INDICI INDIVIDUALI Indicii individuali VH� FDOFXOHD] � FD� LQGLFL� VLPSOL� IRORVLQG� GDWHOH� vQUHJLVWUDWH� SHQWUX� ILHFDUH�
YDULDELO �OD�QLYHOXO�XQLW LL�GH�REVHUYDUH�IRORVLW � • Pentru fenomenul complex y:
00
11
0
1
0/1 fx
fx
y
yi y == ,
unde:
y - fenomenul complex, de tipul fxy ⋅= x - factorul de tip calitativ f - factorul de tip cantitativ
• Pentru factorul calitativ x:
0
1
0/1 x
xi x =
Indici statistici
• Pentru factorul cantitativ f:
0
1
0/1 f
fi f =
&HL�WUHL�LQGLFL�YHULILF �vQWRWGHDXQD�UHOD LD�GH�VLVWHP�
fxy iii 0/10/10/1 ⋅= 5HOD LL�XWLOH�
( ) 1000/1%0/1 +=yy ri
( ) 1000/1%0/1 +=xx ri
( ) 1000/1%0/1 +=ff ri ,
unde:
yr 0/1 -�ULWPXO�GH�GLQDPLF �SHQWUX�IHQRPHQXO�FRPSOH[�y
xr 0/1 - ritmuO�GH�GLQDPLF �SHQWUX�IDFWRUXO�FDOLWDWLY�x
fr 0/1 -�ULWPXO�GH�GLQDPLF �SHQWUX�IDFWRUXO�FDOLWDWLY�f
INDICI DE GRUP Indicii de grup VH�FDOFXOHD] �OD�QLYHOXO�JUXSHL�VDX�SH�vQWUHJXO�DQVDPEOX� Sisteme de ponderare folosite la construirea indicilor de grup factoriali a) Sistemul de ponderare propus de E. Laspeyres, la care ponderile folosite sunt cele din
SHULRDGD�GH�ED] � • pentru factorul cantitativ:
∑∑=
00
10)(0/1 fx
fxI fy
• pentru factorul calitativ:
∑∑=
00
01)(0/1 fx
fxI xy
b) Sistemul de ponderare propus de H. Paasche, la care ponderile utilizate sunt cele din
SHULRDGD�FXUHQW � • pentru factorul cantitativ:
∑∑=
01
11)(0/1 fx
fxI fy
• pentru factorul calitativ:
∑∑=
10
11)(0/1 fx
fxI xy
c) Sistemul propus de Edgeworth�VH�ED]HD] �SH�FXPXODUHD�FDQWLW LORU�GLQ�SHULRDGD�GH�ED] �FX�
FHOH�GLQ�SHULRDGD�FXUHQW � úL� IRORVLUHD�DFHVWRUD�FD�SRQGHUH� OD�P VXUDUHD�YDULD LHL� UHODWLYH�D�SUH XULORU��3UH XO�ILLQG�R�YDULDELO �FDOLWDWLY ��UHOD LD�JHQHUDO �GLQ�FDUH�UH]XOW �LQGLFHOH�HVWH�
∑∑
++
=)(
)(
010
011)(0/1 ffx
ffxI x
d) Sistemul de ponderare propus de I. Fisher presupune calcularea indicelui de grup al
SUH XULORU� FD� R� PHGLH� JHRPHWULF � D� FHORU� GRL� LQGLFL� DJUHJD L�� GH� WLS� /DVSH\UHV� úL� GH� WLS�Paasche.
Generalizând,
• pentru factorul calitativ:
∑∑
∑∑
⋅=10
11
00
01)(
01 fx
fx
fx
fxI xy
• pentru factorul cantitativ:
∑∑
∑∑
⋅=01
11
00
10)(
01 fx
fx
fx
fxI fy
0RGDOLW L�GH�FDOFXO�DO�LQGLFLORU�GH�JUXS
∑∑
=00
11),(0/1
fx
fxI
fxy pentru fenomenul complex
∑∑
=00
10)(0/1
fx
fxI fy pentru factorul cantitativ
10
11)(0/1 ∑
∑=
fx
fxI
xy pentru factorul calitativ
Indicii de gruS� IDFWRULDOL� FDOFXOD L� FX� VLVWHPH� GLIHULWH� GH� SRQGHUDUH�� YHULILF � UHOD LD� GH� VLVWHP��
úL�DQXPH�
( ) ( ))(
0/1
)(
0/1
),(0/1
xy
P
fy
L
fxy III ⋅=
0RGLILFDUHD� DEVROXW � VH� FDOFXOHD] �� vQ� JHQHUDO�� FD� GLIHUHQ � vQWUH� QXP U WRUXO� úL� QXPLWRUXO�
indicelui:
∑∑ −=∆ 0011),( fxfxfxy pentru fenomenul complex
∑∑ −=∆ 0010)( fxfxfy pentru factorul cantitativ
∑∑ −=∆ 1011)( fxfxxy pentru factorul calitativ ùL�vQ�FD]XO�PRGLILF ULORU�DEVROXWH�VH�YHULILF �UHOD LD�GH�VLVWHP�
)()(),( xyfyfxy ∆+∆=∆ 3H�ED]D�DFHVWHL�UHOD LL��VH�FDOFXOHD] �FRQWULEX LD�UHODWLY �D�ILHF UXL�IDFWRU�OD�PRGLILFDUHD�DEVROXW ��
pe total:
100),(
)()( ⋅
∆
∆=fxy
fyfyK , respectiv 100
),(
)()( ⋅
∆
∆=fxy
xyxyK
Exemplificare pentru fond de salarii (FS)� FD� IHQRPHQ� FRPSOH[� FX� GRL� IDFWRUL� GH� LQIOXHQ ��
salariul mediu ( S ��úL�QXP UXO�GH�VDODULD L��7��
∑∑
=00
11),(0/1
TS
TSI
TSFS
∑∑
=00
10)(0/1
TS
TSI
TFS
10
11)(0/1 ∑
∑=
TS
TSI
SFS
)(
0/1)(
0/1),(
0/1SFSTFSTSFS III ⋅=
∑∑ −=∆ 0011),( TSTSTSFS
∑∑ −=∆ 0010)( TSTSTFS
∑∑ −=∆ 1011)( TSTSSFS
)()(),( SFSTFSTSFS ∆+∆=∆
100),(
)()( ⋅
∆
∆=TSFS
TFSTFSK
100),(
)()( ⋅
∆
∆=TSFS
SFSSFSK
,QGLFL�GH�JUXS�FDOFXOD L�FD�PHGLH�GH�LQGLFL�LQGLYLGXDOL� • pentru fenomenul complex:
∑∑ ⋅
=00
000/1),(0/1
fx
fxiI
y
fxy sau
∑
∑=
11
0/1
11),(
0/1 1fx
i
fxI
y
fxy
• pentru factorul cantitativ:
∑∑ ⋅
=00
000/1)(0/1
fx
fxiI
f
fy
• pentru factorul calitativ:
1
11
0/1
11)(0/1
∑
∑=
fxi
fxI
x
xy
([HPSOLILFDUH�SHQWUX�LQGLFLL�YDORULL��YROXPXOXL�IL]LF�úL�DO�SUH XULORU:
∑∑ ⋅
=00
000/1),(0/1
qp
qpiI
vqpv
sau
∑∑
=
11
0/1
11),(0/1 1
qpi
qpI
v
qpv
∑∑ ⋅
=00
000/1)(0/1
qp
qpiI
q
qv
1
11
0/1
11)(0/1
∑∑
⋅=
qpi
qpI
p
pv
,QGLFLL�GH�JUXS�FDOFXOD L�FD�UDSRUW�D�GRX �PHGLL • SHQWUX�IHQRPHQXO�FRPSOH[��LQGLFH�FX�VWUXFWXU �YDULDELO ��
( ) ( )
100:
100:
*%00
*%11
0
00
1
11
0
1),( * ∑∑∑
∑∑
∑===
fxfx
f
fx
f
fx
x
xI fxxSV
∑∑
==*
00
*11
0
1),( *
fx
fx
x
xI fxxSV , unde ∑
=i
ii
f
ff *
• SHQWUX�IDFWRUXO�FDQWLWDWLY��LQGLFHOH�YDULD LHL�VWUXFWXULL��
∑∑
∑∑
==0
00
1
10
0
*)( :
*
f
fx
f
fx
x
xI fxVS sau ∑
∑==
*00
*10
0
*)( *
fx
fx
x
xI fxSV
• SHQWUX�IDFWRUXO�FDOLWDWLY��LQGLFH�FX�VWUXFWXU �IL[ ���
∑∑
∑∑
==1
10
1
11
*
1)( :f
fx
f
fx
x
xI xxSF sau ∑
∑==
*10
*11
*
1)(
fx
fx
x
xI xxSF
,QGLFHOH�FX�VWUXFWXU �YDULDELO ��FX�VWUXFWXU �IL[ �úL�DO�YDULD LHL�VWUXFWXULL� IRUPHD] �vPSUHXQ �XQ�
sistem de indici:
)()(),( ** fxVS
xxSF
fxxSV III ⋅=
MoGLILFDUHD� DEVROXW � D� PHGLHL� VXE� LQIOXHQ D� XQXLD� VDX� DOWXLD� GLQ� IDFWRUL� VH� FDOFXOHD] � FD�
GLIHUHQ �GLQWUH�QXP U WRUXO�úL�QXPLWRUXO�LQGLFHOXL�IDFWRULDO�FRUHVSXQ] WRU��5HOD LLOH�GH�FDOFXO�YRU�IL�
*1*10*
111
10
1
11)( xxfxfxf
fx
f
fxxx −=−=−=∆ ∑∑∑
∑∑
∑
0*
00*
10
0
00
1
10)( **
xxfxfxf
fx
f
fxfx −=−=−=∆ ∑∑∑
∑∑
∑
ùL� vQ� DFHVW� FD]�� PRGLILFDUHD� PHGLHL� HVWH� HJDO � FX� VXPD� PRGLILF ULORU� GDWRUDWH� IDFWRULORU� GH�
LQIOXHQ ��UHVSHFWLY�
)()(),( ** fxxxfxx ∆+∆=∆ ([HPSOLILFDUH�SHQWUX�LQGLFLL�SURGXFWLYLW LL�PXQFLL
∑∑
∑∑
∑∑
∑∑
===0
00
1
10
0
00
1
11
0
1),( ::*
T
qp
T
qp
T
Tw
T
Tw
w
wI TwwSV , unde ∑
=i
ii
T
TT *
∑∑
∑∑
==0
00
1
10
0
*)(
:*
T
Tw
T
Tw
w
wI
Tw
VS
∑∑
∑∑
==1
10
1
11
*
1)( :T
Tw
T
Tw
w
wI wwSF
)()(),( ** TwVS
wwSF
TwwSV III ⋅=
01
0
00
1
11*),( wwT
Tw
T
TwTww −=−=∆
∑∑
∑∑
*1
1
10
1
11)( wwT
Tw
T
Twww −=−=∆
∑∑
∑∑
0*
0
00
1
10*)( wwT
Tw
T
TwTw −=−=∆
∑∑
∑∑
)()(),( ** wwTwTww ∆+∆=∆
'(6&20381(5($�3(�)$&725,�$�9$5,$ ,(,�818,�)(120(1�&203/(;
Metoda indicilor
ÌQ�WHRULD�úL�SUDFWLFD�VWDWLVWLF �GHVFRPSXQHUHD�LQGLFHOXL�JHQHUDO�vQ�SURGXVXO�LQGLFLORU�IDFWRULDOL�VH�QXPHúWH� GHVFRPSXQHUH� JHRPHWULF �� LDU� VHSDUDUHD� PRGLILF ULL� DEVROXWH� WRWDOH� vQ� VXPD� PRGLILF ULORU�DEVROXWH��GDWRUDWH�IDFWRULORU��HVWH�GHQXPLW �GHVFRPSXQHUH�DQDOLWLF .
MetRGD�VXEVWLWX LHL�vQ�ODQ
3UHVXSXQH�DSOLFDUHD�XUP WRDUHORU�UHJXOL� • LQGLFHOH� LQIOXHQ HL� SULPXOXL� IDFWRU�� GH� UHJXO � FHO� FDQWLWDWLY�� VH� FRQVWUXLHúWH� IRORVLQG� GUHSW�
SRQGHUH�FHDODOW �VDX�FHOHODOWH�YDULDELOH�OD�QLYHOXO�SHULRDGHL�GH�ED] � • XQ�IDFWRU�RGDW �VXEVWLWXLW�U PkQH�GUHSW�SRQGHUH�OD�QLYHOXO�SHULRDGHL�FXUHQWH�SH�WRW�SDUFXUVXO�
GHVFRPSXQHULL�SHQWUX�FHLODO L�LQGLFL�IDFWRULDOL� ,QGLFLL�IDFWRULDOL�úL�PRGLILF ULOH�DEVROXWH�VH�FDOFXOHD] �SH�ED]D�UHOD LLORU� Varianta I (se substituie mai întâi factorul cantitativ)
;
00010)(
00
10)(
01
∑∑∑∑∑
∆=−=∆
=
ffy
fy
xfxfx
fx
fxI
∑∑∑∑∑
∆=−=∆
=
xxy
xy
ffxfx
fx
fxI
11011)(
10
11)(
01;
Varianta II (se substituie mai întâi factorul calitativ)
∑∑∑∑∑
∆=−=∆
=
xxy
xy
ffxfx
fx
fxI
00001)(
00
01)(
01;
∑∑∑∑∑
∆=−=∆
=
ffy
fy
xfxfx
fx
fxI
10111)(
01
11)(
01;
0HWRGD�LQIOXHQ HORU�L]RODWH�D�IDFWRULORU��PHWRGD�UHVWXOXL�QHGHVFRPSXV� Pentru cazul a doi facWRUL�� LQGLFLL� IDFWRULDOL� VH�RE LQ�DSOLFkQG�VLVWHPXO�GH�SRQGHUDUH�SURSXV�GH�
/DVSH\UHV��úL�DQXPH�
( ) ∑∑
=00
10)(
fx
fxI fyL
, respectiv ( ) ∑
∑=
00
01)(
fx
fxI xyL
LDU�PRGLILF ULOH�DEVROXWH�VH�FDOFXOHD] �SH�ED]D�UHOD LLORU�
∑∑∑ ∆=−=∆ ffy xfxfx 00010)(
∑∑∑ ∆=−=∆ xxy ffxfx 00001)( )RORVLQG� DFHODúL� VLVWHP�GH�SRQGHUDUH�SHQWUX� DPELL� IDFWRUL� QX� VH�PDL�YHULILF � UHOD LD�GH� VLVWHP�
GHRDUHFH�U PkQH�XQ�³UHVW�QHGHVFRPSXV´�FDUH�DUDW �LQIOXHQ D�VLPXOWDQ �D�DPELORU�IDFWRUL�
∑∑
∑∑
=∩
00
01
10
11)( :fx
fx
fx
fxI fxy
( ) ( ) ∑∑∑∑∑ ∆∆=−−−=∆ ∩ fxfxy fxfxfxfx 00011011)(
ModificarHD�DEVROXW �SH�WRWDO�
∑∑∑ ∆∆+∆+∆=∆ fxxffxy fx 00),( 5HSDUWL]DUHD�UHVWXOXL�QHGHVFRPSXV�SH�IDFWRUL�GH�LQIOXHQ �VH�SRDWH�IDFH�vQ�XUP WRDUHOH�YDULDQWH� a) VH�DWULEXLH�LQWHJUDO�XQXLD�GLQ�IDFWRUL��VLWXD LH�FDUH�FRQGXFH�OD�SURFHGHXO�VXEVWLWX LHL�vQ�ODQ �� b) se repartizHD] �vQ�PRG�HJDO�SH�IDFWRUL� c) VH� UHSDUWL]HD] �SURSRU LRQDO�FX� LQIOXHQ HOH� L]RODWH�DOH� IDFWRULORU� (kx, kf)�� �FDUH� VH�GHWHUPLQ �
astfel:
∑∑∑
∆+∆∆
=xf
xx
fx
fk
00
0, respectiv
∑∑∑
∆+∆∆
=xf
ff
fx
xk
00
0
Sporul total al variabilei y care revine factorului f:
fxfffy kx ∆∆+∆=∆ ∑ ∑0)( Sporul total al variabilei y care revine factorului x:
fxxxxy kf ∆∆+∆=∆ ∑ ∑0)( &RQWULEX LD�UHODWLY �D�IDFWRULORU�OD�IRUPDUHD�VSRUXOXL�WRWDO�
100 respectiv , 100),(
)(
),(
)(
⋅∆∆⋅
∆∆
fxy
xy
fxy
fy
PROBLEME REZOLVATE
1. Într-R�VRFLHWDWH�FRPHUFLDO �V-au înregistUDW�XUP WRDUHOH�GDWH�FX�SULYLUH�OD�WUHL�P UIXUL��$��%�úL�&���
vQ�GRX �OXQL�FRQVHFXWLYH��YH]L�WDEHOXO�������
6LWXD LD�FDQWLW LORU�úL�SUH XULORU�GH�YkQ]DUH�SHQWUX�WUHL�SURGXVH�SULQFLSDOH
Tabelul 7.1.
&DQWLW L�YkQGXWH 3UH XO�XQLWDU� (mii lei/U.M.) 0 UIXULOH
U/M
perioada GH�ED]
perioada FXUHQW
perioada GH�ED]
perioada FXUHQW
A B 1 2 3 4 I II III
buc. buc. Kg
500 800 300
600 1000
200
20 12 30
30 20 60
Total - - - - - Se cere: 1. V �VH�FDOFXOH]H�LQGLFLL�LQGLYLGXDOL�DL�YDORULL��YROXPXOXL�IL]LF�úL�DL�SUH XULORU�SHQWUX�FHOH�WUHL�
P UIXUL� 2. V � VH� FDOFXOH]H� LQGLFLL� GH� JUXS� DL� YDORULL�� YROXPXOXL� IL]LF� úL� DO� SUH XULORU� úL� V � VH� YHULILFH�
UHOD LD�GLQWUH�HL� 3. V � VH� FDOFXOH]H�� SH� WRWDO�� PRGLILF ULOH� DEVROXWH� SHQWUX� YDORDUH�� SUH XUL� úL� YROXP� IL]LF��
specificându-VH�FDUH�HVWH�SRQGHUHD�IDFWRULORU�GHWHUPLQDQ L� 4. V �VH�YHULILFH�HJDOLWDWHD�GLQWUH�LQGLFLL�DJUHJD L�úL�LQGLFLL�GH�JUXS�FDOFXOD L�FD�PHGLH�DULWPHWLF �
VDX�DUPRQLF �D�LQGLFLORU�LQGLYLGXDOL� 5. V �VH�UHSUH]LQWH�JUDILF�VWUXFWXUD�YDORULL�vQ�IXQF LH�GH�YDORDUHD�FHORU�WUHL�P UIXUL�vQ�FHOH�GRX �
perioade.
Rezolvare 1. &DOFXOXO�LQGLFLORU�LQGLYLGXDOL�DL�YDORULL��YROXPXOXL�IL]LF�úL�DL�SUH XULORU
00
11
0
1
0/1 qp
qp
v
vi v == ;
0
1
0/1 q
qi q = ;
0
10/1 p
pi p =
3HQWUX� LQGLFHOH� YDORULL� HVWH� QHFHVDU� V � VH� FDOFXOH]H� YDORULOH� GLQ� FHOH� GRX � SHULRDGH�
(vezi tabelul 7.2.).
&DOFXOXO�LQGLFLORU�LQGLYLGXDOL�úL�GH�JUXS�DL�YDORULL��YROXPXOXL�IL]LF�úL�DL�SUH XULORU
Tabelul 7.2.
&DQWLW LOH�YkQGXWH�
(U.M.) 3UH XO�XQLWDU (mii lei/ U.M.)
9DORDUHD�P UIXULORU (mii. lei)
0 UIXUL U.M. SHU��GH�ED]
(qo) per. crt.
(q1)
per.de ED] (po)
per. crt. (p1)
per. de ED] (q0p0)
perioada FXUHQW (q1p1)
în per. crt. în SUH XULOH�SHU�
GH�ED] ���
(q1p0) A B 1 2 3 4 5 6 7
I buc. 500 600 20 30 10000 18000 12000
II buc. 800 1000 12 20 9600 20000 12000
III Kg 300 200 30 60 9000 12000 6000
Total - - - - - 28600 50000 30000
=⋅
=⋅
=⋅
==
)IIImarfapentru(%67,66100300
200
)IImarfapentru(%125100800
1000
)Imarfapentru(%120100500
600
0
10/1 q
qi q
=⋅
=⋅
=⋅
==
)IIImarfapentru(%20010030
60
)IImarfapentru(%67,16610012
20
)Imarfapentru(%15010020
30
0
10/1 p
pi p
=⋅
=⋅
=⋅
==
)IIImarfapentru(%33,1331009000
12000
)IImarfapentru(%3,2081009600
20000
)Imarfapentru(%18010010000
18000
00
110/1 qp
qpi v
2. Indicii de grup VH�SRW�FDOFXOD�vQ�DFHVW�FD]�VXE�IRUP �GH�LQGLFL�DJUHJD L�
%8,174sau748,128600
50000
00
11),(0/1 === ∑
∑qp
qpI qpv
%89,104sau0489,128600
30000
00
10)(0/1 === ∑
∑qp
qpI qv
%67,166sau6667,130000
50000
10
11)(0/1 === ∑
∑qp
qpI pv
5HOD LD�GLQWUH�FHL�WUHL�LQGLFL�
)(0/1
)(0/1
),(0/1
pvqvqpv III ⋅=
748,174816,16667,10489,1 ≅=⋅ 3. 0RGLILF ULOH�DEVROXWH�DOH�YDORULL��YROXPXOXL�IL]LF�úL�DOH�SUH XULORU:
2140028600500000011),(
0/1 =−=−=∆ ∑∑ qpqpqpv mii lei
140028600300000010)(
0/1 =−=−=∆ ∑∑ qpqpqv mii lei
2000030000500001011)(
0/1 =−=−=∆ ∑∑ qpqppv mii lei
21400200001400)(0/1)(
0/1),(
0/1 =+=∆+∆=∆pvqvqpv mii lei
Ponderea celor doi factori:
%54,610021400
1400100
),(0/1
)(0/1)( =⋅=⋅
∆
∆=
qpv
qv
qvK
%46,9310021400
2000100
),(0/1
)(0/1)( =⋅=⋅
∆
∆=
qpv
pv
pvK
4. Orice indice agregat se poate substitui printr-un indice mediu aritmetic sau armonic al indicilor individuali FRUHVSXQ] WRUL�
0489,128600
3,30000
28600
90006667,0960025,1100002,1
00
00)(0/1 ==
⋅+⋅+⋅==
∑∑
qp
qpiI
qqv
sau 104,89%
6667,16,29997
50000
2
12000
6667,1
20000
5,1
1800050000
111
11)(0/1 ==
++==
∑∑
qpi
qpI
p
pv sau 166,67%
5. 5HSUH]HQWDUHD�JUDILF �D�VWUXFWXULL�YDORULL�GLQ�FHOH�GRX �OXQL�FRQVHFXWLYH
Tabelul 7.3.
6WUXFWXUD�YDORULL�YkQ] ULORU���� 0 UIXUL
SHULRDGD�GH�ED] ��3%� perioada cXUHQW ��3&� A 1 2 I II III
35,0 33,6 31,4
36 40 24
Total 100% 100%
36,00
33,6040,00
31,4024,00
35,00
0
20
40
60
80
100
PB PC
%
III
II
I
)LJXUD������6WUXFWXUD�YDORULL�GHVIDFHULORU�GH�P UIXUL
2. Într-R�VRFLHWDWH�FRPHUFLDO �VH�FXQRVF�XUP WRDUHOH�GDWH�FX�SULYLUH�OD�GHVIDFHULOH�GH�P UIXUi:
9DORDUHD�P UIXULORU�YkQGXWH�vQ�SHULRDGD�GH�ED] �úL�FXUHQW
Tabelul 7.4.
9DORDUHD�P UIXULORU� (mil. lei)
0 UIXUL
perioada GH�ED]
perioada FXUHQW
Modificarea volumului fizic
(%)
A 1 2 4 A B C
500 600 800
1500 900
1400
+7 + 10 - 20
Total 1900 3800
Se cere: 1. V �VH�FDOFXOH]H�LQGLFLL�LQGLYLGXDOL�DL�YDORULL��YROXPXOXL�IL]LF�úL�DL��SUH XULORU� 2. LQGLFLL�GH�JUXS�DL�YDORULL��YROXPXOXL�IL]LF�úL�DO�SUHWXULORU� 3. PRGLILF ULOH�DEVROXWH�DOH�YDORULL��YROXPXOXL�IL]LF�úL�DOH�SUH XULORU� 4. FRQWULEX LD�FHORU�GRL�IDFWRUL�DVXSUD�GLQDPLFLL�YDORULL�P UIXULORU�YkQGXWH� Rezolvare 1. Indicii individuali ai valorii se pot calcula pe baza datelor din tabel, iar indicii individuali ai
SUH XULORU�SH�ED]D�UHOD LHL�GLQWUH�FHL�WUHL�LQGLFL�
• indicii valorii�GHVIDFHULORU�GH�P UIXri:
=
=
=
==
C)marfa(pentru%175sau75,1800
1400
B)marfa(pentru%150sau5,1600
900
A)marfa(pentru%300sau3500
1500
00
110/1 qp
qpi v
• indicii volumului fizic
( )
=+−
=+
=+
=+=
)Cmarfapentru(%8010020
)Bmarfapentru(%11010010
)Amarfapentru(%1071007
100%0/1
qq ri
• LQGLFLL�SUH XULORU�VH�FDOFXOHD] �SH�ED]D�UHOD LHL�
pqv iii 0/10/10/1 ⋅= ,
de unde:
=
=
=
==
)Cmarfapentru(%75,218sau1875,28,0
75,1
)Bmarfapentru(%36,136sau3636,11,1
5,1
)Amarfapentru(%4,280sau804,207,1
3
0/1
0/10/1 q
vp
i
ii
2. &DOFXOXO�LQGLFLORU�GH�JUXS�DL�YDORULL��YROXPXOXL�IL]LF�úL�DO�SUH XULORU
• indicele de grup al valorii�VH�RE LQH�GLUHFW�GLQ�GDWHOH�GLQ�WDEHO�
%200sau21900
3800
00
11),(0/1 === ∑
∑qp
qpI qpv
• indicele de grup al volumului fizic nu se poate calcula aici decât ca un indice mediu
DULWPHWLF� SRQGHUDW� FX� YDORDUHD� P UIXULORU� GLQ� SHULRDGD� GH� ED] �� 3Hntru aceasta se SRUQHúWH�GH�OD�UHOD LD�
9659,01900
1835
1900
8008,06001,150007,1
00
00)(0/1 ==
⋅+⋅+⋅=
⋅=
∑∑
qp
qpiI
qqv
• LQGLFHOH�GH�JUXS�DO�SUH XULORU�SRUQHúWH�FD�úL�vQ�FD]XO�LQGLFLORU�LQGLYLGXDOL�GH�OD�UHOD LD�
pqv III 0/10/10/1 ⋅= , de unde:
0706,29659,0
2
0/1
0/10/1 === q
vp
I
II sau 207,06%
3. 0RGLILF ULOH� DEVROXWH� DOH� YDORULL�� YROXPXOXL� IL]LF� úL� DOH� SUH XULORU� VH� FDOFXOHD] � SH� ED]D�
indicilor de grup respectivi:
1900190038000011),(
0/1 =−=−=∆ ∑∑ qpqpqpv mil. lei
65190018350000)(
0/1 −=−=−⋅=∆ ∑∑ qpqpi qqv mil. lei
)(0/1
)(0/1
),(0/1
pvqvqpv ∆+∆=∆ , de unde:
1965)65(1900)(0/1),(
0/1)(
0/1 =−−=∆−∆=∆qvqpvpv
mil. lei
4. &RQWULEX LD�FHOor doi factori
%42,31001900
65100
),(0/1
)(0/1)( −=⋅−=⋅
∆
∆=
qpv
qv
qvK
%42,1031001900
1965100
),(0/1
)(0/1)( =⋅=⋅
∆
∆=
qpv
pv
pvK
3. Se cunosc datele:
Tabelul 7.5.
9DORDUHD�vQFDVDW ��PLO�OHL� Categorii de
confort perioada de ED]
perioada FXUHQW
Modificarea SUH XULORU
(%)
A 1 2 4 1 2 3 4
1500 2000
400 300
2500 5500
520 380
+75 +125
- -25
Total 4200 8900
Se cere: 1. FDOFXOXO�LQGLFLORU�LQGLYLGXDOL�DL�YDORULL��YROXPXOXL�IL]LF�úL�DL�SUH XULORU� 2. FDOFXOXO�LQGLFHOXL�GH�JUXS�DO�SUH XULORU��SUHFL]kQGX-VH�FH�IHO�GH�IRUPXO �VH�SRDWH�DSOLFD�úL�GH�
ce; 3. indicele de grup�DO�YDORULL�úL�DO�YROXPXOXL�IL]LF� 4. PRGLILF ULOH�DEVROXWH�DOH�YDORULL��YROXPXOXL�IL]LF�úL�SUH XULORU��JUDGXO�GH�LQIOXHQ �D�FHORU�GRL�
IDFWRUL�DVXSUD�GLQDPLFLL�vQFDV ULORU�
Rezolvare 1. &DOFXOXO�LQGLFLORU�LQGLYLGXDOL�DL�YDORULL��YROXPXOXL�IL]LF�úL�DL�SUH XUilor
• indicii individuali ai valorii:
=
=
=
=
==
)confortde4categoriapentru(%67,126sau2667,1300
380
)confortde3categoriapentru(%130sau3,1400
520
)confortde2categoriapentru(%275sau75,22000
5500
)confortde1categoriapentru(%67,166sau6667,11500
2500
00
110/1 qp
qpi v
• LQGLFHOH� SUH XULORU� VH� YD� FDOFXOD� SH� ED]D� UHOD LHL� GLQWUH� LQGLFH� úL� ULWP�� GHRDUHFH� vQ� WDEHOXO� ������ vQ� FRORDQD� �� VH� G � SURFHQWXO� GH� PRGLILFDUH� D� SUH XULORU�� DGLF � ULWPXO� GH�modificare
=+−
=+
=+
=+
=+=
%75sau75,0100
10025
%100sau1100
1000
%225sau25,2100
100125
%175sau75,1100
10075
100
1000/1
qq ri
• indicele volumului fizic�VH�RE LQH�GLQ�UHOD LD�
pqv iii 0/10/10/1 ⋅= ,
de unde:
=
=
=
=
==
%89,168sau6889,175,0
2667,1
%130sau3,10,1
3,1
%2,122sau222,125,2
75,2
%2,95sau952,075,1
6667,1
0/1
0/10/1 p
vq
i
ii
2. &DOFXOXO�LQGLFHOXL�GH�JUXS�DO�SUH XULORU�VH�YD�IDFH�vQ�DFHVW�H[HPSOX�FD�PHGLH�DUPRQLF ��SH�
ED]D�UHOD LHL�
816,17,4899
8900
75,0
380
1
520
25,2
5500
75,1
2500
8900
111
11)(0/1 ==
+++=
⋅=
∑∑
qpi
qpI
p
pv sau 181,6%
1RW � Nu s-D� SXWXW� FDOFXOD� XQ� LQGLFH� DJUHJDW� DO� SUH XULORU�� GHRDUHFH� QX� VH� FXQRVF� VHSDUDW�
FDQWLW LOH�úL�SUH XULOH� 3. ,QGLFHOH�GH�JUXS�DO�YDORULL�úL�DO�YROXPXOXL�IL]LF:
119,24200
8900
00
11),(0/1 === ∑
∑qp
qpI qpv sau 211,9%
1667,1816,1
119,2
0/1
0/10/1 === p
vq
I
II sau 116,67%
4. 0RGLILF ULOH�DEVROXWH�DOH�YDORULL��YROXPXOXL�IL]LF�úL�DOH�SUH XULORU:
4700420089000011),(
0/1 =−=−=∆ ∑∑ qpqpqpv mil. lei
3,40007,489989001
1111)(
0/1 =−=−=∆ ∑∑ qpi
qpp
pv mil. lei
7,6993,40004700)(0/1),(
0/1)(
0/1 =−=∆−∆=∆pvqpvqv
mil. lei
&RQWULEX LD�FHORU�GRL�IDFWRUL
%9,141004700
7,699100
),(0/1
)(0/1)( =⋅=⋅
∆
∆=
qpv
qv
qvK
%1,851004700
3,4000100
),(0/1
)(0/1)( =⋅=⋅
∆
∆=
qpv
pvpvK
Deoarece )( pvK > )(qvK UH]XOW �F �vQ�SULQFLSDO�FUHúWHUHD�VXPHL�vQFDV ULORU�vQ�SHULRDGD�FXUHQW �ID �
GH�SHULRDGD�GH�ED] �FX������PLO��OHL�VH�GDWRUHD] �vQ�SULQFLSDO�FUHúWHULL�SUHWXULORU���������úL�QXPDL�����% pe VHDPD�FDQWLW LORU�
4. 3HQWUX�R�VRFLHWDWH�FRPHUFLDO �VH�FXQRVF�GDWHOH�
Tabelul 7.8.
0 UIXUL Valoarea
vQFDV ULORU�vQ�
PB (mil. lei)
Dinamica volumului fizic (%)
Modificarea SUH XULORU�
(%) 0 1 2 3
A 100 120 150 B 400 107 230 C 600 130 50 Total 1100 ... ...
Se cere: 1. LQGLFLL�LQGLYLGXDOL�DL�YDORULL�úL�DL�SUH XULORU� 2. LQGLFLL�GH�JUXS�DL�YDORULL��YROXPXOXL�IL]LF�úL�DO�SUH XULORU� 3. V �VH�GHVFRPSXQ �YDORDUHD�DEVROXW �SH�WRWDO
• IRORVLQG�PHWRGD�VXEVWLWX LHL�vQ�ODQ • folosind metoda restului nedescompus.
Rezolvare: 1. ,QGLFLL�LQGLYLGXDOL�DL�SUH XULORU�VH�GHWHUPLQ �XWLOL]kQG�UHOD LLOH�
( ) 10001%01 +=pp ri
De exemplu, pentru marfa „A”:
( ) %250100150%01 =+=pi
,QGLFLL�LQGLYLGXDOL�DL�YDORULL�VH�GHGXF�GLQ�UHOD LD�GH�VLVWHP�
pqv iii010101
⋅=
35,22,101
=⋅=vi pentru marfa „A”.
5H]XOWDWHOH�FDOFXOHORU�VXQW�SUH]HQWDWH�vQ�WDEHOXO�������FRORDQHOH������úL����
Tabelul 7.9.
0 UIXUL
Valoarea vQFDV ULORU�
în PB
00 qp (mil. lei)
qi pi vi viqpqp ⋅= 0011 0010 qpiqp
q ⋅= qi
qpqp 1101 =
0 1 2 3 4 5 6 7 A 100 1,2 2.5 3 300 120 250 B 400 1,07 3,3 3,53 1412 428 1320 C 600 1,3 1,5 1,95 1170 780 900 Total 1100 1,2073 2,1702 2,62 2882 1328 2470
2. PeQWUX� FDOFXOXO� LQGLFLORU� GH� JUXS� VH� FDOFXOHD] � YDORDUHD� vQFDV ULORU� vQ� SHULRDGD� FXUHQW �( 11 qp ��úL�YDORDUHD�vQFDV ULORU�vQ�SUH XUL�FRPSDUDELOH�� 10 qp ���YH]L�FRORDQHOH���úL����
( ) 62,21100
2882
00
11,01
===∑∑
qp
qpI qpv sau 262%
( ) 2073,11100
1328
00
10
01===
∑∑
qp
qpI qv sau 120,73%
( ) 1702,21378
2882
10
11
01===
∑∑
qp
qpI pv sau 217,02%
3. a) 'HRDUHFH�SUH XULOH�DX�FUHVFXW�PDL�UDSLG�GHFkW�FDQWLW LOH��SHQWUX�GHVFRPSXQHUHD�SH�IDFWRUL�
D� PRGLILF ULL� DEVROXWH�� IRORVLQG� PHWRGD� VXEVWLWX LHL� vQ� ODQ , vom utiliza varianta I (se substituie mai întâi factorul cantitativ):
( ) 2280010 =−=∆ ∑∑ qpqpqv mil. lei
( ) 17821011 =−=∆ ∑∑ qpqppv mil. lei
0RGLILFDUHD�DEVROXW �SH�WRWDO�
( ) 17820011, =−=∆ ∑∑ qpqpqpv mil. lei
3H�ED]D�DFHVWHL� UHOD LL� VH�SRDWH�GHWHUPLQD�FRQWULEX LD� IDFWRULORU� OD�PRGLILFDUHD�DEVROXW �SH�total:
( )( )
( ) %79,12100, =⋅∆∆=
qpv
qvqvK
( )( )
( ) %21,87100, =⋅∆∆=
qpv
pvpvK
b) Metoda restului nedescompus 6H� GHWHUPLQ � PDL� vQWkL� LQIOXHQ D� L]RODW � D� IDFWRULORU� �YDORULOH� 10 qp sunt prezentate în tabelul 7.9., coloana 6).
( ) 2280010 =−=∆ ∑∑ qpqpqv ii mil. lei
( ) 13700001 =−=∆ ∑∑ qpqppv ii mil. lei
$SRL�GH�GHWHUPLQ �UHVWXO�QHGHVFRPSXV�
( ) ( ) 1841598178213702281782, =−=+−=∆−∆= v iiqpvRN mil lei ,
unde 1598=∆v ii 3HQWUX� UHSDUWL]DUHD� UHVWXOXL� QHGHVFRPSXV� SH� IDFWRUL� GH� LQIOXHQ � VH� SRDWH� XWLOL]D� XQD� GLQ�variantele: Varianta I: Se atribuie, în cazul nostru, tot restul nedescompus factorului calitativ:
( ) 228=∆ qv mil. lei
( ) ( ) 15541841370 =+=+∆=∆ RNpv iipv mil. lei
&RQWULEX LD�IDFWRULORU�HVWH�FHD�GH�OD�PHWRGD�VXEVWLWX LHL�vQ�ODQ .
Varianta a II-a: Se distribXLH��vQ�PRG�HJDO��UHVWXO�QHGHVFRPSXV�SH�FHL�GRL�IDFWRUL�GH�LQIOXHQ �
( ) ( ) 320922282
1 =+=+∆=∆ RNqv iiqv mil. lei
( ) ( ) 14629213702
1 =+=+∆=∆ RNpv iipv mil. lei
&RQWULEX LD�UHODWLY �D�IDFWRULORU�vQ�DFHVW�FD]�
( ) %96,17=qvK
( ) %04,82=pvK
Varianta a III-a: 6H� UHSDUWL]HD] � UHVWXO� QHGHVFRPSXV� SH� IDFWRULL� GH� LQIOXHQ � LQkQG� FRQW� GH� SRQGHUHD�IDFWRULORU�vQ�PRGLILFDUHD�GDWRUDW �LQIOXHQ HL�L]RODWH�D�DFHVWRUD�
( ) ( )( )
( ) 2568,254184%27,14228, =⋅+=⋅∆
∆+∆=∆ RN
qpvii
qviiqv
iiqv mil. lei
( ) ( )( )
( ) 7432,1527184%73,851370, =⋅+=⋅∆
∆+∆=∆ RN
qpvii
pviipv
iipv mil. lei
&RQWULEX LD�UHODWLY �D�IDFWRULORU�vQ�acest caz este:
( ) %25,14=qvK
( ) %75,85=pvK
2EVHUYD LH� Valorile cele mai realiste sunt cele de la varianta a III-a a metodei restului nedescompus deoarece PHWRGD� VXEVWLWX LHL� vQ� ODQ � DFFHQWXHD] � LQIOXHQ D� XOWLPXOXL� IDFWRU� VXEVWLWXLt, în FD]XO�QRVWUX�LQIOXHQ D�SUH XULORU�
5. 3HQWUX�GRL�DJHQ L�FDUH�GHVI úRDU �DFHHDúL�DFWLYLWDWH�VH�FXQRVF�GDWHOH�
Tabelul 7.10.
3URGXF LD��vQ�SUH XUL�FXUHQWH�PLO��OHL� 1U��VDODULD L Agent economic
PB PC PB PC Modificarea
SUH XULORU���� 0 1 2 3 4 5
A 260 300 23 17 +15 B 200 240 22 25 +20 Total 460 540 45 42
Se cere: 1. SURGXFWLYLWDWHD�PXQFLL�SH�ILHFDUH�DJHQW�HFRQRPLF�úL�SH�WRWDO�vQ�FHOH�GRX �SHULRDGH� 2. LQGLFLL�LQGLYLGXDOL�DL�SURGXFWLYLW LL�PXQFLL� 3. LQGLFLL�SURGXFWLYLW LL�PXQFLL�FX�VWUXFWXU �YDULDELO ��FX�VWUXFWXU �IL[ �úL�DO�YDULD LHL�VWUXFWXULL� 4. PRGLILFDUHD�DEVROXW �D�SURGXFWLYLW LL�PHGLL�D�PXQFLL�FX�HYLGHQ LHUHD�LQIOXHQ HL�IDFWRULORU� 5. PRGLILFDUHD�SURGXF LHL��SH�WRWDO��SH�VHDPD�PRGLILF ULL�QXP UXOXL�VDODULD LORU�
Rezolvare 1. Pentru calculul SURGXFWLYLW LL� PXQFLL� GLQ� SHULRDGD� FXUHQW � WUHEXLH� FDOFXODW � YDORDUHD�
SURGXF LHL� vQ� SUH XUL� FRPSDUDELOH� �FRQVWDQWH��� DGLF � vQ� SUH XULOH� SHULRDGHL� GH� ED] �
(pi
qpqp
01
1110 = ). Rezultatele calculului sunt prezentate în tabelul 7.11., coloana 2.
304,1123
260
0
000 === T
qpw �PLO��OHL�SHUVRDQ
0909,922
200
1
101 === T
qpw �PLO��OHL�SHUVRDQ
Tabelul 7.11.
9DORDUHD�SURGXF LHL�vQ�SUH XUL�
constante (mil. lei) Agent economic
PB PC 0
000
T
qpw =
1
101
T
qpw = 10 Tw
(mil. lei)
wi01
0 1 2 3 4 5 6 A 260 260,86956 11,304 15,345 192,168 1,3574 B 200 200 9,0909 8 227,2725 0,88 Total 460 460,86956 10,222 10,973 419,4405 1,0734
3H�WRWDO��DJUHJDUHD�YDORULORU�LQGLYLGXDOH�SRDWH�IL�UHDOL]DW �QXPDL�SULQ�LQWHUPHdiul mediei ( )w :
222,1045
460
0
00
0
000 ====
∑∑
∑∑
T
Tw
T
qpw �PLO��OHL���SHUVRDQ
973,1042
869,460
1
101 ===
∑∑
T
qpw �PLO��OHL���SHUVRDQ
2. ,QGLFLL�LQGLYLGXDOL�DL�SURGXFWLYLW LL�PXQFLL�VH�FDOFXOHD] �GXS �UHOD LD�
0
101 w
wi w = ,
úL�DQXPH�
3574,1304,11
345,1501
==wi sau 135,74% pentru agentul economic „A”
88,00909,9
801
==wi sau 88% pentru agentul economic „B”
3. ,QGLFLL�SURGXFWLYLW LL�PHGLL�D�PXQFLL�
a) FX�VWUXFWXU �YDULDELO
( )∑
∑∑
∑∑
∑∑
∑===
0
00
1
11
0
00
1
01
0
1, ::T
Tw
T
Tw
T
qp
T
pq
w
wI
Tgwwvs
( ) 0734,1
222,10
973,10, ==Tgww
vsI sau 107,34%
3HQWUX�FDOFXOXO� LQGLFLORU�GH�JUXS� IDFWRULDOL� WUHEXLH�FDOFXODW �SURGXFWLYLWDWHD�PXQFLL� *w IRORVLQG�XUP WRDUHD�UHOD LH�
∑∑
=1
10*
T
Tww
Valorile 10 Tw sunt prezentate în tabelul 7.11., coloana 5.
9867,942
4405,419* ==w
b) DO�YDULD LHL�VWUXFWXULL��GH�WLS�/DVSH\HUV�
( ) 977,0222,10
9877,9
0
* ===w
wI
Tgwvs sau 97,70%
5H]XOW � F � SURGXFWLYLWDWHD� PHGLH� D� PXQFLL� DU� IL� VF ]XW� FX� ����� GDF � V-ar fi modificat QXPDL�VWUXFWXUD�VDODULD LORU�
c) FX�VWUXFWXU �IL[ ��GH�WLS�3DDVFKH�
( ) 0987,19867,9
973,10
*
1 ===w
wI wwSF sau 109,87%
'DF �V-DU�IL�PRGLILFDW�QXPDL�SURGXFWLYLWDWHD�PXQFLL�OD�QLYHOXO�ILHF UXL�DJHQW�HFRQRPLF��productivitatea medie a muncii ar fi crescut cu 9,87%. Pe ansamblu, productivitatea medie a muncii a crescut doar cu 7,34%, deoarece o parte GLQ� FUHúWHUHD� GDWRUDW � PRGLILF ULL� SURGXFWLYLW LL� PXQFLL� SDU LDOH� D� IRVW� FRPSHQVDW � GH�VF GHUHD�SURGXFWLYLW LL�PHGLL�D�PXQFLL�GDWRUDW �PXWD LLORU�vQ�VWUXFWXUD�VDODULD LORU�
4. 0RGLILFDUHD�DEVROXW �D�SURGXFWLYLW LL�PHGLL�D�PXQFLL��SH�WRWDO�
( ) 751,0222,10973,1001, =−=−=∆ ww
Tgww mil. lei / pers. = 751 mii lei / pers.
0RGLILFDUHD�DEVROXW �D�SURGXFWLYLW LL�PHGLL�SH�VHDPD�PXWD LLORU�vQ�VWUXFWXUD�VDODULD LORU�
( ) 235,0222,10987,90* −=−=−=∆ wwTgw mil. lei / pers. = - 235 mii lei / pers.
0RGLILFDUHD� DEVROXW � D� SURGXFWLYLW LL� PHGLL� SH� VHDPD� PRGLILF ULL� SURGXFWLYLW LL� PXQFLL�SDU LDOH��SH�ILHFDUH�DJHQW�HFRQRPLF��
( ) 986,0987,9973,10*1 =−=−=∆ wwww mil. lei = 986 mii lei
Verificare:
( ) ( ) ( ) 751986235, =+−=∆+∆=∆ wwTgwgww T mii lei
5. ( ) 9118,0460
4405,419
00
10 ===∑∑
TW
TWI TQ sau 91,18%
( ) 5595,400010 −=−=∆ ∑∑ TWTWTQ mil. lei
9DORDUHD�SURGXF LHL�SH�WRWDO�D�VF ]XW�FX��������FHHD�FH�vQ�YDORDUHD�DEVROXW �UHSUH]LQW �R�VF GHUH�FX�–40,5595 mil. lei.
PROBLEME PROPUSE
1. 3HQWUX�GRX �SURGXVH�VH�FXQRVF�GDWHOH�
Tabelul 7.12.
9DORDUHD�YkQ] ULORU��PLO��OHL� Produs
PB PC
Modificarea SURFHQWXDO �D�
SUH XULORU 0 1 2 3
A 300 375 +20 B 600 900 +60
Se cere: 1. LQGLFLL�LQGLYLGXDOL�DL�YDORULL��YROXPXOXL�IL]LF�úL�DL�SUH XULORU� 2. PRGLILFDUHD�DEVROXW �úL�UHODWLY �D�YDORULL�GHVIDFHULORU�SH�WRWDO�úL�LQIOXHQ D�IDFWRULORU� 3. úWLLQG� F �QXP UXO�SHUVRQDOXOXL�� SH� WRWDO�� D� FUHVFXW� vQ�SHULRDGD�FXUHQW � ID �GH�SHULRDGD�GH�
ED] �FX�����V �VH�GHWHUPLQH�PRGLILFDUHD�UHODWLY �D�SURGXFWLYLW LL�PXQFLL�
2. /D�R�VRFLHWDWH�FRPHUFLDO �V-au înregistrat datele:
Tabelul 7.13.
Structura valorii vâQ] ULORU�� Marfa
PB PC
Dinamica volumului fizic
(%)
Modificarea UHODWLY �D�
SUH XULORU���� 0 1 2 3 4
A 35,0 35,0 120 50 B 33,6 40,0 125 66,7 C 31,4 25,0 66,7 100
Se cere: 1. LQGLFLL�LQGLYLGXDOL�DL�SUH XULORU�úL�DL�YDORULL�YkQ] ULORU� 2. PRGLILFDUHD�UHODWLY �D�YDORULL��YROXPXOXL�IL]LF�úL�D�SUH XULORU��SH�WRWDO� 3. V �VH�UHSUH]LQWH�JUDILF�VWUXFWXUD�YDORULL�YkQ] ULORU�vQ�FHOH�GRX �SHULRDGH�
3. 3HQWUX�GRL�DJHQ L�HFRQRPLFL�VH�FXQRVF�GDWHOH�
Tabelul 7.14.
Salariul mediu (mii. lei/pers.) Structura�DQJDMD LORU���� Agent economic PB PC PB PC
0 1 2 3 4 A 2400 2880 50 45 B 2700 3200 50 55
Se cere:
1. dinamica salariului mediu pe fiecare agent economic; 2. VDODULXO�PHGLX�SH�WRWDO�vQ�FHOH�GRX �SHULRDGH� 3. LQGLFLL� GH� JUXS� DL� VDODULXOXL� PHGLX� FX� VWUXFWXU � YDULDELO �� FX� VWUXFWXU � IL[ � úL� DO� YDULD LHL�
structurii; 4. PRGLILF ULOH�DEVROXWH�FRUHVSXQ] WRDUH�SH�WRWDO�
4. Se cunosc datele:
Tabelul 7.15.
Produs Structura valorii
YkQ] ULORU�vQ�SHULRDGD�
FXUHQW ����
Dinamica volumului fizic (%)
Modificarea SUH XULORU�
(%) 0 1 2 3
A 35 120 50 B 40 125 66,7 C 25 66,7 100
Se cere:
1. LQGLFLL�LQGLYLGXDOL�DL�YDORULL�úL�DL�SUH XULORU� 2. LQGLFLL�GH�JUXS�SULYLQG�YDORDUHD��YROXPXO�IL]LF�úL�SUH XULOH� 3. úWLLQG�F �QXP UXO�SHUVRQDOXOXL�� SH� WRWDO�� V-D� UHGXV� vQ�SHULRDGD�FXUHQW � ID �GH�SHULRDGD de
ED] �FX�����V �VH�GHWHUPLQH�PRGLILFDUHD�UHODWLY �D�SURGXFWLYLW LL�PXQFLL�
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