econometria guanabana

25
UNIVERSIDAD NACIONAL FEDERICO VILLAREAL FA CULTAD CIENCIAS ECONÓMICAS T ema : Elasticidades Curso : Econometría Profesor : Oscar Samanamud Loyola  Alumna : Lazo Gonzales Rosa A racelli  Aula : 42A Lima 2015

Upload: rosaaracellilazogonzales

Post on 05-Jul-2018

249 views

Category:

Documents


2 download

TRANSCRIPT

Page 1: ECONOMETRIA GUANABANA

8/16/2019 ECONOMETRIA GUANABANA

http://slidepdf.com/reader/full/econometria-guanabana 1/25

UNIVERSIDAD NACIONAL FEDERICOVILLAREAL

FACULTAD CIENCIAS ECONÓMICAS

Tema : Elasticidades

Curso : Econometría

Profesor : Oscar Samanamud Loyola

 Alumna : Lazo Gonzales Rosa Aracelli

 Aula : 42A

Lima 2015

Page 2: ECONOMETRIA GUANABANA

8/16/2019 ECONOMETRIA GUANABANA

http://slidepdf.com/reader/full/econometria-guanabana 2/25

INDICE

LA GUANABANA

  1. INTRODUCCION

2. CLIMA Y SUELOS

3. ZONAS DE CULTIVO Y EPOCAS DE SIEMBRA

4. PROPAGACION

5. SIEMBRA

6. COSECHA

7. METODOLOGIA

8. NIVEL DE PRODUCCION, PRECIOS E INGRESO 1!211 " 1!215

#. EVIE$S " PROCEDIMIENTO

I%&'()*%+ D*-)

E)-/*%+ 0* E*% +( 0* D(/*%+* +( G*%*%* +( 0* S(0*

E*% +( 0* D(/*%+* +( G*%*%* +( 0* )(0*

CALCULO DE ELASTICIDADES PARA LA GUANABANA

  A. ELASTICIDAD PUNTO

E0*)-+*+ *%-+*+ '(

E0*)-+*+ '*+* +( (%() '(0*%*+)

E0*)-+*+ %&'()

  B. ELASTICIDAD ARCO

E0*)-+*+ *' *%-+*+ '(

E0*)-+*+ *' '*+* +( (%() '(0*%*+)

E0*)-+*+ *' %&'()

Page 3: ECONOMETRIA GUANABANA

8/16/2019 ECONOMETRIA GUANABANA

http://slidepdf.com/reader/full/econometria-guanabana 3/25

E)-/*%+ 0* E*% L&*'9-/* +( 0* D(/*%+* +( '(0* ':*

'00*

E*% L&*'9-/* +( 0* D(/*%+* +( '(0* ':* '00*

CALCULO DE ELASTICIDADES LOGARITMICAS PARA LA CIRUELA

RO;A O CRIOLLA

  A. ELASTICIDAD LOGARITMICA PUNTO

E0*)-+*+ 0&*'9-/* *%-+*+ '(

E0*)-+*+ 0&*'9-/* '*+* +( (%() '(0*%*+)

E0*)-+*+ 0&*'9-/* %&'()

  B. ELASTICIDAD LOGARITMICA ARCO

E0*)-+*+ 0&*'9-/* *' *%-+*+ '(

E0*)-+*+ 0&*'9-/* *' '*+* +( (%() '(0*%*+)

E0*)-+*+ 0&*'9-/* *' %&'()

1. C*00 +( (0*)-+*+ /(%)*0 +( 0* '(0* ':* '00* )(&<% 0*)='/0*) *0*+*) *%-(''/(%-(

A. T*0* +( +*-) /(%)*0() +( 0* '(0* ':* '00*B. E0*)-+*+ /(%)*0 +( 0* '(0* ':* '00*

C. E0*)-+*+ 0&*'9-/* /(%)*0 +( 0* '(0* ':* '00*

Page 4: ECONOMETRIA GUANABANA

8/16/2019 ECONOMETRIA GUANABANA

http://slidepdf.com/reader/full/econometria-guanabana 4/25

GUANABANA

  1. INTRODUCCION

L* &*%*%* () '&%*'* +( 0*) '(&%() -'*0() +( A/>'* +(0 S'. E%

C)-* R*, ?*)-* ?*1( ) *@) )0 ?*9* '0() +)(')) )% (/*'&, 0*

/'-*%* ( ?* *+'+ (0 ='- (% (0 /('*+ *&'%+)-'*0, -*%-

%*%*0 / %-('%*%*0, ?* +()('-*+ (0 %-('>) *'* +()*''00*' (0 0-

1/('1*0/(%-(.

A-*0/(%-( (% (0 *9) ?* *'/*+*/(%-( )(-((%-*) ?(-'(*) 0-*+*),

+)-'+*) (% 0*%-*%() +( +) * % ?(1-4'(*).

2. CLIMA Y SUELOS

E) %* ()(( ))(-0( *0 ='9, () 0* *%%(* ) '(('/(%-) +(

0/* () (0 /) -'71*0  0+) ?</(+), *'*-('9)-) +( *0--+()

/(%'() +( 1. /)%/.

R(('( %* -(/('*-'* '/(+ +( 25 * 28C %* '(-*% /(+*

*%*0 +( 1. * 3. // (% +)-'+*, *%( (+( 0-*')( (% %*)

% %* ()-*% )(* /+('*+*.

E)-* ()(( )( +()*''00* +()+( (0 %(0 +(0 /*' ?*)-* 0) 1. /, *%( 0*

*0--+ -/* *'* (0 0- ()- (%-'( 4 * 6 /.

Page 5: ECONOMETRIA GUANABANA

8/16/2019 ECONOMETRIA GUANABANA

http://slidepdf.com/reader/full/econometria-guanabana 5/25

L) )(0) (% ( )( 0*%-( &*%*%* /('*0/(%-( +((% )(' '=%+),

*'(%)) % /2C (% +'(%*:(.

S% /) %(%(%-() 0) )(0) % H (%-'( 5,5 6,5.

3. ZONAS DE CULTIVO Y EPOCAS DE SIEMBRA

C*0(' %* ( -(%&* (0 0/* (0 )(0 *'*+ (+( )(0(%*')(

*'* (0 0- +( ()-( ='2-*0.

E% C)-* R*, 0*) '%*0() 0*%-*%() )( (%(%-'*% (% 0) *%-%() +( S*%

C*'0), U7*0*, G/, L/%, M*-%*, S''(), G*'*-, P*''-*, P9

A&2''(.

4. PROPAGACION

L* &*%*%* )( (+( '*&*' ' )(/00* ' *'0-) %:('-*+).

P*'* '*&*' ' )(/00*, 0* )(/00* +(( '(+(' +( 0) /(:'() ='-)

+( 0) '0() /4) '+-'() ) ='-) )(*% +( 0* /(:' 1*0+*+.

L* '*&*% ' %:('- %-(/0* 0* '+% +( 0) *'0-) *-'%()

0*) C(/*).

L*) (/*) )( +((% -/*' +( '0() % / (%* '+%, -*%- (%

*%-+*+ / (% 1*0+*+. C/ *-'% )( (+( -0*' *0(' - +( *%%*

+( 0* %* 0* /)/* &2*%4*%*.

L) /*'() '(%-*:() +( '(%+/(%- +(0 %:('-, )( ?*% -(%+ /(+*%-(

0*) ->%*) +( %:('- +( (%?*( 0*-('*0 (0 +( C(/*.

Semillero

U%* ( )(0(%*+* 0* )(/00*, )( 0** )( )/('&( (% %* )0% +(

(%/0 B(%0*-(, 1 &!0F, *0(%-*+* * 5C, +'*%-( %( /%-). L(& )(

+(:*% (% (0 *&* +'*%-( 24 ?'*).

E% ()-* (-** )( +((% (0/%*' 0*) )(/00*) ( =0-(%, *'* -(%(' /*'?/&(%(+*+ &' +( 0*) 704%-20*).

E0 )(/00(' (+( ?*(')( +'(-*/(%-( (% (0 )(0 (% ('*) (% *:*) +(

&('/%*%, )2(0 ?** )+ '(*/(%-( +()%=(-*+ % B*)*/+

+*/(-F % *0&<% =/&*%-( +(0 )2(0.

L) )') +(0 )(/00(' )( -'**% % 5 / +( '=%++*+ * 15 / (%-'( (00)

(% (0 =%+ )( *&'(&* =('-0*%-( ='/0* 131 ( 0(& )( '( % %*

((@* '% +( )(0 0*) )(/00*) )( 0*% +( ='/* ( (+*% *0*%*+*)

  )(&+* (%-'( )9, 0(& )( '(% % %* /(0* +( *'(%* +( '9 )(0 (%

*'-() &*0(). L* &('/%*% ''( (%-'( 0) (%-% -'(%-* +9*).

C*%+ 0*) 0%-0*) ?*% *0*%*+ +( 1 * 15 / +( *0-'* +((% )('

-'*)0*%-*+*), 7'(=('0(/(%-( (% 0)*).

Page 6: ECONOMETRIA GUANABANA

8/16/2019 ECONOMETRIA GUANABANA

http://slidepdf.com/reader/full/econometria-guanabana 6/25

Viero

L*) 0%-0*) )( -'*)0*%-*% (% 0)*) +( 0(-0(% +( 31 18 8 / +( =(00(,

00(%*) % *0&<% ))-'*- /()- ' )(0, %* =(%-( '* (% /*-('*

'&%* ( ()-> (% +()/()-*  C &'*%* +( *'' *'(%* +( '9.

E0 0&*' )(0(%*+ *'* (0 (' +(( %-*' % '(& ()-*' *+ */(+* )/'*.

A 0) ? +9*) +(0 -'*)0*%-( )( +(( =('-0*' % *% ='/0* 131

*0(' -'* ='/20* *0-* (% =)=' * '*% +( 5 &!0*%-*. A+(/), ()

%(%(%-( *0*' (0(/(%-) /(%'() 9* =0*'.

E) %(()*' '(*0*' *0*%() ('+*) +( %)(-+*) =%&+*) *%+

)(* %(()*', % (0 =% +( /*%-(%(' / )*%) 0) *'0-).

C*%+ 0*) 0*%-*) (% (0 (' -(%&*% %) 7 / +( *0-'*, (+(% )('

-'*)0*%-*+) *0 1*/7 +(=%-, ) 0* '('+% () ' )(/00* (% (0 *)

+( 0*) 0*%-*) *-'%(), ?*(' (0 %:('-.

I!"er#o

E%-'( 0) % ? /()() +( '(/(%- +(0 *'0- *-'%, (% (0 (',

(+( '(*0*')( (0 %:('-.

A 0*) 0*%-*) %:('-*+*) )( 0() +(( '%+*' '(& %)-*%-( (0/%*'0() 0)

'-() ( )( '+(% (% (0 *-'%, (0 *0 +(( )(' '-*+ *0*-%*/(%-( +(

*''* ?** **: ?*)-* (0 %(0 +( 0* <*. T'() *-' /()() +()>) +(

%:('-*+*), ()-*'% 0)-*) *'* )(' 00(*+*) *0 1*/7.

$. SIEMBRA

E0 -(''(% (% ( )( '(*0( %* 0*%-*% +( &*%*%* +(( -(%(' % )(0

)(0-, (% +'(%*+  C '=%+ ) () ()*+, () %+)(%)*0( 0* %)-'%

+( %='*()-'-'* +( +'(%*:(. A+(/) +(( ()-*' '-(&+ +(0 (%- *'*

(-*' 0* *9+* +( =0'() ='2-).

S( '(/(%+* 0*%-*' 0* &*%*%* * %* +)-*%* +( )(/'* +( 7 / 7 / 8

/ 8 /, (% 2% ))-(/* +( )(/'* *+'*%&0*' (% -'() 000). E% -(''(%)%0%*+) +((% )(&')( '*) +( %(0.

L) ?) +((% -(%(' % /9%/ +( 4 / +( 0*+ 4 / +( =%+.

E% 0* )(/'* () %(%(%-( '(00(%*'0) % -(''* '* (% /*-('* '&4%1*.

%. COSEC&A

L* &*%*%* -(%+( * =0'((' ='-=*' (% ='/* /) /(%) 1%-%2*.

E% 0* %* A-0%-* (0 0- -(%( +) ) +( '+% (0 '/(' )( +* (%

=('(' /*' (0 -' (% 0) /()() +( :%, :0 *&)- () (0 /)/7'-*%-(.

Page 7: ECONOMETRIA GUANABANA

8/16/2019 ECONOMETRIA GUANABANA

http://slidepdf.com/reader/full/econometria-guanabana 7/25

L* ='-=*% +( '0() '(%(%-() +( )(/00* )( %* (%-'( 0) -'()

% *@) (% 0) 4'0() %:('-*+), (%-'( 0) (%-( (%-*-' /()().

L* '+% +( 0) '0(), &(%('*0/(%-( () *:* +(+ * *'*-('9)-*) +(

0*) =0'() ( +=120-*% 0* 0%*% *0 *-*( +( 0*&*) (%=('/(+*+() (0

'(%+/(%- =0-<* (%-'( (%-*-' )()(%-*  *-' ='-) ' '0, %

()) ( *% +( ,25 & * 5 & ' ='2-.

L* '(0(% +(( ?*(')( (% (0 //(%- (% ( (0 ='- *0*%* ) /*+'(

-%*, () +(1' *%+ ('+( *0& +( ) '00 *0& +( ) 0' ('+( )'

  0*) ()%*) +( 0* )*'* )( )(*'*%  C )( %(% /) -'&(%-(). S (0 ='-

/*+'* (% (0 '0 () *-**+ ' :*') *+(/) )( +()7'(%+( =410/(%-(.

S( +(( (-*' )(?*' (0 ='- / ('+( '( 0* 0* % /*+'* (%

*+('( )*' */*'&. A0&%) 9%+() +( )(?* ( )( (+(% %)+('*' )%

0) )&2(%-()H

)*+*+ , * ((), *9+* +( 0) '()-) +( 0*) =0'() (% 0) ='2-)  */ +(

0' ('+( )' * % ('+( 0*' /*-(  *0 &0(*' (0 ='- )( ()?* %)%+ '(-2/*%-(

*0 *('*')( * 0* /*+'( )( %-* %* 0&('* )*+*+ (% (0 (-'(/ +)-*0 +(0

='2-.

P' <0-/, *'* &*'*%-*' %* /*+'( %='/( +(0 ='- +()>) +( 0*

)(?*, )( '(1/(%+* 0*'0 % 0* *'-( +(0 (+<%0 ?** **:.

L*) +'%() +()>) +( 0* )(?*, )( +((% * 0* +0+* * 0* *%-'*1%)).

'. METODOLOGIAL* /(-+0&9* *0*+* *0 )&(%-( -'**: () (0 *%0)) +()'- +(+ * (

+()'/) 0) ?(?) -*0 / )% )('*+), (0 />-+ (0*- * (

?(/) -'*-*+ +( ?*(' '(0*%() +( *)* (=(- (% ()-( *) (0

/'-*/(%- +( 0* (0*)-+*+ *%-( *0&%) */) (% 0* E%/9* / '

(:(/0 0) */) +( '(), *'*%() (% (0 %&'()) */) (% (0 '( +(0

(% '(0*%*+F. E0 '()(%-( -'**: )( *)* (% %* %()-&*% -('* +( /+

( 0*) *0*%() '-*) 0 ?(/) ?(? *0 /9%/ )0(.

Page 8: ECONOMETRIA GUANABANA

8/16/2019 ECONOMETRIA GUANABANA

http://slidepdf.com/reader/full/econometria-guanabana 8/25

(. NIVEL DE PRODUCCION) PRECIOS E INGRESO *1+2*11 , 1*+2*1$

-e/0

G0!0!0 De

L0 Sel0

G0!0!0 De

L0 Sel0

G0!0!0 De

L0 Co#0I!5reo

Prome6io

Di7o!ile

-0mili0r

Me!0l

8IPD-M9Dem0!60

DG:SEL

Preio

Prome6io

PG:SEL

Preio

Prome6io

PG:COS

(%(11 4.68 6.86 6.42 1386.3

=(11 47.88 7.3 7.33 1386.3

/*'11 3#.12 6.16 5.55 1386.3

*'11 72.36 3.72 3.77 1386.3

/*11 45.36 2.56 2.75 1386.3

 :%11 75.24 3.34 3.1 1386.3

 :011 54.48 4.22 3.37 1416.5

*&11 63.#6 6.6# 4.25 1386.3

)(11 65.58 6.#5 4.13 1386.3

-11 5.28 6.6 4.2 1386.3

%11 6.72 6.26 4.18 1386.3

+11 115.44 6.25 4.56 1416.5

(%(12 #4.#2 5.25 4.63 158.8

=(12 ## 5.42 4.71 158.8/*'12 74.16 4.83 4.3# 158.8

*'12 42 4.6 3.45 158.8

/*12 #1.56 3.72 2.65 158.8

 :%12 51.6 3.87 2.53 158.8

 :012 15.48 5.1 3.83 168

*&12 65.52 6.1 4.11 158.8

)(12 66.72 6.58 4.17 158.8

-12 88.5 6.48 4.23 158.8

%12 7#.68 5.87 4.33 158.8

Page 9: ECONOMETRIA GUANABANA

8/16/2019 ECONOMETRIA GUANABANA

http://slidepdf.com/reader/full/econometria-guanabana 9/25

+12 78.48 6 4.35 158.8

(%(13 #1.74 5.41 4.5 1616

=(13 55.86 4.#1 4.6# 1616

/*'13 57.18 4.66 4.71 1616

*'13 65.76 3.67 3.52 1616

/*13 71.4 2.68 2.65 1616

 :%13 65.16 2.#6 2.#4 1616

 :013 15.3 3.74 3.6 162.8

*&13 11#.52 4.6 4.41 1616

)(13 #1.8 5.4 4.47 1616

-13 #1.8 6.31 4.52 1616

%13 68.16 4.76 4.67 1616

+13 #3.12 4.55 4.81 17(%(14 126.72 4.47 4.#3 1656

=(14 #.6 5.76 5.43 1656

/*'14 68.4 4.62 4.46 1656

*'14 61.#2 4.1# 4.13 1656

/*14 7#.62 2.8 2.#1 1656

 :%14 15.48 2.53 2.46 1656

 :014 64.8 4.13 4.7 1656

*&14 62.4 4.# 4.71 1656

)(14 44.22 6.5 5.76 1656

-14 24.24 6.1 6.3 1656

%14 26.4 5.88 5.46 1656

+14 41.4 5.2 4.#6 168#

(%(15 2#.1 5.6# 5.32 1733.3

=(15 24.42 5.4 4.#6 1733.3

/*'15 58.14 2.42 1.86 1733.3*'15 56.76 1.## 1.63 1733.3

/*15 44.16 1.74 1.53 1733.3

 :%15 46.8 2.31 1.#1 1733.3

 :015 3#.66 3.7 2.44 1733.3

*&15 4.56 3.22 2.4# 1733.3

)(15 3.#6 3.23 2.51 1733.3

-15 3# 3.22 2.54 1733.3

;. EVIE<S , PROCEDIMIENTO

Page 10: ECONOMETRIA GUANABANA

8/16/2019 ECONOMETRIA GUANABANA

http://slidepdf.com/reader/full/econometria-guanabana 10/25

I%&'()*%+ D*-)

E)-/*%+ 0* E*% +( 0* D(/*%+* +( G*%*%* +( 0* S(0*

Page 11: ECONOMETRIA GUANABANA

8/16/2019 ECONOMETRIA GUANABANA

http://slidepdf.com/reader/full/econometria-guanabana 11/25

Page 12: ECONOMETRIA GUANABANA

8/16/2019 ECONOMETRIA GUANABANA

http://slidepdf.com/reader/full/econometria-guanabana 12/25

D&-*'

Page 13: ECONOMETRIA GUANABANA

8/16/2019 ECONOMETRIA GUANABANA

http://slidepdf.com/reader/full/econometria-guanabana 13/25

E*% +( 0* D(/*%+* +( G*%*%* +( 0* )(0*

DG:SEL = 12*.%'13 > *.4'3*''PG:SEL > *.32'413PG:COS > *.*3214%IPD-M

|

  CALCULO DE ELASTICIDADES PARA LA GUANABANA

DG:SEL ? C0!#i606 6em0!6060 6e 50!00!0 6e l0 el0.

PG:SEL ? Preio 6e l0 50!00!0 6e l0 el0.

COHEFICIENTES DE LA ECUACION DE LA

DEMANDA

Page 14: ECONOMETRIA GUANABANA

8/16/2019 ECONOMETRIA GUANABANA

http://slidepdf.com/reader/full/econometria-guanabana 14/25

PG:COS ? Preio 6e l0 50!00!0 6e l0 o#0.

IPD-M ? I!5reo 7rome6io 6i7o!ile @0mili0r me!0l.

Si!6ie 8i9 ? C0!#i606 i!ii0l.

Si!6ie 8@9 ? C0!#i606 @i!0l.

A. ELASTICIDAD PUNTO

  El0#ii606 0!#i606 7reio

L* (0*)-+*+ '( %) %+* (% > ''% *'9* 0* *%-+*+ +(/*%+*+*

*%-( %* *'*% ''%*0 (% (0 '(

∂DGSEL

∂PGSEL

× PGSEL

 DGSEL

El0#ii606 0!#i606 7reio 6e l0 50!0!0 6e l0 el0

Reemplazando en la formula∂DGSEL

∂PGSEL

× PGSEL

 DGSEL

=−0.473077×  6.86

40.68=−0.079776505

I%-(''(-*% P' *+* */(%- +(0 1J (% (0 '( +( 0* &*%*%* +(

0* )(0*, 0* *%-+*+ +(/*%+* +( &*%*%* +( 0* )(0* +)/%( (%

7.#776J. P' 0 -*%-, %) (%%-'*/) % % (% (0)-.

  El0#ii606 r060 o 6e ie!e rel0io!06o

L* (0*)-+*+ '*+*, /+( 0* )(%)0+*+ +( 0* +(/*%+* +( % (%, *%-( (0*/ (% (0 '( +( -' (%. L* (0*)-+*+ '*+* %) '%+*

%='/*% /'-*%-( )'( 0* '(0*% (%/* ()-(%-( (%-'( ())

(%(), () +(' ) )% ))---), /0(/(%-*') %+((%+(%-().

∂DGSEL

∂ PGcos

× PG

cos

 DGSEL

El0#ii606 r060 6e l0 50!0!0 6e l0 el0Reemplazando en la formula∂DGSEL

∂ PGcos

× PG

cos

 DGSEL

=−0.327413×  6.42

40.68=−0.051671373

I%-(''(-*% P' *+* */(%- +(0 1J (% (0 '( +( 0* &*%*%* +( 0*)-*, 0* *%-+*+ +(/*%+* +( 0* &*%*%* +( 0* )(0* +)/%( (%.516J. P' 0 -*%-, %) (%%-'*/) % % (% /0(/(%-*'.

 

El0#ii606 i!5reo

A%-( % */(%- +(0 %&'() +( 0) %)/+'(), )*0/(%-( >)-) */(%-*%

) *%-+*+ %)/+*, ((')*. L* (0*)-+*+ %&'() +( 0* +(/*%+* /+(

Page 15: ECONOMETRIA GUANABANA

8/16/2019 ECONOMETRIA GUANABANA

http://slidepdf.com/reader/full/econometria-guanabana 15/25

0* ''% +(0 */(%- (% (0 %)/ +( % '+- *%-( % */

''%*0 (% (0 %&'().

∂ DGSEL

∂IPDFM  × IPDFM 

 DGSEL

El0#ii606 i!5reo 6e l0 50!0!0 6e l0 el0Reemplazando en la formula

∂ DGSEL

∂IPDFM  × IPDFM 

 DGSEL

=−0.032146×1386.3

40.68=−1.095476888

I%-(''(-*% P' *+* */(%- +(0 1J (% (0 %&'() +)%0( +( 0*)=*/0*), 0* *%-+*+ +(/*%+* +( &*%*%* +( 0* )(0* +)/%( (%

1.#54J. P' 0 -*%-, %) (%%-'*/) % % (% %=(''.

B. ELASTICIDAD ARCO

 

El0#ii606 0ro 0!#i606 7reio

E) 0* (0*)-+*+ *00*+* * 0 0*'& +( % %-('*0 +( '() *%-+*+

+(/*%+*+*, +%+( )( %)+('*% % '( *%-+*+ %*0 ! =%*0.

 DGSEL

(¿¿ i+ DGSELf )

∂DGSEL

∂PGSEL

× ( PGSELi+ PG SELf )¿

El0#ii606 0ro 0!#i606 7reio 6e l0 50!0!0 6e l0 el0Reemplazando en la formula

 DGSEL

(¿¿ i+ DG SELf )=−0.473077×  (6.86+7.3 )(40.68+47.88)

∂ DGSEL

∂ PGSEL

×( PGSELi+ PGSELf  )

¿

¿−0.075641038

I%-(''(-*% P' *+* */(%- +(0 1J (% (0 '( +( 0* &*%*%* +( 0*

)(0*, 0* *%-+*+ +(/*%+* +( &*%*%* +( 0* )(0* +)/%( (% 7.5641J.P' 0 -*%-, %) (%%-'*/) % % (% (0)-

El0#ii606 0ro r060 o 6e ie!e rel0io!06o

E) 0* (0*)-+*+ *00*+* * 0 0*'& +( % %-('*0 +( '() +(0 (%

'(0*%*+ *%-+*+ +(/*%+*+* +(0 (% '&%*0, +%+( )( %)+('*%

'( +(0 (% '(0*%*+ *%-+*+ +(0 (% '&%*0 %*0 ! =%*0.

Page 16: ECONOMETRIA GUANABANA

8/16/2019 ECONOMETRIA GUANABANA

http://slidepdf.com/reader/full/econometria-guanabana 16/25

 DGSEL

(¿¿ i+ DGSELf )∂DGSEL

∂ PGcos

×( PG

cosi+ PGcosf )¿

El0#ii606 0ro r060 6e l0 50!0!0 6e l0 el0Reemplazando en la formula

 DGSEL

(¿¿ i+ DG SELf )=−0.327413×  (6.42+7.33 )(40.68+47.88)

∂DGSEL

∂ PGcos

×( PGcosi+ PGcosf  )

¿

¿−0.050834787

I%-(''(-*% P' *+* */(%- +(0 1J (% (0 '( +( 0* &*%*%* +( 0*)-*, 0* *%-+*+ +(/*%+* +( 0* &*%*%* +( 0* )(0* +)/%( (%

5.834J. P' 0 -*%-, %) (%%-'*/) % % (% /0(/(%-*'.

El0#ii606 0ro i!5reo

E) 0* (0*)-+*+ *00*+* * 0 0*'& +( % %-('*0 +( %&'()) *%-+*+

+(/*%+*+*, +%+( )( %)+('*% % %&'() *%-+*+ %*0 ! =%*0.

 DGSEL

(¿¿ i+ DGSELf )∂ DGSEL

∂IPDFM  ×

( IPDFM i+ IPDFM f )¿

El0#ii606 0ro i!5reo 6e l0 50!0!0 6e l0 el0Reemplazando en la formula

 DGSEL

(¿¿ i+ DGSELf )=−0.032146×(1386.3+1386.3 )

(40.68+47.88)∂DGSEL

∂ IPDFM  ×

( IPDFM i+ IPDFM f  )

¿¿−1.006413726

I%-(''(-*% P' *+* */(%- +(0 1J (% (0 %&'() +)%0( +( 0*)

=*/0*), 0* *%-+*+ +(/*%+* +( &*%*%* +( 0* )(0* +)/%( (%1.64J. P' 0 -*%-, %) (%%-'*/) % % (% %=(''.

 

E)-/*%+ 0* E*% L&*'9-/* +( 0* D(/*%+* +( G*%*%* +( 0*

S(0*

Page 17: ECONOMETRIA GUANABANA

8/16/2019 ECONOMETRIA GUANABANA

http://slidepdf.com/reader/full/econometria-guanabana 17/25

D&-*'

Page 18: ECONOMETRIA GUANABANA

8/16/2019 ECONOMETRIA GUANABANA

http://slidepdf.com/reader/full/econometria-guanabana 18/25

E*% L&*'9-/* +( 0* D(/*%+* +( G*%*%* +( 0* )(0*

LOG8DG:SEL9 = 12.$3(*;4 , *.12%(;'LOG8PG:SEL9 *.*%%$$4LOG8PG:COS9 ,

1.12;;4$LOG8IPD-M9

  CALCULO DE ELASTICIDADES LOGARITMICAS PARA LA GUANABANA

Page 19: ECONOMETRIA GUANABANA

8/16/2019 ECONOMETRIA GUANABANA

http://slidepdf.com/reader/full/econometria-guanabana 19/25

A0 &*0 ( 0*) (0*)-+*+() /(%%*+*) *%-(''/(%-(, 0* (0*)-+*+

0&*'9-/* /+( 0* )(%)0+*+ *%-( (0 */ +( %* +( 0*) *'*0()

% '()(- * 0* -'*, -(%(%+ / *'*-('9)-* '%*0 '%+*'

% '()0-*+ /) '().

A. ELASTICIDAD LOGARITMICA PUNTO

 

El0#ii606 lo50r#mi0 0!#i606 7reio

∂LogDG SEL

∂LogPGSEL

× PGSEL

 DGSEL

El0#ii606 lo50r#mi0 0!#i606 7reio 6e l0 50!0!0 6e l0 el0Reemplazando en la formula∂LogDGSEL

∂LogPGSEL

× PGSEL

 DGSEL

=−0.126897×  6.86

40.68

=−0.021399052

  El0#ii606 lo50r#mi0 r060 o 6e ie!e rel0io!06o

∂LogDG SEL

∂ LogPGcos

× PG

cos

 DGSEL

El0#ii606 lo50r#mi0 r060 6e l0 50!0!0 6e l0 el0Reemplazando en la formula

∂LogDGSEL

∂ LogPGcos ×

 PGcos

 DGSEL=0.066554

×

  6.42

40.68=0.01050336

  El0#ii606 lo50r#mi0 i!5reo

∂ LogDGSEL

∂LogIPDFM  × IPDFM 

 DGSEL

El0#ii606 lo50r#mi0 i!5reo 6e l0 50!0!0 6e l0 el0

Reemplazando en la formula

∂ LogDGSEL

∂LogIPDFM  × IPDFM 

 DGSEL

=−1.129945×1386.3

40.68=−38.50645903

B. ELASTICIDAD LOGARITMICA ARCO

  El0#ii606 lo50r#mi0 0ro 0!#i606 7reio

Page 20: ECONOMETRIA GUANABANA

8/16/2019 ECONOMETRIA GUANABANA

http://slidepdf.com/reader/full/econometria-guanabana 20/25

 DGSEL

(¿¿i+ DGSELf )∂LogDG SEL

∂LogPGSEL

×( PG SELi+ PGSELf )

¿

El0#ii606 lo50r#mi0 0ro 0!#i606 7reio 6e l0 50!0!0 6e l0 el0Reemplazando en la formulaReemplazando en la formula

 DGSEL

(¿¿ i+ DGSELf )=−0.126897×  (6.86+7.3)(40.68+47.88)

=−0.020289764

∂ LogDGSEL

∂LogPGSEL

×( PGSELi+ PGSELf )

¿

  El0#ii606 lo50r#mi0 0ro r060 o 6e ie!e rel0io!06o

 DGSEL

(¿¿ i+ DGSELf )∂LogDGSEL

∂ LogPGcos

×( PG

cosi+ PGcosf )¿

El0#ii606 lo50r#mi0 0ro r060 6e l0 50!0!0 6e l0 el0Reemplazando en la formula

 DGSEL

(¿¿ i+ DGSELf 

)=0.066554×  (6.42+7.33 )

( 40.68+47.88 )∂LogDGSEL

∂ LogPGcos

×( PGcosi+ PGcos f  )

¿

¿0.010333305  El0#ii606 lo50r#mi0 0ro i!5reo

 DGSEL

(¿¿ i+ DGSELf )∂ LogDGSEL

∂LogIPDFM 

 ×( IPDFM i+ IPDFM f )

¿

El0#ii606 lo50r#mi0 0ro i!5reo 6e l0 50!0!0 6e l0 el0Reemplazando en la formula

 DGSEL

(¿¿ i+ DG SELf )=−1.129945× (1386.3+1386.3 )

(40.68+47.88 )∂ LogDG SEL

∂LogIPDFM 

 ×( IPDFM i+ IPDFM f  )

¿  ¿−35.37585261

Page 21: ECONOMETRIA GUANABANA

8/16/2019 ECONOMETRIA GUANABANA

http://slidepdf.com/reader/full/econometria-guanabana 21/25

1*. C0llo 6e el0#ii606e me!0le 6e l0 50!0!0 6e l0 el0 e5! l0 @orml0

07li060 0!#eriorme!#e

A. TABLA DE DATOS MENSUALES DE LA GUANABANA DE LA SELVA

Fecha

Guanábana De La

Selva

Guanábana De La

Selva

Guanábana De La

Costa IngresoPromedioDisponibl

eFamiliarMensual(IPDFM)

DemandaDGS!L

PrecioPromedioPGS!L

PrecioPromedioPGC"S

ene-11 40.68 6.86 6.42 1386.3

feb-11 47.88 7.3 7.33 1386.3

mar-11 39.12 6.16 5.55 1386.3

abr-11 72.36 3.72 3.77 1386.3

may-11 45.36 2.56 2.75 1386.3

 jun-11 75.24 3.34 3.1 1386.3

 jul-11 54.48 4.22 3.37 1416.5

ago-11 63.96 6.69 4.25 1386.3

sep-11 65.58 6.95 4.13 1386.3

o!-11 50.28 6.6 4.2 1386.3

no"-11 60.72 6.26 4.18 1386.3

d#-11 115.44 6.25 4.56 1416.5

ene-12 94.92 5.25 4.63 1508.8

feb-12 99 5.42 4.71 1508.8

mar-12 74.16 4.83 4.39 1508.8

abr-12 42 4.6 3.45 1508.8

may-12 91.56 3.72 2.65 1508.8

 jun-12 51.6 3.87 2.53 1508.8

 jul-12 105.48 5.1 3.83 1608

ago-12 65.52 6.1 4.11 1508.8

sep-12 66.72 6.58 4.17 1508.8

o!-12 88.5 6.48 4.23 1508.8no"-12 79.68 5.87 4.33 1508.8

d#-12 78.48 6 4.35 1508.8

Page 22: ECONOMETRIA GUANABANA

8/16/2019 ECONOMETRIA GUANABANA

http://slidepdf.com/reader/full/econometria-guanabana 22/25

ene-13 91.74 5.41 4.5 1616

feb-13 55.86 4.91 4.69 1616

mar-13 57.18 4.66 4.71 1616

abr-13 65.76 3.67 3.52 1616

may-13 71.04 2.68 2.65 1616

 jun-13 65.16 2.96 2.94 1616

 jul-13 105.3 3.74 3.6 1620.8

ago-13 119.52 4.6 4.41 1616

sep-13 91.08 5.04 4.47 1616

o!-13 91.8 6.31 4.52 1616

no"-13 68.16 4.76 4.67 1616

d#-13 93.12 4.55 4.81 1700

ene-14 126.72 4.47 4.93 1656

feb-14 90.6 5.76 5.43 1656

mar-14 68.04 4.62 4.46 1656

abr-14 61.92 4.19 4.13 1656

may-14 79.62 2.8 2.91 1656

 jun-14 105.48 2.53 2.46 1656

 jul-14 64.08 4.13 4.07 1656

ago-14 62.04 4.9 4.71 1656

sep-14 44.22 6.05 5.76 1656

o!-14 24.24 6.01 6.03 1656

no"-14 26.4 5.88 5.46 1656

d#-14 41.04 5.2 4.96 1689

ene-15 29.1 5.69 5.32 1733.3

feb-15 24.42 5.4 4.96 1733.3

mar-15 58.14 2.42 1.86 1733.3

abr-15 56.76 1.99 1.63 1733.3may-15 44.16 1.74 1.53 1733.3

 jun-15 46.8 2.31 1.91 1733.3

 jul-15 39.66 3.07 2.44 1733.3

ago-15 40.56 3.22 2.49 1733.3

sep-15 30.96 3.23 2.51 1733.3

o!-15 39 3.22 2.54 1733.3

B. ELASTICIDAD MENSUAL DE LA GUANABANA DE LA SELVADG_SEL = 120.671 ! 0."7077#G_SEL ! 0.27"1#G_COS ! 0.021"6I#DFM

Page 23: ECONOMETRIA GUANABANA

8/16/2019 ECONOMETRIA GUANABANA

http://slidepdf.com/reader/full/econometria-guanabana 23/25

ELASTICIDAD #UNTO ELASTICIDAD ARCO

!0."7077 !0.27"1 !0.021"6 !0."7077 !0.27"1 !0

STICIDADDAD #RECIO

ELASTICIDADCRU$ADA

ELASTICIDADINGRESO

ELASTICIDAD ARCO#RECIO

ELASTICIDAD ARCOCRU$ADA

ELASTICIDADINGRES

0.079776505 -0.051671373 -1.095476888 -0.075641038 -0.050834787 -1.0064

0.072127446 -0.050124004 -0.930743521 -0.073190993 -0.048472177 -1.0244

0.074492697 -0.046450464 -1.139161549 -0.04192681 -0.027372526 -0.7994

0.024320708 -0.017058416 -0.615865116 -0.025237203 -0.018133985 -0.7571

0.026699231 -0.019849774 -0.982451495 -0.0231439 -0.015881974 -0.7390

0.021000494 -0.013489903 -0.592291332 -0.02757063 -0.016330266 -0.6945

0.036644364 -0.02025297 -0.835807801 -0.043577086 -0.021064565 -0.7607

0.049482257 -0.021755867 -0.696747964 -0.049812956 -0.021180492 -0.6880

0.050135486 -0.02061933 -0.679536441 -0.055327062 -0.023540051 -0.7692

0.062098413 -0.027349535 -0.886316623 -0.054808741 -0.024718207 -0.8029

0.048772431 -0.022539301 -0.733926215 -0.033595557 -0.016244264 -0.5114

-0.02561271 -0.012933154 -0.394445677 -0.025862262 -0.014303696 -0.4470

0.026165763 -0.015970525 -0.510976452 -0.026029969 -0.015769582 -0.500

0.025899771 -0.015576922 -0.489918028 -0.02800323 -0.017206389 -0.560

0.030811245 -0.019381649 -0.654016785 -0.038404925 -0.022098123 -0.8350

0.051813195 -0.026894639 -1.154806781 -0.029469906 -0.014953723 -0.7262

0.019220691 -0.009476239 -0.529727881 -0.025081408 -0.01184688 -0.6775

0.035480775 -0.016053389 -0.939959008 -0.027014901 -0.0132566 -0.6378

0.022873461 -0.011888432 -0.490052787 -0.03098516 -0.015202685 -0.5859

0.044044104 -0.02053827 -0.740260757 -0.045361588 -0.020500451 -0.7335

0.046655376 -0.020463313 -0.726946715 -0.039804056 -0.017718523 -0.6249

0.034638858 -0.015649232 -0.548043896 -0.03473957 -0.016664617 -0.5767

0.034851431 -0.017792398 -0.608708394 -0.035504704 -0.017968796 -0.6133

0.036167966 -0.018147892 -0.618015861 -0.031710778 -0.017022706 -0.5901

0.027897826 -0.016060154 -0.566251755 -0.033076928 -0.020385674 -0.7039

0.041582672 -0.027489563 -0.929966631 -0.040050839 -0.027226488 -0.9191

0.038554369 -0.026969486 -0.908498356 -0.032054103 -0.021918082 -0.8450

0.026401955 -0.017525757 -0.78996253 -0.021959349 -0.014767092 -0.7594

0.017846936 -0.012213464 -0.731249099 -0.019589973 -0.013437876 -0.7628

-0.0214903 -0.014772778 -0.797236587 -0.018594485 -0.01256178 -0.6104

0.016802545 -0.011193607 -0.49479807 -0.017549427 -0.011665235 -0.4628

0.018207448 -0.012080751 -0.434638019 -0.021654617 -0.013805448 -0.4933

0.026178174 -0.016068688 -0.570355029 -0.029360367 -0.016094941 -0.5681

0.032517602 -0.016120989 -0.565881656 -0.0327392 -0.018810487 -0.6495

0.033037654 -0.022432786 -0.762146948 -0.027308698 -0.019245258 -0.6609

0.023115339 -0.016912119 -0.586857818 -0.019410274 -0.014506016 -0.4907

0.016687612 -0.012737895 -0.420089773 -0.022269362 -0.015608313 -0.489

0.030076419 -0.019623097 -0.587569272 -0.030953979 -0.020411716 -0.6711

0.032122512 -0.021461816 -0.782389418 -0.032069932 -0.021641102 -0.8192

0.032012155 -0.021838109 -0.859718605 -0.023363065 -0.016285061 -0.7522

Page 24: ECONOMETRIA GUANABANA

8/16/2019 ECONOMETRIA GUANABANA

http://slidepdf.com/reader/full/econometria-guanabana 24/25

0.016636719 -0.011966489 -0.668598041 -0.013622369 -0.009498692 -0.5751

0.011347031 -0.007635912 -0.504681229 -0.018581581 -0.012609147 -0.6279

0.030490137 -0.020795426 -0.830739326 -0.033871593 -0.022793261 -0.8441

0.037364238 -0.02485679 -0.858055706 -0.048750171 -0.032260626 -1.0019

0.064724465 -0.042648098 -1.203839349 -0.083337841 -0.0563862 -1.5551

0.117293431 -0.081448036 -2.196112871 -0.111075939 -0.074288613 -2.102

-0.10536715 -0.067714961 -2.016430909 -0.077723801 -0.050587833 -1.594

-0.05994153 -0.039570382 -1.32296769 -0.073450364 -0.047986964 -1.5684

0.092501998 -0.059856947 -1.914730646 -0.098027353 -0.062888745 -2.082

0.104611622 -0.066501576 -2.281681482 -0.044809377 -0.027046471 -1.3497

-0.0196912 -0.010474513 -0.958353316 -0.018157263 -0.009944921 -0.9698

0.016586033 -0.009402452 -0.981653661 -0.017484911 -0.010251933 -1.1042

0.018640262 -0.011343793 -1.261745059 -0.021063785 -0.012382374 -1.225

0.023350596 -0.013362368 -1.190569697 -0.029437361 -0.016472896 -1.2888

0.036619929 -0.020143412 -1.404908265 -0.037093672 -0.020121492 -1.3891

0.037556902 -0.020100058 -1.373734265 -0.042664243 -0.022889611 -1.5581

0.049355255 -0.026544142 -1.799698379 -0.04361559 -0.023634014 -1.5928

0.039059178 -0.021323821 -1.428683636 -0.039059178 -0.021323821 -1.4286

C. ELASTICIDAD LOGARITMICA MENSUAL DE LA GUANABANA DE LA SELVALOG%DG_SEL& = 12.5'0(" ) 0.126'(7LOG%#G_SEL& * 0.06655"LOG%#G_COS& ) 1.12(("5LOG%I#DFM&

ELASTICIDAD LOGARITMICA #UNTO ELASTICIDAD LOGARITMICA ARCO

!0.126'(7 0.06655"   !1.12(("5 !0.126'(7 0.06655" !1.

CIDAD LOG.RECIO

ELASTICIDAD LOG.CRU$ADA

ELASTICIDAD LOG.INGRESO

ELASTICIDAD LOG.ARCO #RECIO

ELASTICIDAD LOG.ARCO CRU$ADA

ELASTICIDADARCO INGR

0.021399052 0.01050336 -38.50645903 -0.020289764 0.010333305 -35.375

0.019347287 0.010188822 -32.71601407 -0.01963257 0.009853052 -36.010

0.019981736 0.009442094 -40.04199268 -0.011246343 0.005564077 -28.10

0.006523726 0.003467504 -21.64790981 -0.006769565 0.003686137 -26.613

0.007161735 0.00403491 -34.5335704 -0.006208062 0.003228366 -25.977

-0.00563312 0.002742124 -20.81928168 -0.007395477 0.003319491 -24.414

0.009829393 0.004116868 -29.37898481 -0.011689009 0.004281843 -26.73

0.013272998 0.004422366 -24.49097488 -0.013361704 0.004305408 -24.18

0.013448218 0.004191339 -23.88598282 -0.014840794 0.004785041 -27.040

0.016657124 0.005559403 -31.15439048 -0.014701761 0.005024527 -28.224

0.013082596 0.004581616 -25.79780556 -0.009011589 0.003302009 -17.978

-0.00687029 0.002628952 -13.8649263 -0.006937229 0.002907545 -15.713

0.007018639 0.003246366 -17.96103051 -0.006982214 0.00320552 -17.583

-0.00694729 0.003166357 -17.22081834 -0.007511517 0.003497583 -19.691

0.008264732 0.003939753 -22.98895653 -0.010301642 0.004491937 -29.353

0.013898243 0.005466936 -40.59192895 -0.007904934 0.003039678 -25.529

-0.00515571 0.001926257 -18.6201509 -0.006727775 0.002408143 -23.817

0.009517275 0.00326321 -33.03994217 -0.00724641 0.0026947 -22.420

-0.00613552 0.002416589 -17.22555518 -0.008311382 0.003090285 -20.595

Page 25: ECONOMETRIA GUANABANA

8/16/2019 ECONOMETRIA GUANABANA

http://slidepdf.com/reader/full/econometria-guanabana 25/25

0.011814281 0.004174862 -26.02046728 -0.01216768 0.004167174 -25.784

0.012514722 0.004159625 -25.55247326 -0.010676941 0.003601685 -21.967

0.009291441 0.003181056 -19.26396628 -0.009318456 0.003387455 -20.274

0.009348461 0.003616702 -21.39634809 -0.009523694 0.003652559 -21.558

0.009701606 0.003688964 -21.72350938 -0.00850602 0.003460245 -20.742

0.007483244 0.003264585 -19.90397994 -0.008872473 0.004143843 -24.74

0.011154033 0.005587867 -32.68870605 -0.010743138 0.005534391 -32.30

0.010341728 0.00548215 -31.93408744 -0.008598113 0.004455339 -29.705

0.007081995 0.003562501 -27.76750487 -0.005890321 0.003001741 -26.695

0.004787218 0.002482659 -25.70370383 -0.005254766 0.002731548 -26.813

0.005764505 0.003002897 -28.02319091 -0.004987738 0.002553462 -21.456

0.004507073 0.00227535 -17.39235381 -0.004707415 0.002371219 -16.268

0.004883921 0.002455682 -15.27770348 -0.005808581 0.002806266 -17.340

0.007021968 0.003266319 -20.04821168 -0.007875552 0.003271656 -19.969

0.008722441 0.003276951 -19.89097081 -0.008781882 0.003823651 -22.830

0.008861938 0.004559964 -26.78977582 -0.007325217 0.003912028 -23.232

0.006200401 0.003437766 -20.62829145 -0.005206564 0.002948672 -17.249

0.004476244 0.002589262 -14.7663267 -0.005973478 0.003172738 -17.220

0.008067624 0.003988832 -20.65329934 -0.008303019 0.004149137 -23.590

0.008616463 0.004362593 -27.50130688 -0.008602359 0.004399037 -28.796

0.008586861 0.004439083 -30.2194593 -0.006266851 0.003310302 -26.44

0.004462592 0.002432456 -23.50149359 -0.00365403 0.001930821 -20.218

0.003043699 0.00155217 -17.73975085 -0.004984277 0.00256309 -22.071

0.008178599 0.004227135 -29.20082584 -0.009085632 0.004633239 -29.673

-0.01002249 0.005052697 -30.16100774 -0.013076625 0.006557692 -35.219

-0.01736153 0.008669178 -42.31544369 -0.022354336 0.011461754 -54.665

0.031462499 0.016556131 -77.19426238 -0.029794734 0.015100819 -73.9010.028263423 0.013764577 -70.87836818 -0.02084844 0.010283106 -56.044

0.016078567 0.008043563 -46.50285344 -0.019702143 0.009754421 -55.132

0.024812506 0.01216726 -67.30356249 -0.026294614 0.012783541 -73.188

0.028060762 0.01351793 -80.20203393 -0.012019556 0.005497799 -47.445

0.005281918 0.002129179 -33.68650961 -0.004870459 0.002021527 -34.091

0.004448996 0.001911258 -34.50552622 -0.004690109 0.002083934 -38.813

0.005000018 0.002305879 -44.350853 -0.005650097 0.002516994 -43.063

0.006263506 0.0027162 -41.84901001 -0.007896205 0.003348484 -45.304

0.009822839 0.004094598 -49.38309805 -0.009949914 0.004090142 -48.829

-0.01007417 0.004085786 -48.28731924 -0.011444151 0.004652824 -54.760.013238931 0.005395689 -63.26013141 -0.011699337 0.004804141 -55.990

0.010477137 0.004334543 -50.21881201 -0.010477137 0.004334543 -50.218

D((/) '('+*' ( *'* (0 *%0)) (0 *0' +(( +( 0* (0*)-+*+ +((

)(' )- *0' *)0-F (% (0 *) +( 0* el0#ii606 7reio 6e l0

6em0!60  ) EK1 (%-%() () %(0)-, ) E1 () (0)- ) E1 ()

%-*' (% (0 *) +( 0* el0#ii606 r060  ) EK )% (%()

/0(/(%-*'), ) E )% ))---) ) E % -(%(% '(0*% *0&%*

' <0-/ (% (0 *) +( 0* el0#ii606 i!5reo 6e l0 6em0!60 ) E ()% (% )('' %'/*0, ) EK () % (% %=('' ) E () % (%

%+((%+(%-(