I$(&1$%"'("*/$*8(&/&:$:*:"/*&':&1&:8-*"'*,$)-*. *. A?*.
(13) :"*)8.*#"+-#($#*)8*&'I#")-*$*/$*$8(-#&:$:*C&),$/*O#"+#")"'($':-*($/*+-)&.&/&:$:*"'*/$* "6&)("',&$*:"*8'*1$/-#*+-)&(&1-*"'*/$*#")($* Y − D QG**** Dt − Dts < qMtY + λ (Y − D) *************************************OA?Q*. >/*"1$/8$#*/$*,-':&,&2'*:"*+$I-*O^$QM*)"*-.(&"'"*/$*:")&I8$/:$:**OA?QG*9$:-*"/* )"'(&:-* :"* /$* %&)%$M* /$* ,8/+$* :"."#=$* %-(&1$#* "/* ,8%+/&%&"'(-M* +-#* ($'(-M* $C",($* +-)&(&1$%"'("*"/*/$:-*:"#",H-*:"*/$*",8$,&2'G** * *. E8'>0#"F;'5G?",0%"&:)*' * ;$#$* +-'"#* $* +#8".$* "/* %-:"/-* ")(8:&$:-M* )"* :&)"[2* 8'* ")K8"%$* "6+"#&%"'($/G*c-#I/"#*O?@@]Q*&')&)("*"'*K8"*fg*"'*/-)*"6+"#&%"'(-)*(#&.8($#&-)*:"* /$.-#$(-#&-* OgQ* /$* +-)&.&/&:$:* :"* ,-'(#-/$#* 1$#&$./")* OgQ* +"#%&("* "C",(8$#* 8'$* %":&,&2'*+#",&)$*)-.#"*"C",(-)*")+",=C&,-)h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i* &',"'(&1-)* &':&1&:8$/")* $* /$* "1$)&2'* $J'* ,8$':-* "/* +$I-* (-($/* :"/* I#8+-* ,-'//"1"* 8'* %$F-#* .&"'")($#* :"* (-:-)* /-)* ,-'(#&.8F"'(")* G* 0'* (N#%&'-)* :"/* %-:"/-* :"/* $,(-#* #$,&-'$/M* "//-* )"* +/$)%$#=$M* +-#* "':"M* "'* "/* &',8%+/&%&"'(-*:"*/$*:")&I8$/:$:*O^,QG** *. *. A]*.
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