Стоимость в экономических системах. Светлов Н.М. - 127 стр.

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127
=
(1) () (1)
i i ij j j ij j
iI jJ jJ iI
tpbxt xt bp
β
⎞⎛
⎟⎜
⎟⎜
⎠⎝
∈∈
+=+
∑∑






Ç˚ÔÛÒÍ ·Î‡„‡ i ‚ ÏÓÏÂÌÚ t+1
ëÚÓËÏÓÒÚ¸ ·Î‡„‡ i, ‚˚ ÔÛ˘ÂÌÌÓ„Ó ‚
ÏÓÏÂÌÚ t+1, ‚ÏÂÒÚÂ Ò ðÂÌÚÓÈ,
ÔðËÌÂÒÌÌÓÈ ËÏ Í ÏÓÏÂÌÚÛ t+2
ëÚÓËÏÓÒÚ¸ ‚ÒÂı ·Î‡„, ‚˚ÔÛ˘ÂÌÌ˚ı
‚ ÏÓÏÂÌÚ t+1, ‚ÏÂÒÚÂ Ò ðÂÌÚÓÈ,
ÔðËÌÂÒÌÌÓÈ ËÏË Í ÏÓÏÂÌÚÛ t+2
ëÚÓËÏÓÒÚ¸ ‚˚ÔÛÒ͇ ‚ÒÂı
ÚÂıÌÓÎӄ˘ÂÒÍËı ÔðÓˆÂÒÒÓ‚ ‚
ÏÓÏÂÌÚ t+2
ëÚÓËÏÓÒÚ¸ ÒÓ‚ÓÍÛÔÌÓ„Ó ‚˚ÔÛÒ͇
ÚÂıÌÓÎӄ˘ÂÒÍÓ„Ó ÔðÓˆÂÒÒ‡ j
ÏÓÏÂÌÚ t+2
ëÚÓËÏÓÒÚ¸ ÒÓ‚ÓÍÛÔÌÓ„Ó ‚˚ÔÛÒ͇
ÚÂıÌÓÎӄ˘ÂÒÍÓ„Ó ÔðÓˆÂÒÒ‡ j,
ÙÛÌ͈ËÓÌËðÛ˛˘Â„Ó Ò Â‰ËÌ˘ÌÓÈ
ËÌÚÂÌÒË‚ÌÓÒÚ¸˛
êËÒ. 5. ùÍÓÌÓÏ˘ÂÒÍÓ ÒÓ‰ÂðʇÌË ҂ÁË ðÂÌÚ˚ Ò ÒÓ‚ÓÍÛÔÌ˚Ï
˚ÔÛÒÍÓÏ ‚ ÏÓ‰ÂÎË ð‡Ò¯Ëðfl˛˘ÂÈÒ ˝ÍÓÌÓÏËÍË
åÓ‰ÂÎËðÛÂÏÓÈ ˝ÍÓÌÓÏËÍ ÔðËÒÛ˘‡ ÒÎÂ‰Û˛˘ Ò‚Á¸ ÏÂÊ‰Û ‚‡-
ÎÓ‚ÓÈ ÔðÓ‰Û͈ËÂÈ Ë ðÂÌÚÓÈ Ò Á‡Ô‡ÒÓ‚, ÍÓÚÓð˚ÏË ð‡ÒÔÓ·„‡ÂÚ ˝ÍÓÌÓ-
Ï˘ÂÒ͇ ÒËÒÚÂχ:
iI
β
i
(t + 1) p
i
jJ
b
ij
x
j
(t) =
jJ
x
j
(t + 1)
iI
b
ij
p
i
. (3.41)
ùÍÓÌÓÏ˘ÂÒÍÓ ÒÓ‰ÂðʇÌË ˝ÚÓÈ Ò‚ÁË Ôð‰ÒÚ‡‚ÎÂÌÓ Ì‡ ðËÒ. 5. ä‡Í
‚ˉËÏ, ÒÚÓËÏÓÒÚ¸
‚‡ÎÓ‚ÓÈ ÔðÓ‰Û͈ËË ÚÂıÌÓÎӄ˘ÂÒÍËı ÔðÓˆÂÒÒÓ‚,
ÙÛÌ͈ËÓÌËðÓ‚‡‚¯Ëı ‚ ÏÓÏÂÌÚ
t + 1 (Ú.Â. ‰ÓÒÚÛÔÌ˚ı ‰Î ÔÓÚð·ÎÂÌË
ÏÓÏÂÌÚ
t + 2), Ôð‰ÒÚ‡‚ÎÂÌ̇ Ôð‡‚Ó˛ ˜‡ÒÚ¸˛ Ûð‡‚ÌÂÌË, ð‡‚̇ ÒÚÓË-
ÏÓÒÚË ·Î‡„, ‰ÓÒÚÛÔÌ˚ı ‰Î ÔÓÚð·ÎÂÌË ‚ ÏÓÏÂÌÚ
t + 1, ‚ÍÛÔÂ Ò ðÂÌ-
ÚÓÈ, ÔðËÌÂÒÌÌÓÈ ËÏË Í ÏÓÏÂÌÚÛ
t + 2. ëÓÓÚÌÓ¯ÂÌË (3.41)
Ôð‰ÒÚ‡‚ÎÂÚ ÒÓ·ÓÈ Á‡ÍÓÌ ÙÛÌ͈ËÓÌËðÓ‚‡ÌË ÙË̇ÌÒÓ‚ÓÈ ÒËÒÚÂÏ˚
ÏÓ‰ÂÎËðÛÂÏÓÈ ˝ÍÓÌÓÏËÍË. éÌÓ ÔðÏÓ ÒΉÛÂÚ ËÁ ÓÔð‰ÂÎÂÌË ðÂÌÚ˚.
                                                                                                                        ⎞                             ⎛                                                                        ⎞
        ∑
                                      ⎛
                                      ⎜   β i (t +1) pi                                  ∑ bij x j (t ) ⎟⎟ =                         ∑                ⎜⎜    x j (t +1) ∑ bij p j ⎟⎟
                                      ⎝                                                                                 ⎠                              ⎝                                                                       ⎠
       i∈I                                                                               j∈J                                         j∈J                                                        i∈I



                                               ÏÓÏÂÌÚ t+1, ‚ÏÂÒÚÂ Ò ðÂÌÚÓÈ,




                                                                                 ‚ ÏÓÏÂÌÚ t+1, ‚ÏÂÒÚÂ Ò ðÂÌÚÓÈ,




                                                                                                                                                                                                ÚÂıÌÓÎӄ˘ÂÒÍÓ„Ó ÔðÓˆÂÒÒ‡ j,
                                             ÔðËÌÂÒfiÌÌÓÈ ËÏ Í ÏÓÏÂÌÚÛ t+2




                                                                                ÔðËÌÂÒfiÌÌÓÈ ËÏË Í ÏÓÏÂÌÚÛ t+2




                                                                                                                                        ÏÓÏÂÌÚ t+2




                                                                                                                                                                                                            ËÌÚÂÌÒË‚ÌÓÒÚ¸˛
        Ç˚ÔÛÒÍ ·Î‡„‡ i ‚ ÏÓÏÂÌÚ t+1




                                                                                                                        ÚÂıÌÓÎӄ˘ÂÒÍËı ÔðÓˆÂÒÒÓ‚ ‚
                                                                                                                            ëÚÓËÏÓÒÚ¸ ‚˚ÔÛÒ͇ ‚ÒÂı
                                          ëÚÓËÏÓÒÚ¸ ·Î‡„‡ i, ‚˚ÔÛ˘ÂÌÌÓ„Ó ‚




                                                                              ëÚÓËÏÓÒÚ¸ ‚ÒÂı ·Î‡„, ‚˚ÔÛ˘ÂÌÌ˚ı




                                                                                                                                                                               ÏÓÏÂÌÚ t+2

                                                                                                                                                                                             ëÚÓËÏÓÒÚ¸ ÒÓ‚ÓÍÛÔÌÓ„Ó ‚˚ÔÛÒ͇
                                                                                                                                                             ÚÂıÌÓÎӄ˘ÂÒÍÓ„Ó ÔðÓˆÂÒÒ‡ j ‚
                                                                                                                                                           ëÚÓËÏÓÒÚ¸ ÒÓ‚ÓÍÛÔÌÓ„Ó ‚˚ÔÛÒ͇




                                                                                                                                                                                             ÙÛÌ͈ËÓÌËðÛ˛˘Â„Ó Ò Â‰ËÌ˘ÌÓÈ
                                                                                                                  =


    êËÒ. 5. ùÍÓÌÓÏ˘ÂÒÍÓ ÒÓ‰ÂðʇÌË ҂flÁË ðÂÌÚ˚ Ò ÒÓ‚ÓÍÛÔÌ˚Ï
            ‚˚ÔÛÒÍÓÏ ‚ ÏÓ‰ÂÎË ð‡Ò¯Ëðfl˛˘ÂÈÒfl ˝ÍÓÌÓÏËÍË

      åÓ‰ÂÎËðÛÂÏÓÈ ˝ÍÓÌÓÏËÍ ÔðËÒÛ˘‡ ÒÎÂ‰Û˛˘‡fl Ò‚flÁ¸ ÏÂÊ‰Û ‚‡-
ÎÓ‚ÓÈ ÔðÓ‰Û͈ËÂÈ Ë ðÂÌÚÓÈ Ò Á‡Ô‡ÒÓ‚, ÍÓÚÓð˚ÏË ð‡ÒÔÓ·„‡ÂÚ ˝ÍÓÌÓ-
Ï˘ÂÒ͇fl ÒËÒÚÂχ:
                         ∑    ⎛
                              ⎜βi (t + 1) pi
                              ⎜
                                                bij xj (t)⎞⎟ =
                                                           ⎟
                                                                                        ∑                                   ∑            ⎛
                                                                                                                                         ⎜xj (t + 1)
                                                                                                                                         ⎜
                                                                                                                                                         bij pi⎞⎟ .
                                                                                                                                                                ⎟
                                                                                                                                                                                ∑                                              (3.41)
                          i∈I ⎝              j∈J           ⎠   j∈J                                                                       ⎝           i∈I        ⎠
ùÍÓÌÓÏ˘ÂÒÍÓ ÒÓ‰ÂðʇÌË ˝ÚÓÈ Ò‚flÁË Ôð‰ÒÚ‡‚ÎÂÌÓ Ì‡ ðËÒ. 5. ä‡Í
‚ˉËÏ, ÒÚÓËÏÓÒÚ¸ ‚‡ÎÓ‚ÓÈ ÔðÓ‰Û͈ËË ÚÂıÌÓÎӄ˘ÂÒÍËı ÔðÓˆÂÒÒÓ‚,
ÙÛÌ͈ËÓÌËðÓ‚‡‚¯Ëı ‚ ÏÓÏÂÌÚ t + 1 (Ú.Â. ‰ÓÒÚÛÔÌ˚ı ‰Îfl ÔÓÚð·ÎÂÌËfl ‚
ÏÓÏÂÌÚ t + 2), Ôð‰ÒÚ‡‚ÎÂÌ̇fl Ôð‡‚Ó˛ ˜‡ÒÚ¸˛ Ûð‡‚ÌÂÌËfl, ð‡‚̇ ÒÚÓË-
ÏÓÒÚË ·Î‡„, ‰ÓÒÚÛÔÌ˚ı ‰Îfl ÔÓÚð·ÎÂÌËfl ‚ ÏÓÏÂÌÚ t + 1, ‚ÍÛÔÂ Ò ðÂÌ-
ÚÓÈ, ÔðËÌÂÒfiÌÌÓÈ ËÏË Í ÏÓÏÂÌÚÛ t + 2. ëÓÓÚÌÓ¯ÂÌË (3.41)
Ôð‰ÒÚ‡‚ÎflÂÚ ÒÓ·ÓÈ Á‡ÍÓÌ ÙÛÌ͈ËÓÌËðÓ‚‡ÌËfl ÙË̇ÌÒÓ‚ÓÈ ÒËÒÚÂÏ˚
ÏÓ‰ÂÎËðÛÂÏÓÈ ˝ÍÓÌÓÏËÍË. éÌÓ ÔðflÏÓ ÒΉÛÂÚ ËÁ ÓÔð‰ÂÎÂÌËfl ðÂÌÚ˚.

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