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Y FmNS8'p$#yo/+gb0ϒ~ ~6yA+e.߲[3@ݦ_B̃yvL*ӓ4(    0Equation Equation.30,Microsoft Equation 3.00!1Equation Equation.30,Microsoft Equation 3.00XEquation Equation.30,Microsoft Equation 3.00Ecuacin Equation.30DMicrosoft Editor de ecuaciones 3.0/ 00DTimes New Roman|dv 0|( 0 De0}fԚ New Roman|dv 0|( 0  DMonotype Sorts|dv 0|( 0 0DSymbole Sorts|dv 0|( 0 e3 .  @n?" dd@  @@`` j b TT.  .0/m7$t+y6R3gdI " $ !!%8(  )%*W%-v-G,*a,-+/ *    * > (b$gO Z6ˬy"3$$$b$ $~ouM.2"3b$Bl{WKfA2fb$t^̬K`m+ b$~~d!2_g3vb$<IWA䄠'42$(#7 ~v.pF,b$S}3D3J-b$GBAEWWNb=`04?a2$L~yLN(d9ob$@* LҪ)b$rrCܮD4f3kb$G@/D۞'O0 E**b$kOi\e,)o$b$*B*m:d$x)bH$$$2$/ŃsW'ڥGq2$nYф#o$ECs$$$$$2$_4*G}2$t :     A 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E|| ff@fj[8  $g4BdBdv 0p(ppp@  <4BdBd 0,g4ddv 0pp@ ppʚ;2Nʚ;<4!d!d{ 0<4dddd{ 02*___PPT9 z? -O =./0123456789%*.3+,-: < > E GQSZ[dn|z{~*()j ` 333WcL+᷷Ҫ` 333WcL+᷷Ҫ` 999>?" dd@,?dd@ l2 " d@ ` n?" dd@   @@``@n?" dd@  @@``PR    @ ` ` p>>   l( [ 4   # <  c $޽h ? 333WcL+᷷Ҫ  Serene  H@(     B CE,F    : C  @   `8j   s *g p g L cN NN}/kGrjL#j_    c $ g  `   g N cN NN}/kGr!kjL#j_   c $$e `` g ^* 2Wc  c $\ `  e F*(2Wc  c $L `  ^ F*(2Wc<  c $޽h ? 333WcL+᷷Ҫ0 jb$( w $ $ 01" P   " P*   $ 05"    " \* d $ c $ ?  " $ 0X9"  @ " 8 cN NN}/kGreW[#j_ ,{Nd\ ,{ Nd\ ,{Vd\ ,{Nd\   $ 6L=" `P  " P*   $ 6<" `  " R*  H $ 0޽h ? ̙33H (    0hu P   u Z*G 3    0,t    u \*G 3    6%t `P  u Z*G 3    6lI `  u \*G 3  H  0޽h ? ̙33 ;3 (      T fj[>?0@  =[Diferentes Formas Funcionales y Otras Cosas del Analisis de Regresion + Un poco de repaso"\ \f$3                  0$E P   R     H   0޽h ? 333WcL+᷷Ҫ 0$(  :  0UE 0El significado de los coeficientes de regresin:*1 20\      0_E0 @E(Y| X2, X3) = b1 + b2X2 + b3X3  ! 2<   F `  `*  6lE` D E(Y|X2, X3)b 2  fB  6D  6pEL ZDX28 2&  6uE @  = b2P 2 *     0(|E P0 @ d: b2@ 2   0xE ` ocmide el cambio en el valor medio de Y, por un cambio de una unidad en X2, manteniendo X3 constante.Xd 2G         0TEP 5o 28   0܏E  El efecto  directo de un cambio en una unidad en X2 sobre el valor medio de Y, neto de X3.d] 2 ! %    0XE   :?????? 2XB  0D0 0 F `  `  $  0\]"` D E(Y|X2, X3)b 2  `B  0D  0e"L ~DX38 2 4  0Tm" @  = b3P 2 >   H  0޽h ? ̙33 XP@ (    C hAPD:\COURSE\ECON2170\GUJARATI\tab701c.bmp` }F         6ԲE   _Y. d`  `B  0D    6E@   |sYH `    6E  JLY=E(Y|X2,X3)+u =b1 + b2 X2 + b3 X3 + u' `h`h` ' X2  00  L  @8   #  0    6E 48  |suH `     68E @  _^. d`  X   0 H  0޽h ? ̙33    P')   (      0EP  {Tasa de inflacion actual(%) 2$  2   6E0 P  7 Y ^B   6D0 0   <`E@: DE(Y|X2,X3)n 2  dB   <D)   <E2 ZDX28 2   <E |= b2 = -1.3925D 2    6"E>  0*Y = b12 + b22X2 + u2 2D      <"E`  8 P   <"Ea! 9 F   <" 2   6I0P  ^ X2 > ^B   6D  ^B  @ 6D     BI w , 2dB   <DH    <I  ZDX38 2    <4$I l  = b3= 1.4700D 2      0)I 00  Tasa de inflacion esperada (%)6    0 I p  oTasa de Paro(%)$Q   01I `@  X3 = g31 + g32X2 + u23 2AA0      0;I0  8X2 = g21 + g23X3 + u23 2 E E   D    JF      x  !  0GI   ZDX38 2`B "  0D   #  0LIx   ZDX28 2 $  0lRIp 0  = g32 = 1.1138B 2E    %   fBTCt DEF<%%D` 4 @d @\ d l t d 8 T % %  { ^   ClgX"dTApR }  -  -`@             tX  &  6ZpXIP Efecto directo de X2 `4     '  0T\I P  Efecto indirecto via X3 `4      (  696``I nEfecto directo de X3 `  * )  6m@5K" @:B DE(Y|X2,X3)n 2  H   0޽h ? ̙33 }`$ (  $R $ 0hI  &Efecto total de X2 sobre E(Y|X2,X3): ' 2   &   $ 0qIP *db2 + b3 * g32 = -1.392472 + (1.470032)(1.11385)3 2#  %XB $ 0DQQXB $ 0D  $ 6 {IdT 7 Z $ 6~IdT 7 Z $ 0IP 2 directo +  indirecto  2,    $ 0DI@ J= -1.392472 + 1.637395 2  $ 0$I > = 0.244923 2   $ 6PI` P  DE(Y|X2)D 2 ^B  $ 6D   $ 6I  ZDX28 2 $ 6I    = b22P 2  $ 0|I  T= 0.24490 2 $ 6I  B F   $ P 5N P  $ ` 2 $ 6I P  PX22 fB $B 6D 2 $ 64IP  5Y $ 04I` P  t.E(Y| X2 )= b12+b22X2  2x      fB $ 6DԔ  H $ 0޽h ? ̙33R p((  ( ( C hAPD:\COURSE\ECON2170\GUJARATI\tab701a.bmp0 ( 6IP  XBY=E(Y|X2)+u2 = b12 + b22 X2 + u2" `h`h` " X2 ( 00< ( 6I` n   u2 incluye X3n `dl `h`&   X ( 0  M H ( 0޽h ? ̙33 >6,(  , , C hAPD:\COURSE\ECON2170\GUJARATI\tab701c.bmp Pp`X , 0` P  , 6IP ` 82X3 = g31 + g32 X2 + u32   `h`  H , 0޽h ? ̙33 TL0(  0S 0 0I@ 'Efecto total de X3 sobre E(Y|X2, X3): ( 2   &   0 0I ,fb3 + b2 * g23 = 1.470032 + (-1.392472) (0.369953)4 2%  'XB 0 0DQQXB 0 0D  0 6$IdT DZ  0 6IdT 7 Z 0 0I ` @ 2 directo +  indirecto  2,    0 0I m@ J= 1.470032 - 0.515149 2  0 0lL ? = 0.9548828 2   0 6L`   DE(Y|X3)D 2 ^B  0 6D `@  0 6H L  ZDX38 2 0 6 L @   = b23P 2  0 0LL  V = 0.9548830 2  0 6L  B F   0  5N P  0 ` 2 0 6L P  PX32 fB 0B 6D 2 0 6p LP  5Y 0 0d$L` P  0*Y = b13 + b23 X3 + u3 2D   fB 0 6DԔ  H 0 0޽h ? ̙33 3+4(  4 4 C hAPD:\COURSE\ECON2170\GUJARATI\tab701e.bmp  4 60L  0 -X2 = g21 + g23 X3 + u23 `h`  X 4 00  H 4 0޽h ? ̙33g 8(  8 8 C hAPD:\COURSE\ECON2170\GUJARATI\tab701d.bmp0R 8 6  @ 6LP` B  @ 64LR  B #F   @   w @ 0TL  u1 = l1 + l2u2 + v 2 EMEM 0   @ 6 L @  5  @ 6xL  5   @ 0|L P  [cmide el efecto directo del cambio en una unidad de X2 sobre Y. (productividad marginal del trabajo)2d 24 /   @ 0 LP Pp  dl2* 2E  F t   @  t   @ 0L  l2 = D 2E    @ 6Lt 4| C &xP @ 0@L  @ (Paso II : regresar X2 sobre X3 y obtenerf) 2   >  @ 0Lpp 8X2 = g21 + g23 X3 + u2 2 E E   D     @ 6`O@ 0 B  @ 0O , 2-L p0 @# p0n @ 0"Op0 Lu2 = X2 - g21 - g23 X3 = X2  E(X2|X3)' 2  E E               @ 6x3Op0  B  @ 65OP 5 X @ 03fp X2 @ 0 ` @ c $A ?? < 0  @ H" ?  m y obtener( 2 3E3   H @ 0޽h ? ̙33 %.4(  4 4 0@IO ^EJEMPLOS DE MODELOS LINEALES Ejemplo 1: Capital Asset Pricing Model (CAPM) para la accion i s :(2C 2 9B '   4 <PO= E((G&33  4 <0UO = E)(G&33 4 <WO ' = E((G&33 4 <]O9= E)(G&33 4 <`aOX Cf&33 4 <eO @X Cm&33 4 6iO x F C2&33 4 <mOX Cf&33 4 < 8  H +4 H )4 6O H C2&33 *4 6XO x Gb*G33 #4 0O @ &>1 ==> una accion volatil o agresiva  ' 2%3H 8  .4 ,4 6O8 C2&33 -4 6Ox Gb*G33 %4 0Op <1 ==> una accion defensiva  23> H 4 0޽h ? 333WcL+᷷Ҫ` 8 ( G 8 8 0O  [Ejemplo 1:(cont.) 2  8 6Oo cf2 f d3   8 6   c22 fd3   l< 6Uk   eb4 g%d3  * j< 0UpP `*  6Linea de la paridad encubierta de los tipos de interes7 27ZH < 0޽h ? 333WcL+᷷Ҫr  "  0)6@( G @ @ 0 U@ ` ben la regresion: 2  @ 0 U@  [Ejemplo 2:(Cont.) 2 4B @ #  w @ 6U} ci2 fd3    @ 6,U f i c22 fd3   !@ 6DU( i c12 fd3   "@ 6 U -s cu2 f(d3   #@ 6U f ce2 f(d3   $@ 6U  ce2 f(d3   %@ 6dU 4  cF2 f(d3   &@ 6,Us ci2 f(d3   '@ 6U0 s ci2 f(d3   (@ 6U)t e+4 g(d3   )@ 6U t e-4 g(d3   *@ 6LU` t e+4 g(d3   +@ 6U&t e=4 g(d3   ,@ 6U2t e-4 g(d3   -@ 6Urs c)2 f(d3   .@ 6lUk V s c(2 f(d3   /@ 6Yu`s c)2 f(d3   0@ 6Ys c(2 f(d3   1@ 6 Y  c*2 fd3   2@ 6(YW t eb4 g(d3   3@ 6Y& eb4 g(d3  :8 2 M  @M2  @ 6Y l R @3  @ 6Y) l) R @3  @ 6$Y l R @3  @ 6 Y M 3 @3  @ 6$Y %  @3  @ 6'Y2 l2 R @3  @ 6h)Y- M- 3 @3 `8 s 4@   @ 0.Y  B 2I @ q  s @q " s @ 601Y  s @  @ 63Yq q  @I  @ 06Y  B 2  5@ T9Y ?P e  Si la teoria de la paridad encubierta es cierta, b1=0 y b2=1 Todavia estamos en la etapa de entender a interpretar los coeficientes de una regresin. MUY PRONTO aprenderemos a contrastar diferentes hiptesis sobre los valores de los coeficientes; pero 13GOEE3GOG@  1   , 6@ HX ? @ (PRIMERO LO PRIMERO (First things First) 6( 2(E32    H @ 0޽h ? 333WcL+᷷Ҫs #@(  d  <1?``d  <1?`G  TxLYxaxaj[)? # Formas Funcionales de la Regresion $0#(\         T  T\Yxaxa8c?&_ @El termino lineal en un modelo de regresion simple significa que es lineal en los parametros; pero en las variables de la regresion puede ser lineal o no. Definicin: Una funcin es lineal en alguno de sus argumentos si la primera derivada parcial de la funcin con respecto dicho argumento no contiene este argumento.rA $$OA$ $>$                                                 H  0޽h ? 333WcL+᷷Ҫ P C(  d  <1?m`d  <1?m  TgYxaxa1?\  &Yi = b1 + b2Xi + ui$ $$C$ $$C$ $$ $$ $&      ZTrYxaxap?`  Ejemplos de Modelos Lineales"  4     =  ZxYxaxap? +  Ejemplos de Modelos No-Lineales"   N      XB  0p? h XB  0p?h  T(~Yxaxa1?p  .ln(Yi) = b1 + b2Xi + ui$ $$C$ $$C$ $$ $$ $4      TYxaxa1?]q  Z0Yi = b1 + b2 ln(Xi) + ui$ $$C$ $$C$ $$ $$ $$ $Z          Z@Yxaxa1? W &Yi = b1 + b2Xi + ui$ $$C$ $$C$ $$ $$ $&     Z`Yxaxap? E2  F   D       ZYxaxa1?  D  *Yi = b1 + b2Xi + ui$ $$C$ $$C$ $$ $$ $&     Z԰Yxaxap?   Xb3$A    TеYxaxa1?K2` n>Yi = b1 + b2Xi + exp(b3Xi) + ui $ $$C$ $$C$ $$ $$C$ $$ $$ $$ $&     Z$Yxaxa1? `  *Yi = b1 + b2Xi + ui$ $$C$ $$C$ $$ $$ $&     ZDYxaxap? _ {  Xb3$A     NdYxaxafj[?~  Lineal vs. Nonlineal,606&    H  0޽h ? 333WcL+᷷Ҫ PH`(  '  TYxaxaj[)? Diferentes Formas Funcionales,N          ZYxaxap?`I |  )Q1. Lineal 2. Log-Log 3. Semilog Lineal-Log Log-Lineal 4. ReciprocatR , ,, ,I,,, ,,@        T Yxaxap? $  :LPresta Atencion a la pendiente y a la elasticidad de cada una de las formasMM                 H  0޽h ? 333WcL+᷷ҪF FFpbsL` F( G L2 L 0$Y) 0 .Formas Funcionales de los modelos de regresion&/ 2.3Z   L 0Zp@ 1. Modelo log-log :L 2 3 [8 Yc k LY  L 6ZR NR  @3  L 6$ Z c  Xui:Z333 L 6HZk  ' Ce&(33 L 6ZU  ' AX$(33  L 6ZY' AY$(33  L 6Z P  @3   L 6Z- k A1$33  L 64!Z 2 w Zb2<G3O33  L 6 %Z8 Gb*G(33 L 6)ZY  w E-(G33 L 6.Z7 E=(G(33 L 0X1Z`  'Tomando Logs lo convertimos en lineal :$( 2'I3$   L <p6Z   Ci&33 L <:Z 9o  Cu&$33 L <8?Z o  AX$$33 L <8BZ $o  AY$$33 +L <FZ j M  E+(G$33 ,L <JZ M M  E+(G$33 -L <,OZ OM  E=(G$33 4L <TRZ "  A*$33 5L <VZ  A*$33 6L <xZZ B  A2$33 7L <T^Z  g  A*$33 8L <bZ #  A1$33 9L <fZ 5  A*$33 ?L <_Z . M  Eb(G$33 @L <0oZ 9M  Eb(G$33 8  (  rL (  L <rZ (  Ci&33  L <vZn,   Cu&$33 !L <zZ   AX$(33 "L <Y ,  ^ln&$33 #L <Z,   AY$$33 $L <؄Z,   ^ln&$33 .L <Z =d  E+(G$33 /L <؍Z d  E-(G$33 0L <Z .d  E=(G$33 :L <Z~  A2$33 ;L <Z_   A*$33  ^ln&$33 1L < Z" z E+(G$33 2L <Zs  z E-(G$33 3L <Z .z E=(G$33 =L <Z I  A2$33 CL <ZO  z Eb(G$33 DL 6Z` ^ z \b1>G$3O$33 L 0Z0 0@P  7==> 23 L 00Z 0@0  7==> 23 GL <DZ d  A2$ 33 HL <hZD   A*$ 33 IL <Z fd  A2$ 33 JL <Z@ ,:  Gb*G33 KL <Z@ Z:  Gb*G33 LL <(Z@ :  E-(G33 ML <[@ :  E=(G33 NL <[W Q  adonde&33 XL < [ @3 18 ?  oLR iHB RL C 3?HB SL C 3>  HB TL C 3g d } HB UL C 3g 8 HB VL C 31  WL <ZP C*&P33 YL <[@` A*$33 ZL <l[, |p A*$33 [L <,[   4ln3 \L <d[1  4ln3 ]L <[ Vb28E3M33 ^L <#[c C=&E33 _L <([M   C=&E33 `L <&[Y C=&E33 aL </[  AX$33 bL <4[;  \dX$33 cL <9[ ' AY$33 dL <;[f 1  \dY$33 eL <@['   AX$33 fL <E[A   Ad$33 gL <pH[T  AY$33 hL <L[i  Ad$33 iL <P[A \dX$33 jL <T[m 8 \dY$33 nL 0X[  {Coef de elasticidad  2$ , pL N\[ ?0 Este es un modelo no-lineal  d3N       H L 0޽h ? 333WcL+᷷Ҫ ph!*P( G P P <Lf[  pCantidad Demandada 2$ XB P 0D @@@  P 0`k[` 1Y 2XB P 0D@ @ @  P 0@o[  1X 2  P 0r[ @  Pprecio 2  P  BC@DEFo pl@@  P  "P 6u[$B  c22 f d3   #P 68z[t S c12 fd3   $P 6Lm[  eb4 gd3   %P 6[/F eb4 g#d3   &P 6[l e-4 gd3   'P 6ȉ[*F e=4 g#d3   (P 6[" cX2 f#d3   )P 6[v" cY2 f#d3  XB P 0D@ @  XB P 0D @   P 0[ `  _lnY& 2 P 0[P 0p  MlnX 2^B P 6Do  `P  P 6[.7a cX2 f d3   P 6l[.$a cY2 f d3   P 6L[.a fln2 f d3  P 6[.a fln2 f d3  P 6[.a fln2 f d3  P 6[y c22 fd3   P 6ط[\ c12 fd3   P 6p[D eb4 g d3   P 6[D eb4 g d3    P 6P[^M e-4 g d3   !P 6[& e=4 g d3  0 *P Z[ ?`N .Formas Funcionales de los modelos de regresion//3:   H P 0޽h ? 333WcL+᷷ҪP< <;YxT@x;( X T T 0|[@ 2. Modelo Semi log:H 233   T 0[` .Formas Funcionales de los modelos de regresion$/.3 6   T 0[ {Modelo Log-lineal o lineal-log:& 233g 8 66 T66 T 6|[9 Ci&33  T 6[ 9 Ci&33  T 6[90 Ci&33  T 6[O[ Cu&(33  T 6[ [  CX&(33  T 6[w[) CY&(33 T 6$\l6 E+(G(33 T 68\ 6  E+(G(33 T 6\6L  E=(G(33 T 6 \ 9  A2$33 T 6d\A 9  A1$33 T 6\6[/ Bln$(33 T 6x\ 6t  Ga*G(33 T 6\u 6?  Ga*G(33g 8 sv9  %T`/C  T 6h\y9  Ci&33 T 6#\,yX9  Ci&33 T 6'\y9  Ci&33 T 6*\c  Cu&(33 T 6@[i (  CX&(33 T 6T1\s"  CY&(33 T 65\vN E+(G(33 T 69\g v  E+(G(33 T 6`=\nv  E=(G(33  T 6pA\Z O   Bln$(33 !T 6`E\ y1 9  A2$33 "T 6xI\ y2 9  A1$33 #T 6[: v  Gb*G(33 $T 64P\J v  Gb*G(33 T 0XT\P+ 9o0F23 ;T <lX\i O @3  DT 0Z\`   7y 23 ZT <_\9   @3 8   vT  w@ " <  CT" <  @T 6a\" <U  E=(G 33 AT 6e\( h  A2$33 BT 6ti\" $U  Ga*G 33`B 'T 0D3 0  (T 0m\  nCambio relativo en y$ 23 )T 0Dr\p  nCambio absoluto en x$ 2I3 @ `   _T`  HB JT C 3  HB KT C 34  HB LT C 3  HB MT C 3  HB NT C 3   OT <x\5   CY&33 PT <T|\ {  ^dX&33 QT <\   ^dY&33 RT <\\   ^dX&33 ST <L\   CY&33 TT <$\  ^dY&33 UT <\h F  ^dX&33 VT <\q   CY&33 WT <\ m  Cd&33 XT <(\&   A1$33 YT <t\ 8  Bln$33 [T <Ȥ\9 b)  E=(G33 \T <\ 9 w)  E=(G33 ]T <\` 9 )  E=(G33 rT 6\l 99R @3 L " C dT#  3 aT 6d\" CU E=(G 33 bT 6ܷ\0 p A2$33 cT 6L\" -U Gb*G 33^B FT 6D3pp0 p GT 6\P p p jCambio absoluto en y  2I HT 6\  jCambio relativo en x  2 lT <\ @3 8  (g xT gTHB eT C 3U  HB gT C 3  HB hT C 3 g  iT <<\ A1$33 jT <\ Bln$33 kT <`\( CX&33 mT <\ ^dX&33 nT <L\( ^dY&33 oT <\k CX&33 pT <T\W   Cd&33 qT <(\( ^dY&33 sT <\^^ E=(G33 tT <\  ^ E=(G33H T 0޽h ? 333WcL+᷷Ҫ$ ##/5XR#( G X  X 0t\0w %3. Transformacion reciproca o inversa8& 23", 8 y.7 X.y7HB  X C 3 e f  X <^s7  Ci&33  X <^ 1  Ci&33  X <^s*  Ci&33  X < ^r   Cu&33 X <p^ D  CX&33 X <\^y CY&33 X <^   E+(G33 X <^s E+(G33 X < ^& E=(G33 X <X$^ @  A)$33 X <D(^ .c X A1$33 X <,^ k  A($33 X <0^ s  A2$33 X <4^Qs  A1$33 X <@8^j  Gb*G33 X <,<^' Gb*G33 X 0A^7 5Formas Funcionales de los modelos de regresion (cont)$653 6   X 6hE^c !  ci2 fd3   X 6G^c W  ci2 fd3    X 64N^c :  ci2 fd3   !X 6Q^   cu2 fd3   "X 6V^ f  cX2 fd3   #X 6Y^7  cY2 fd3   $X 6]^   e+4 gd3   %X 6la^  e+4 gd3   &X 64e^E  e=4 gd3   'X 6h^   c)2 fd3   (X 6l^L =   c(2 fd3   )X 6p^ $ H  c*2 fd3   *X 6Tt^c m  c22 fd3   +X 6x^c   c12 fd3   ,X 6{^  eb4 gd3   -X 6^F  eb4 gd3   X 0^  3==> 2 X 0^p  Tdonde   2 4B .X # H |I  /X 6^ F  ci2 fd3   0X 6t^T   ci2 fd3   1X 6<^l Ry  cX2 fd3   2X 6^   cX2 fd3   3X 6ș^/W  c12 fd3   4X 64^6  c*2 fd3   5X 6ܡ^)&  e=4 gd3  H X 0޽h ? 333WcL+᷷Ҫ+ 5+-+EQ\*( G \ \ 0^ ,Algunas caracteristicas del modelo reciproco&- 2,3$58 u aQ Q\au QBB G\ 3 3uTU H\ 6d^kQ CX&33 I\ 6^u   CY&33 J\ 6Ը^uaG A1$33 K\ 6^_ B3  L\ 6^_ B3  M\ 64^: Xb2:E3M33 N\ 6^* Xb1:E3M33 O\ 6P^X E+(E33 P\ 6^@ E=(E33B8  L F\ L B\ 6$^i C0&33 C\ 6H^k k L B3  D\ 6h^ B G>*G33 E\ 6^   ^b1@nG3O338 PP p '\PP p`B \ 0D3pP`B \ 0D3P P \ 0^Pp =Y  23fB \ 6D`   \ BCDEF3H(x@  @p `@ P  \P   \ 60^`  C1&   \ 68^P Kb.G \ 0`^   5X 23 \ 0^Ppp 50 2 \ 0^` 5y 2,8 ~ A\~ =\ 6(^ C0&33 >\ 6_5 C2& 33 ?\ 6_z G>*G33 @\ 6_~ Gb*G33 \ 0$ _0  =Y  23XB \ 0D30 0XB \ 0D30  0  \ 0_  5X 23^B \ 6D@` @F P  \   \ 0_`  C1&  \ 0_P L-b.G \ 0x_   50 23 \ 0 _ P@  A+$ 23  \ BCDEF3`0X@  0 p0  "\ 0$_ @  A-$ 2358  a8Q  <\a 8Q BB 2\ 3 3T 8U  3\ 6)_k *Q  CX&33 4\ 6d-_   CY&33 5\ 61_aG  A1$33 6\ 66__   B3  7\ 69__   B3  8\ 64<_j  Xb2:E3M33 9\ 6@_Z  Xb1:E3M33 :\ 6E_  E+(E33 ;\ 6I_p  E=(E33.8 _ ,  ,\ _ ,  (\ 6M_ ,  C0&33 )\ 6Q_ ,  C1& 33 *\ 6dT_3 }  G<*G33 +\ 6Y__ }  Ib,G33 %\ 0@]_   5y 2,8    1\   -\ 6`_M   C0&33 .\ 6e_17 e  C2& 33 /\ 6c_ !  G>*G33 0\ 6l_ %  Gb*G33H \ 0޽h ? 333WcL+᷷Ҫ A9)2`(  ,  ` ` 0*G33 %` 6_ k  Ib,G33 ` 0`_@ 5y 2,8 !( !`!( ` 6_( C0&33 ` 6_ C2& 33 ` 6_ G<*G33  ` 6_! Gb*G33H ` 0޽h ? 333WcL+᷷ҪGB AA^fdA(  d d 0_`` l Ejemplo 1:, 2  I 3 d 0_p 7Sea 23X8  \D fd \D Pd 6,_\D C3&33 Qd 6$`PD C2&33 Rd 68`?D C4&33 Sd 6`'gw C2&33 Td 6 ` D C2&33 Ud 6x`  D C3&33 Vd 6` < D C2&33 Wd 6L` + D C2&33 Xd 6p`]D C1&33 Yd 6$`l) EX( 33 Zd 6\#`\) EX( 33 [d 6`(  ) EX( 33 \d 6 +`H  ) EX( 33 ]d 6x/` ) EY( 33 ^d 61`h  Ib,G 33 _d 6$6`<   Ib,G 33 `d 69`T   Ib,G 33 ad 6>`   Ib,G 33 bd 6A`5  G+*G 33 cd 6E`}   G+*G 33 dd 6dH`!  G+*G 33 ed 6\N`Y  G=*G 33 d 0hQ` 0 ] transformando 23  d 0U`@  X3* = X22h 23 3 33 3 33 d 0]`@  X4* = X2X3h 23 3 33 33 3  d 0c` Squeda 238  ~4 Od ~4 :d 6g`>~g C*&33 ;d 6k`;4 C4&33 d 6w` 4 C3&33 ?d 6{`  4 C3&33 @d 6x` < 4 C2&33 Ad 6ă` + 4 C2&33 Bd 6`]4 C1&33 Cd 6`G EX( 33 Dd 6t`(   EX( 33 Ed 6``H   EX( 33 Fd 6`  EY( 33 Gd 6Л`S Ib,G 33 Hd 6`<   Ib,G 33 Id 6\`T   Ib,G 33 Jd 6H`  Ib,G 33 Kd 6`  G+*G 33 Ld 6`}   G+*G 33 Md 6`!  G+*G 33 Nd 6D`Y G=*G 33^B  d 6DԔPP  d 0`  j Ejemplo 2:* 2  I38 x   9dx  BB -d 3 3   .d 6`D   C3& 33 /d 6` #  C2& 33 0d 6`/ c !  C1& 33 1d 68` ^  Ib,G33 2d 6 ` xD r  Ib,G33 3d 6`   Ib,G33 4d 6` k  G+*G33 5d 6` 8  G+*G33 6d 6 `  G=*G33 7d 6` O  EX(33 8d 6`   EY(33 d 0`@ W  ] transformando 23 8   ,d  BB "d 3 3  #d 6`y  C3& 33 $d 6 ` d  C*& 33 %d 6l`O  o  C2& 33 &d 6$a"   A1$33 'd 68a D  Gb*E33 (d 6a v  E+(E33 )d 6 a( a G  E=(E33 *d 6xa   CX&33 +d 6aw  ]  CX&338 J ]q !dP ew d 6a)N ]  C*& 33 d 6a q C2& 33 d 6haz q C2& 33 d 6#a/ c q C1& 33 d 6'a b n \ EX(33 d 6P+ab \ EY(33 d 6t/a J + D Ib,G33 d 62a J D Ib,G33 d 6(7a J 8 D G+*G33  d 6:aJ D G=*G33 d 0x>aP @@p Squeda 23' d 0Ba`  -Sin embargo, X2* no se puede calcular porque @. 23 3 336` d c $A ??  d 0Ha `  c no se conoce. 23H d 0޽h ? 333WcL+᷷Ҫ= b=Z=Wch<( % h h 0Oaj[Ԕ` k Aplicaciones:( 2  33  h 0Ta`' %1. Funcion de Producion Cobb-Douglas:<& 23"3,  Wh <PZaa   Eu(33 Xh <8_ab9  Ee(33 Yh <bab[  EK(33 Zh <`gab^  EL(33 [h <eab" EY(33 ^h <oa s C1&33 _h 60saP@ 0  \b3>G3O33 `h 6`xaQ{ k  \b2>G3O33 ah <}aG3g Ib,G33 bh <؁aGg G=*G33  h 0a \Transformando: 23 8 E3 VhE3 3h 6apR Eu( 33 4h 68ap EK( 33 5h 6a; p  EL( 33 6h 6 a]p EY( 33 7h 6Da3  Eu( 33 8h 6a  EK( 33 9h 6Ȣa   EL( 33 :h 6a]  EY( 33 ;h 6Pa S G+*G 33 h 6aS G=*G 33 ?h 6daz G+*G 33 @h 6ľa x G+*G 33 Ah 6a   G+*G 33 Bh 6a G=*G 33 Ch 6xap Dln& 33 Dh 6a5 p  Dln& 33 Eh 6aEp  Dln& 33 Fh 6a  Dln& 33 Gh 6a   Dln& 33 Hh 6a  Dln& 33 Ih 6aE   Dln& 33 Jh 60a  C3&33 Kh 6a   C2&33 Lh 6a  C1&33 Mh 6,ai8 C3&33 Nh 6Da  8 C2&33 Oh 6a  8 C1&33 Ph 6$d Sn Ib,G 33 Qh 68d S  Ib,G 33 Rh 6dS Ib,G 33 Sh 6 dP Ib,G 33 Th 6xd ~  Ib,G 33 Uh 6d  Ib,G 33  h 0LdpP 7==> 23 8 HR >  2hR H> BB (h 3 3g HB C  )h 6dL   C2& 33 *h 6dX M>  Bln$33 +h 6l#dR P8  Bln$33 ,h 6L'dQ   Eb(E33 -h 6*d :  E=(E33 .h 6.dOX >  CL&33 /h 61dJX >  Cd&33 0h 6p4d[R 8  CY&33 1h 69dLR 8  Cd&33 8 :2   'h2 : BB h 3 3g :" #  h 6>d,   C3& 33 h 6Bd8 ?  Bln$33  h 64Fd2 R  Bln$33 !h 6Jdd w  Eb(E33 "h 6Nd Lw  E=(E33 #h 6QdA8   CK&33 $h 6Vd<8   Cd&33 %h 6Yd]2   CY&33 &h 6^dN2   Cd&33 h 0had p  ': elasticidad del output c.r al trabajo( 2(3,  h 0edp   }': elasticidad del output c.r al capital( 2(3 8  0 h 0]@  . h . h 6jd. A1$33 h 60od C3& 33 h 6rd : C2& 33 h 6\vd7  E=(E33 h 6zd  E+(E33 h 6~d1  Eb(E33 h 6d  Eb(E33 h 0,d 0 =>  23 h 0Њdp0 =<  23 h 0tOd `0 ,Informacion sobre los rendimientos de escala0- 233$#H h 0޽h ? 333WcL+᷷Ҫ* **?Hl*(  l l 0ܗd ``2. modelo de regresion polinomial: Funcion de Costes Marginales o funcion de Costes TotalesVa 333=3 *8    l  l 0d ?costs 2`B l 0D0 `B l 0D0 @0  l 0dd@  3y 2  l BCDEF3x@@  0P  l 0d  @MC" 23  l 0d  8i.e. 23\8   l  l 0d ]coste" 23`B l 0D0 `B l 0D0 @0  l 0ܵd@  Ay$ 23 l  BCDEF3x@@  0PA 8 |  Hl|  9l 6Xd# Eu(33 :l 6|dh EX(33 ;l 6d   EX(33 l 6xd Y G+*G33 ?l 6dd #  G+*G33 @l 6d   G=*G33 Al 6dHT C2& 33 Bl 6?djG C2& 33 Cl 6d j  C1& 33 Dl 6`dD jt  C0& 33 El 6d Ib,G33 Fl 6Xd]   Ib,G33 Gl 6d /  Ib,G33 l 0d 8(Cm) 23 l 0|d   >or  23 8  w "lM   l 6e 0  acoste& 233fB l 6D@ @ fB l 6D@   l 60e w 7y 23 l BpCDE(F3 ` `p @   @   l 0 e3  8TC 238  =  8l =  $l 6ld =  Eu(33 %l 6leQ   EX(33 &l 6e v  EX(33 'l 6 e g  EX(33 (l 6\e   EY(33 )l 6!eO   G+*G33 *l 6$e n  G+*G33 +l 6(e   G+*G33 ,l 6+e   G+*G33 -l 6\0e0  G=*G33 .l 604e T  C3& 33 /l 67e j ;  C3& 33 0l 6;e T  C2& 33 1l 6 @ej   C2& 33 2l 6DDe j  C1& 33 3l 6HeC j s  C0& 33 4l 6Ke   Ib,G33 5l 6Oe<   Ib,G33 6l 6Te?  Ib,G33 7l 6,Xe ;  Ib,G33 #l 0\e P  8(CT) 23H l 0޽h ? 333WcL+᷷Ҫ]@  @@^p?(  p p 0be ?` iResumen, 23 p 0,ge ?pp`  \ Del modelo 2  p 0Xke ?P @  e Pendiente& 2   p 0oe ?  g Elasticidad& 2  4B jp # l  kp 6pte  c)2 f%d3   lp 6p 6fs C2& II ?p 6f  EY(II Ap 6f IL Gb*GII4B ^p # g 4B _p # g ~"4B `p # o``cg ap 6ev  c)2 fd3   bp 6df<  c(2 fd3   cp 0fjP ]X, `d3   dp 6fTj rdX2 fd3   ep 6fx. cY2 fd3   fp 0  C(&II p 6qf  C2& II p 6ufc  EX(II p 6 zff   EY(II p 6}f T  `dX(II  p 6f H  `dY(II !p 6f3  Ib,GII "p 6f  G=*GII #p 6 f  BI  p B@f ?  9==> 2IvB hp N D?  H p 0޽h ? 333WcL+᷷ҪZ Z}Zt0 Z(   t8 %y  ty%  t 6f-   EX(33 t 6f EY(33 t 6f&  C2& 33 t 6Ԥf&E C1& 33 t 6f% Dln&33 t 68fDy| Ib,G33 t 6fy| Ib,G33 t 6fy| G+*G33 t 6|fy;| G=*G33 t 6ļf ?p`j L Log-lineal& 2 s8 } t} t 6xf= EX(II t 6fo$ C2& II t 6f} Ib,GII t 0df ?  lResumen(Cont.)( 23} 8   t BB wt 3 I p BB xt 3 I4H  BB yt 3 IC  zt 6fd  C2& II {t 6dfH   Dln&II |t 6fI Ib,GII }t 6$fF G=*GII ~t 6Hf   G=*GII t 6fL  `dX(II t 6 f   EY(II t 6fJ  `dY(II t 6f6   `dX(II t 6f u  EY(II t 6f   Ed(II&8   vt BB nt 3 I   ot 6gB EY(II pt 6g   `dX(II qt 6P g   `dY(II rt 6 gEu7 C2& II st 6g -(  Ib,GII tt 6g -~  G=*GII ut 6,g-   BI   t 0Lg ?  L Lineal-log& 2 8  # t # t 6P g$   EX(33 t 6$g EY(33 t 6(g: Dln&33 t 6,g# C2& 33 t 6L0g:# C1& 33 t 684g9 Ib,G33 t 68g~ Ib,G33 t 6 ] `dX(II ht 6   C1&33 t 6|g^   C2& 33 t 6g   C1& 33 t 6tgi @l  Ib,G33 t 6,gi l  Ib,G33 t 6g i l  G+*G33 t 6dgIi l  G=*G33g 8     4t  BB  t 3 I4 BB !t 3 I BB "t 3 I4 v BB #t 3 I\   $t 6g R  C2& II %t 6g% Q 2  C2& II &t 64g E   C)&II 't 6g% }  C1&II (t 6g[ E   C(&II )t 6g v  C1&II *t 6g_Z -  Ib,GII +t 6gZ -  G=*GII ,t 6g  G-*GII -t 6g Z  -  G=*GII .t 6Dg E   `dX(II /t 6g ,  EX(II 0t 6h   `dY(II 1t 6 h)  EX(II 2t 68 h E   Ed(II 3t 6g  c  `dY(II@B t C ID   t `BCDEFI@ t <h VX28III t <hH   `dX(II t <8hF   `dY(II t <8hr D-1&II t <#hug C2& II t <&h] X: Ib,GII t <*h]I : G=*GII t 6H/h]A A  B3  5t `B(CDEFI(@ Px  6t <2h p  C)&II 7t <6h2 9  D-1&II 8t <9h @p  C(&II 9t <>h   C2& II :t < 2I t BMh ?  G==>( 2I3 mt B$Rh ?@ : G==>( 2I3vB t N D? t 0Vh ?   a Pendiente" 2   t 0[h ?  c Elasticidad" 2  H t 0޽h ? 333WcL+᷷Ҫ NF  (   ! 8  j   v{ @  g   g   6@dhg g  C2&33  6hhv  vO  F5325& 33  6Tkh6  v O  C.& 33   6xph  7 O  C1& 33   60thp  O  E304& 33   6xh0  p O  C.& 33   6h|h 3 O  E100& 33   6hw LO  EM( 33  6`h2 O  EP( 33  6h 3O  EN( 33  6h O  EG( 33  6Ph 2  G+*G 33  6th  2  G=*G 33  6Hh X  E^( 33  0h ?p j  =(1.368) 23  08h ? p j  =(39.20) 23  C dALC:\COURSE\ECON2170\GUJARA\tab603c.bmp   Nh f?  k Modelo Lineal  d3  H  0޽h ? 333WcL+᷷Ҫ@ 0 x( 6 g x x C dALC:\COURSE\ECON2170\GUJARA\tab603a.bmpp 8 0 z  x0 pz@  : x` z x 0`h ? g sGNP = -1.6329.21 + 2584.78 lnM28 2333 x 0,h ?`@ : >(-23.44) 2 3 x 0Xh ?P @ : =(27.48) 23 x NLh ?0 0  e^4 f$3d3    x Nh f?  mModelo Lin-log   d3   H x 0޽h ? 333WcL+᷷Ҫ @ |X( =&+ |8 pP j | p | 0h ?pP  lnGNP = 6.8612 + 0.00057 M28 2333 | 0@h ?pj >(100.38) 2 3 | 0ph ? p j =(15.65) 23 | C dALC:\COURSE\ECON2170\GUJARA\tab603b.bmp@  | NHh ? `P  e^4 f$3d3    | Nph f? p Modelo Log-lin   d34    H | 0޽h ? 333WcL+᷷Ҫ[  P( Xz@   8 P r   Pr: @ U w  P r   6h7 w  C2&33  6 hei &  Dln&33  6h_ i O  F9882&33  6h! i _  C.&33   6h i  C0&33   6hi  F5529&33   6hi   C.&33   6hi   C0&33   6hUi   Dln&33  6mLi   EM(33  6mi   FNP(33  6m/i   EG(33  6 m L w v  G+*G33  6pm^L v  G=*G33  6\mr   G^*Z33  0m ?p   =(3.194) 23  0m ? p  =(42.29) 23  C dALC:\COURSE\ECON2170\GUJARA\tab603d.bmp`0p,   Npm f?`  mModelo Log-log   d3   H  0޽h ? 333WcL+᷷Ҫ  K C ` (  vB  N D3? vB  N D3?   0l(m ?   =Wage(y) 23  0,m ?0 ? unemp.(x) 2 3vB  N D3?   000m ? `  9RRM 23pB  H D3?    03m ?@ `  ;10.43 2 3  C dA LC:\COURSE\ECON2170\GUJARA\tab604a.bmp 8 pb  @ 0 a@ p  p   07m ?p  Owage=10.343-3.808(unemploy) 2I  0x;m ? P =(4.862) 2I  00?m ?  =(-2.66) 2I  NAm ?b "  e^4 f(Id3    NHFm f?p  k Modelo Lineal  d3  H  0޽h ? 333WcL+᷷Ҫ nfp7(  pB  H D3? pB  H D3?   . 6 NmU 6  C)&33 / 6 L ' %> L '<B   #   ! 6pxm L  C)&II " 6|m   C1&II # 6 m>  C(&II $ 6Ąm $ ' Ex(II  0m ?@  >(-.0690) 2 I  08m ?  =(3.063) 2I 3 Nh{m ?`   e^4 f(Id3   4 C dA LC:\COURSE\ECON2170\GUJARA\tab604b.bmp`  7 Nm f?@   Modelo Reciproco  d34     H  0޽h ? 333WcL+᷷Ҫ  5( #    Hpm ?[ `{ #lnwage = 1.9038 - 1.175ln(unemploy)&$ 2#33$  HPm ?h h O >(10.375) 2 3  Hm ?h0 O >(-2.618) 2 3  Tpm ?   e^4 f(d    C dA LC:\COURSE\ECON2170\GUJARA\tab604c.bmp `   NHm f?`  mModelo Log-log   d3   H  0޽h ? 333WcL+᷷Ҫ C; $( d@  ! C dALC:\COURSE\ECON2170\GUJARA\tab604d.bmp 8  P  #   Bdm ? P  hLnwage = 1.9038 + 1.175 ln 23x@       BB  3 3h O P   68m   C)&33  6mh L  C1&33  6m M  C(&33  6ms _  EX(33  B4m ?  =(10.37) 23  Bm ?`  =(2.618) 23 " Nm ?   Q^  f(  H  0޽h ? 333WcL+᷷Ҫ1 11CVp1( hz@  H <,m2 5 X + uiB3333 I <m2o 5 CY&33 J <tm/cC C2& 33 K <4mfC C1& 33 L <Dm Gb*G33 M <mU Gb*G33 N <mS G+*G33 O <pm G=*G33  HTm j[Ԕ? Escala y unidades de medida, 2$$36 8  G E 6sv C2& 33 F 6sw Gb*G33  Bs ?p $: pendiente de la recta de regresion% 2%3,  8 Is CIs A 6ses C2& 33 B 6sIGL Gb*G33  Bs ?p 5= 23>8  q' D    Bs ? p  B 23 HB 7 C 3  HB 8 C 3Z q  9 <s_$g' ndX6333 : <t s]e ndY6333 ; <$s) F o( < <(s $' CX&33 = <H,s  CY&33 > <40s W  GD*G33 ? <4s U  GD*G33y  B8s ? [  si Y* = 1000Y X* = 1000X 23333333333  BCs ? z  Xentonces 2 3  <HsI   B3 8  L  S S  # <Js/; L  Ei( 33 $ <Ns   Eu(33 % <Rs ]  CX&33 & <Vs E  CY&33 ' < Zsz   DP3  ( <T]s *  B3  ) <`s   B3  * <csG   k1000 $3  + <hs\  D1000$3 , <8msG   D1000$3 - <qs3 3 f  B3  . <`tsm ;  C2& 33 / <8xsK;   C1& 33 0 <x|s  f  B3  1 <s $  G+*G33 2 <s 8  G+*G33 3 <ds   G=*G33 4 <Ps N  Gb*G33 5 <s :  Gb*G33  <s  :   C*& 33  <s *   C*& 33  <؛s  L  C2& 33  < s   C1& 33  <s x  C*& 33  <s  Eu(33  <Ps   CX&33  <~s |  CY&33  <sn ) q  G+*G33  <ضsn eq  G+*G33  <ĺsn #q  G=*G33  <sn X  q  b*>G3O33  ! <sn q  ^b*>3N33 U Ns ?   f10002 dd3   V Ns ?   S==>  d3  H  0޽h ? 333WcL+᷷Ҫ LD(    Tsxaxa)?P   Cambios en la escala de X e Y  0B        Z(sxaxap?x 6Yi/k = (b1/k)+b2Xi/k + ui/k ( ((((C( ((((C( (( ((( (( ((((&     Z\sxaxap?  &Yi = b1 + b2Xi + ui( ((C( ((C( (( (( (&   d  <p?7d wF     B  Z`sxaxap?  b1 = b1/k l C( ((C( ((( (     Ztxaxap?# 5  E*     ZPtxaxap?9 Ey     N txaxap?@d )Cambia el R2?, cambian los coefficientes?$* &   F      ` 0 f_    ZLtxaxap?   4(Yi = b1 + b2X*i+ u*i(((G(((G((( ((( ((    Ztxaxap? C  >    Zltxaxap? +  >    Z!txaxap?g Y  E*     Z$txaxap?@ 2   E*   F tF   AN  Z(txaxap?t"F  Xi = Xi/k Z ( (( ((( (4      Zl1txaxap?{ E*   F      W   Zx5txaxap?x j=  E*   K  Z9txaxap?    ui = ui/kX ( (( ((((4    IF      @6 #  Z@txaxap?     Yi = Yi/kX ( (( ((((    Z`Htxaxap?S r  Wdonde     ZKtxaxap?  _  E*   H  0޽h ? 333WcL+᷷Ҫ VN(    ThRtxaxa)?0  Cambio de escala de x 0B       Z8Wtxaxap?H h4Yi = b1 + (kb2)(Xi/k) + ui( ((C( (((C( (( (((( (( (@       Zftxaxap?P4 &Yi = b1 + b2Xi + ui( ((C( ((C( (( (( (&   F      *   Zrtxaxap?   \(Yi = b1 + b2X* i+ ui(((G(((G((( ((((( (&     Ztxaxap?   E*      Ztxaxap? tI  >  ]F  j     (   ZLtxaxap? j b2 = kb2V C( (((C( (     ZXtxaxap? r  E*   F 3 T    N  Z,txaxap?3 T  Xi = Xi/k Z ( (( ((( (4      Ztxaxap? Q E*     Z|txaxap?p  Wdonde     Ztxaxap?P P B Ey   N  NHtxaxafp? (Cambia el R2?, Cambian los coeficientes?*)  Z        H  0޽h ? 333WcL+᷷Ҫ 0( Z   Ttxaxa)?P`  Cambio de escala de Y 0B     B  Ztxaxap? 8  @Yi/k = (b1/k) + (b2/k)Xi + ui/k !( ((((C( (((( ((C( (((( (( ((((@       Ztxaxap?D &Yi = b1 + b2Xi + ui( ((C( ((C( (( (( (&   d  <p?7d wF     B  Z$txaxap?  b1 = b1/k l C( ((C( ((( (     Z`txaxap?# 5  E*     Z4txaxap?9 Ey   5  TG)" z"C4K[6V o~gP4%A7*{3>f{\v'.M۝N'bw8V8whm6JQfo)% <^*n8}wՔXӗnd E?IBaXJk T?_cE'c\om y[[\ S.Tc #^o9κTߨ_g Ehz%!KtDfʫz2DW=6sDVir3GH818Ы2ڗ{HFF13biZ 59U{5*uEelv>UhJX4y災{͖L0/ef0/I OcI-K1m"Hr-E<→iZU 8_isRNVk y?Wò?v!t%cB>Jd:6PߥwF5u?ѫlwד$:9'fWqVaxV?oPƉU`EQ,,($RHKi\ RVU~X >0sw~ .*?%ޟ=ˇ{^L A&bcB5  8Q8–QPWlK h&tGKoq 2z INWnn܃upRqaq+@waX-H$/xt`R)֯{j3&ex\N+Dx#C35߼uU߮~ksY` r(GBi~zNO:yv# H>r_Y,/4"$*R9rgXػ6qU;=a-w7ԙ w8#B˔w{{(0\{F`.7]c/8%mB-3Xi䂾69,|fU#@Y+:Pd+Ϭ+yi)Jn_HYw;~dkSFBJ\aS_}]Oj^5kv ttm؂M[?`AI6~$ᤜ(Hqȴ[GkxVnAv⳥8?!Jq b$1((b0Bd"BҤP!  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