, . ( ), ( ), ( ) ..
2 : , 1, , , 0.
, , () I. , i. , , . , Iq iq q.
, , .
2 : .
, , , . i. : , (2).
, , (170), ( ) :
iQ=Q 1 /Q 0. (170)
(170) (171), (, ) :
∆ Q = Q 1 Q 0. (171)
(, , ..).
, p ( . price) ( , ) q ( . quantity) .. (172) (173):
ip=p 1 /p 0, (172) iq=q 1 /q 0. (173)
, (174):
iQ=iqip. (174)
, 5 . 50 , 7 . 20 . (172): ip = 7/5 = 1,4, 1,4 , 40%. (173): iq = 20/50 = 0,4, 40% , 60%. (174): iQ = 0,4*1,4 = 0,56, 56% , 44%. Q 0 = 50*5 = 250 (.) Q 1 = 20*7 = 140 (.), (170): iQ = 140/250 = 0,56. , (171) : ∆ Q = 140 250 = 110 (.), 110 . ( 44%), 0,4 ( 60%) 1,4 ( 40%).
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(170) (174) :
Q 1 =iqipQ 0. (175)
(175) , , ( ) ( ), :
∆ Q = ∆ Qq + ∆ Qp, (176)
∆ Qq q ( );
∆ Qp p ( ).
(176) (), :
1) q, p ( 1- , 2-)[54];
2) p, q ( 1- , 2-).
: (175) 1- 2-. , 1- , 2-, (177), :
Q 1 =ipiqQ 0. (177)
1- , . (175) 1- (178), (177) (179):
∆ Qq= iqQ 0 Q 0 = (iq 1) Q 0, (178) ∆ Qp= ipQ 0 Q 0 = (ip 1) Q 0. (179)
, 1- , 2-, (177) , , 1- (179): ∆ Qp= (1,41)*250 = 100 (.), 5 7 . 100 ., 110 ., 2- .
2- , 1- . , (171) (178) (176), :
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∆ Qp = ∆ Q ∆ Qq = (Q 1 Q 0) (iqQ 0 Q 0) = iqipQ 0 Q 0 iqQ 0 +Q 0 = (iqip 1 iq + 1) Q 0 = iq (ip 1) Q 0.
(180):
∆ Qp = iq (ip 1) Q 0. (180)
, (171) (177) (176) :
∆ Qq = ∆ Q ∆ Qp = (Q 1 Q 0) (ipQ 0 Q 0) = ipiqQ 0 Q 0 ipQ 0 +Q 0 = (ipiq 1 ip + 1) Q 0 = ip (iq 1) Q 0.
(181):
∆ Qq = ip (iq 1) Q 0. (181)
(181): ∆ Qq = 1,4*(0,41)*250 = 210 (.), 50 20 210 . (176): ∆ Q = 100 + (210) = 110, , (171).
[55]. : i - , 1- i - i - . (80), (100%).
, (M) (q), (m) (p) .. M = qmp. ( q - 1- , m 2- p 3-):
(182)
, , ∆ M = M 1 M 0 :
1) ∆ Mq = T q M 0 = (iq 1) M 0;
2) ∆ Mm = iqT m M 0 = iq (im 1) M 0;
3) ∆ Mp = iqimTpM 0 = iqim (ip 1) M 0.
, . , . . , , , , .
2- : .
, ( . aggregatus , ) , (), ( ). .
, ( q p), ..
∑Q = ∑qp. (183)
, , . (), ( ) :
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I Q= . (184)
(184) () (185), (, ) :
∆∑ Q = ∑ Q 1 ∑ Q 0 = ∑ q 1 p 1 ∑ q 0 p 0. (185)
, : , 2 51:
51. 2
, . | , | |||
(p 0) | (p 1) | (q 0) | (q 1) | |
(183):
: ∑Q 1 = 18*160+25*120 = 5880 (.) ;
: ∑Q 0 = 20*100+22*150 = 5300 (.) .
:
(184): I Q= 5880/5300 = 1,1094, 1,1094 , 10,94%.
(185): ∆∑ Q = 5880 5300 = 580, 580 .
() . () .
, :
; (186) . (187)
(186) , 1- , (187) 1- .
, :
; (188) . (189)
(188) , 2- , (189) 2- .
:
IQ = ;(190) IQ = . (191)
ػ , 111 - ( ). ػ, , ( ).
( ) 1- , 2-. (187):
= 1,0472, 1,0472 ( 4,72%).
(188):
= 1,0594, 1,0594 ( 5,94%).
(191): I Q = 1,0472*1,0594 = 1,1094, 1,1094 ( 10,94%) 1,0472 ( 4,72%) 1,0594 ( 5,94%).
(186) (189) , , ≠ ≠ . , , [56], > > .
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( 1- ) (186) (187) (188) (189). (186) (189) :
; (192) . (193)
, (193) (192), : , 1-.
(190) (191) , (184) ∑ Q 1:
∑ Q 1= Q 0, (194)∑ Q 1= Q 0. (195)
(194) , 1- , 2-, (195) , 1- , 2-. , , , ( ) ( ) () . .
(187), (195). , , ∆∑ Q = ∑ Q 1 ∑ Q 0 :
1) ∆∑ Qq = ( 1) ∑ Q0 = (1,05941)*5300 ≈ 315 (.)
2) ∆∑ Qp = ( 1) ∑ Q0 = 1,0594*(1,04721)*5300 ≈ 265 (.)
: ∆∑ Q = 265 + 315 = 580, , (185).
, . , (196) (197) :
(196) (197)
(196) , (197) .
:
; (198) ; (199)
; (200) . (201)
( ) . , , ..
(), , ( ).
x, f, (x f), . 3 : , .
( ) x ( ) f, x. ( ) (202):
. (202)
, ( ), , .. .
x, . f 1, [57] (203):
. (203)
, () , ( ).
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f x. , x 0 [58] (204):
, (204)
(203) (204) , (1- ) (2- )[59].
f () (6), (202) (204) :
; (205) ; (206) . (207)
(202) (207) (, , , , ..) x f .
, (202) (207) :
; (208)
; (209) . (210)
, :
. (211)
(211) , , , .
(208):
, 99,06% , 21,2 . 21,0 . , 0,94%.
, (209)[60]:
.
( , ) , (210):
=0,9838.
(211): 1,0069*0,9838 = 0,9906.
, . , () , , :
1) , , .
2) () (, ), , .
, : .
(, , , .) , , , .
. , , , , .. , , . . , , , . , .
. , . , , .
:
1. , ( ) ( ), ( ) - .
2. ( , ),
I / I / = 1, (212)
I / ( ) ;
I / ( ) .
3. ,
I / = I /: I /, (213)
I / ( ) ;
I / ( ) .
, , ( ), , , I / I /.
4. , ( ), , , .
5. , :
. (214)
. , .
- (, ), . , .
, .
, () 4 :
1) ( , 300 );
2) - , - (i 1, i 2, i 3, , in);
3) - :
, (215)
( ) -;
4) ( ) (199) (201), Q :
, (216) ; (217)
5) ( ) (193);
6) .
, 2 (186) (188) (192).
, : , -, .
[61], , , .. j:
, (218)
; j; j ; n , .
(218) , . -.
- , , , , :
, (219)
qij i - j - ; pij i - j - ; i - .
(219) , .
, , , :
, (220)
i - ; i - , .
(220) , , ; ( ) (, ). (220) , , , , .
, , , , . -, , ( , -).
, (, ) - , , , , .
(. 52) 3- (A, B C).
52.
, . | , . | , . | , . | |||||||
1 | 2 | 1 | 2 | 1 | 2 | 1 | 2 | |||
1 | 6 | |||||||||
2 | 7 | |||||||||
3 | 8 | |||||||||
4 | 9 | |||||||||
5 | 10 | |||||||||
, , . .
.. . .: , 1996 | |
: / .., .. .: , 2001. 228 . | |
. . . .: , 1968 | |
: / . .. . 4- ., . . .: , 2002. 480 . | |
: . / . .. . .: , 2003. 416 . | |
: . / . .. . . 2-, . . .: -, 2006. 384 . | |
: / . .. . . 2-, . . .: -, 2005. 476 . | |
: ( . ..). . 4-, ., . .: , 2007. 656 . | |
.., .. . - . 1. : , 2007. 87 . | |
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