Стоимость в экономических системах. Светлов Н.М. - 96 стр.

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96
ÔÓÚð·ËÚÂÎfl ‚ Â„Ó ÏÌÓÊÂÒÚ‚Â X
i
∩ B
i
Ì ÒÛ˘ÂÒÚ‚ÛÂÚ Ì‡·ÓðÓ‚, ÍÓ-
ÚÓð˚ ÓÌ ÏÓ„ ·˚ Ôð‰ÔÓ˜ÂÒÚ¸ ‚˚·ð‡ÌÌÓÏÛ Ì‡·ÓðÛ x
i
.
àÁ ÓÔð‰ÂÎÂÌËfl ÍÓÌÍÛðÂÌÚÌÓ„Ó ð‡‚ÌÓ‚ÂÒËfl ÒΉÛÂÚ, ˜ÚÓ ÓÌÓ fl‚-
ÎflÂÚÒfl ˜‡ÒÚÌ˚Ï ÒÎÛ˜‡ÂÏ ð˚ÌÓ˜ÌÓ„Ó ð‡‚ÌÓ‚ÂÒËfl, ÍÓ„‰‡ ‰ÓÒÚË„‡˛ÚÒfl
ÓÔÚËÏÛÏ˚ Ôð‰ÔÓ˜ÚÂÌËÈ ‚ÒÂı ÔÓÚð·ËÚÂÎÂÈ Ë Ï‡ÍÒËÏÛÏ˚ ÔðË·˚ÎË
‚ÒÂı ÔðÓËÁ‚Ó‰ËÚÂÎÂÈ.
ÇÂÍÚÓðÓÏ ð‡‚ÌÓ‚ÂÒÌ˚ı ˆÂÌ Ì‡Á˚‚‡ÂÚÒfl ‚ÂÍÚÓð p, ÔðË ÍÓÚÓðÓÏ
‰ÓÒÚË„‡ÂÚÒfl ÍÓÌÍÛðÂÌÚÌÓ ð‡‚ÌÓ‚ÂÒËÂ. äÓÏÔÓÌÂÌÚ˚ ˝ÚÓ„Ó ‚ÂÍÚÓð‡ ̇-
Á˚‚‡˛ÚÒfl ð‡‚ÌÓ‚ÂÒÌ˚ÏË ˆÂ̇ÏË.
óÚÓ·˚ ÔÓÌflÚ¸, ͇ÍËÏ Ó·ð‡ÁÓÏ ˆÂÌ˚ ÏÓ„ÛÚ ÒÓ-
‰ÂÈÒÚ‚Ó‚‡Ú¸ ‰ÓÒÚËÊÂÌ˲ ÍÓÌÍÛðÂÌÚÌÓ„Ó ð‡‚ÌÓ-
‚ÂÒËfl, ð‡ÒÒÏÓÚðËÏ Á‡‚ËÒËÏÓÒÚ¸ ‚Â΢ËÌ Ë̉Ë-
‚ˉۇθÌÓ„Ó Ôð‰ÎÓÊÂÌËfl Ë ÒÔðÓÒ‡ ÓÚ ‚ÂÍÚÓð‡ p. ç‡ Ôð‰ÎÓÊÂÌËÂ
‚ÂÍÚÓð p ‚ÎËflÂÚ ÔÓÚÓÏÛ, ˜ÚÓ ËÁÏÂÌfl˛ÚÒfl ‚Â΢ËÌ˚ ÔðË·˚ÎÂÈ, ÒÓÓÚ‚ÂÚ-
ÒÚ‚Û˛˘Ëı ð‡Á΢Ì˚Ï ÚÂı
ÌÓÎӄ˘ÂÒÍËÏ ÔðÓˆÂÒÒ‡Ï ËÁ ÚÂıÌÓÎӄ˘ÂÒÍÓ„Ó
ÏÌÓÊÂÒÚ‚‡ Í‡Ê‰Ó„Ó ÔðÓËÁ‚Ó‰ËÚÂÎfl. ç‡ ÒÔðÓÒ — ÔÓÚÓÏÛ, ˜ÚÓ ÏÂÌflÂÚÒfl
·˛‰ÊÂÚÌÓ ӄð‡Ì˘ÂÌË ‚ÒΉÒÚ‚Ë ËÁÏÂÌÂÌËfl ÒÓ‚ÓÍÛÔÌÓÈ ÒÚÓËÏÓÒÚË
̇˜‡Î¸ÌÓÈ ÒÓ·ÒÚ‚ÂÌÌÓÒÚË, Ò Ó‰ÌÓÈ ÒÚÓðÓÌ˚, ‚Â΢ËÌ ð‡ÒÔð‰ÂÎflÂÏÓÈ
ÔðË·˚ÎË, Ò ‰ðÛ„ÓÈ.
à̉˂ˉۇθ̇fl ÙÛÌ͈Ëfl Ôð‰ÎÓÊÂÌËfl ÔðÓËÁ‚Ó‰ËÚÂÎfl k Á‡ÔË-
Ò˚‚‡ÂÚÒfl ÒÎÂ‰Û˛˘ËÏ Ó·ð‡ÁÓÏ:
ш
k
(p) = {y
k
| ‹ p, y
k
› = max ‹ p, y' ›, y' ∈ Y
k
}. (3.11)
á̇˜ÂÌË ˝ÚÓÈ ÙÛÌ͈ËË Ôð‰ÒÚ‡‚ÎflÂÚ ÒÓ·ÓÈ, Í‡Í ‚ˉÌÓ ËÁ ÙÓðÏÛÎ˚,
ÏÌÓÊÂÒÚ‚Ó ‚ÂÍÚÓðÓ‚ y
k
, χÍÒËÏËÁËðÛ˛˘Ëı ÔðË·˚θ ÔðÓËÁ‚Ó‰ËÚÂÎfl k
ÔðË Á‡‰‡ÌÌÓÏ ‚ÂÍÚÓð ˆÂÌ p.
óÚÓ·˚ ‚‚ÂÒÚË Ë̉˂ˉۇθÌ˚ ÙÛÌ͈ËË ÒÔðÓÒ‡, Ì‡Ï ÔÓÚð·ÛÂÚ-
Òfl Ë̉˂ˉۇθ̇fl ÙÛÌ͈Ëfl ÔðË·˚ÎË ÔðÓËÁ‚Ó‰ËÚÂÎfl:
р
k
(p) = ‹ p, ш
k
(p) › = max ‹ p, y' ›, y' ∈ Y
k
. (3.12)
á̇˜ÂÌË ˝ÚÓÈ ÙÛÌ͈ËË — ‚¢ÂÒÚ‚ÂÌÌÓ ˜ËÒÎÓ, ð‡‚ÌÓ ÔðË·˚ÎË, ÔðË-
ÌÓÒËÏÓÈ ÔðÓËÁ‚Ó‰ËÚÂβ ‚˚·ð‡ÌÌ˚Ï ÚÂıÌÓÎӄ˘ÂÒÍËÏ ÔðÓˆÂÒÒÓÏ y
k
.
à̉˂ˉۇθÌ˚ ÙÛÌ͈ËË ÒÔðÓÒ‡ ‚ÓÁ‚ð‡˘‡˛Ú ÏÌÓÊÂÒÚ‚Ó ‚ÂÍ-
ÚÓðÓ‚ x
i
, ̇˷ÓΠÔð‰ÔÓ˜ÚËÚÂθÌ˚ı ‰Îfl ÔÓÚð·ËÚÂÎfl i ‚ ð‡Ï͇ı „Ó
·˛‰ÊÂÚÌÓ„Ó Ó„ð‡Ì˘ÂÌËfl ÔðË ˆÂ̇ı p:
îÛÌ͈ËË ÒÔðÓÒ‡ Ë Ôð‰-
ÎÓÊÂÌËfl
      ÔÓÚð·ËÚÂÎfl ‚ Â„Ó ÏÌÓÊÂÒÚ‚Â Xi ∩ Bi Ì ÒÛ˘ÂÒÚ‚ÛÂÚ Ì‡·ÓðÓ‚, ÍÓ-
                                                                  i
        ÚÓð˚ ÓÌ ÏÓ„ ·˚ Ôð‰ÔÓ˜ÂÒÚ¸ ‚˚·ð‡ÌÌÓÏÛ Ì‡·ÓðÛ x .
        àÁ ÓÔð‰ÂÎÂÌËfl ÍÓÌÍÛðÂÌÚÌÓ„Ó ð‡‚ÌÓ‚ÂÒËfl ÒΉÛÂÚ, ˜ÚÓ ÓÌÓ fl‚-
ÎflÂÚÒfl ˜‡ÒÚÌ˚Ï ÒÎÛ˜‡ÂÏ ð˚ÌÓ˜ÌÓ„Ó ð‡‚ÌÓ‚ÂÒËfl, ÍÓ„‰‡ ‰ÓÒÚË„‡˛ÚÒfl
ÓÔÚËÏÛÏ˚ Ôð‰ÔÓ˜ÚÂÌËÈ ‚ÒÂı ÔÓÚð·ËÚÂÎÂÈ Ë Ï‡ÍÒËÏÛÏ˚ ÔðË·˚ÎË
‚ÒÂı ÔðÓËÁ‚Ó‰ËÚÂÎÂÈ.
        ÇÂÍÚÓðÓÏ ð‡‚ÌÓ‚ÂÒÌ˚ı ˆÂÌ Ì‡Á˚‚‡ÂÚÒfl ‚ÂÍÚÓð p, ÔðË ÍÓÚÓðÓÏ
‰ÓÒÚË„‡ÂÚÒfl ÍÓÌÍÛðÂÌÚÌÓ ð‡‚ÌÓ‚ÂÒËÂ. äÓÏÔÓÌÂÌÚ˚ ˝ÚÓ„Ó ‚ÂÍÚÓð‡ ̇-
Á˚‚‡˛ÚÒfl ð‡‚ÌÓ‚ÂÒÌ˚ÏË ˆÂ̇ÏË.
îÛÌ͈ËË ÒÔðÓÒ‡ Ë Ôð‰- óÚÓ·˚ ÔÓÌflÚ¸, ͇ÍËÏ Ó·ð‡ÁÓÏ ˆÂÌ˚ ÏÓ„ÛÚ ÒÓ-
ÎÓÊÂÌËfl               ‰ÂÈÒÚ‚Ó‚‡Ú¸ ‰ÓÒÚËÊÂÌ˲ ÍÓÌÍÛðÂÌÚÌÓ„Ó ð‡‚ÌÓ-
                       ‚ÂÒËfl, ð‡ÒÒÏÓÚðËÏ Á‡‚ËÒËÏÓÒÚ¸ ‚Â΢ËÌ Ë̉Ë-
‚ˉۇθÌÓ„Ó Ôð‰ÎÓÊÂÌËfl Ë ÒÔðÓÒ‡ ÓÚ ‚ÂÍÚÓð‡ p. ç‡ Ôð‰ÎÓÊÂÌËÂ
‚ÂÍÚÓð p ‚ÎËflÂÚ ÔÓÚÓÏÛ, ˜ÚÓ ËÁÏÂÌfl˛ÚÒfl ‚Â΢ËÌ˚ ÔðË·˚ÎÂÈ, ÒÓÓÚ‚ÂÚ-
ÒÚ‚Û˛˘Ëı ð‡Á΢Ì˚Ï ÚÂıÌÓÎӄ˘ÂÒÍËÏ ÔðÓˆÂÒÒ‡Ï ËÁ ÚÂıÌÓÎӄ˘ÂÒÍÓ„Ó
ÏÌÓÊÂÒÚ‚‡ Í‡Ê‰Ó„Ó ÔðÓËÁ‚Ó‰ËÚÂÎfl. ç‡ ÒÔðÓÒ — ÔÓÚÓÏÛ, ˜ÚÓ ÏÂÌflÂÚÒfl
·˛‰ÊÂÚÌÓ ӄð‡Ì˘ÂÌË ‚ÒΉÒÚ‚Ë ËÁÏÂÌÂÌËfl ÒÓ‚ÓÍÛÔÌÓÈ ÒÚÓËÏÓÒÚË
̇˜‡Î¸ÌÓÈ ÒÓ·ÒÚ‚ÂÌÌÓÒÚË, Ò Ó‰ÌÓÈ ÒÚÓðÓÌ˚, ‚Â΢ËÌ ð‡ÒÔð‰ÂÎflÂÏÓÈ
ÔðË·˚ÎË, Ò ‰ðÛ„ÓÈ.
        à̉˂ˉۇθ̇fl ÙÛÌ͈Ëfl Ôð‰ÎÓÊÂÌËfl ÔðÓËÁ‚Ó‰ËÚÂÎfl k Á‡ÔË-
Ò˚‚‡ÂÚÒfl ÒÎÂ‰Û˛˘ËÏ Ó·ð‡ÁÓÏ:
                 k         k       k
               ш (p) = {y | ‹ p, y › = max ‹ p, y' ›, y' ∈ Yk}.       (3.11)
á̇˜ÂÌË ˝ÚÓÈ ÙÛÌ͈ËË Ôð‰ÒÚ‡‚ÎflÂÚ ÒÓ·ÓÈ, Í‡Í ‚ˉÌÓ ËÁ ÙÓðÏÛÎ˚,
                       k
ÏÌÓÊÂÒÚ‚Ó ‚ÂÍÚÓðÓ‚ y , χÍÒËÏËÁËðÛ˛˘Ëı ÔðË·˚θ ÔðÓËÁ‚Ó‰ËÚÂÎfl k
ÔðË Á‡‰‡ÌÌÓÏ ‚ÂÍÚÓð ˆÂÌ p.
       óÚÓ·˚ ‚‚ÂÒÚË Ë̉˂ˉۇθÌ˚ ÙÛÌ͈ËË ÒÔðÓÒ‡, Ì‡Ï ÔÓÚð·ÛÂÚ-
Òfl Ë̉˂ˉۇθ̇fl ÙÛÌ͈Ëfl ÔðË·˚ÎË ÔðÓËÁ‚Ó‰ËÚÂÎfl:
                 k             k
                р (p) = ‹ p, ш (p) › = max ‹ p, y' ›, y' ∈ Yk .       (3.12)
á̇˜ÂÌË ˝ÚÓÈ ÙÛÌ͈ËË — ‚¢ÂÒÚ‚ÂÌÌÓ ˜ËÒÎÓ, ð‡‚ÌÓ ÔðË·˚ÎË, ÔðË-
                                                                      k
ÌÓÒËÏÓÈ ÔðÓËÁ‚Ó‰ËÚÂβ ‚˚·ð‡ÌÌ˚Ï ÚÂıÌÓÎӄ˘ÂÒÍËÏ ÔðÓˆÂÒÒÓÏ y .
     à̉˂ˉۇθÌ˚ ÙÛÌ͈ËË ÒÔðÓÒ‡ ‚ÓÁ‚ð‡˘‡˛Ú ÏÌÓÊÂÒÚ‚Ó ‚ÂÍ-
       i
ÚÓðÓ‚ x , ̇˷ÓΠÔð‰ÔÓ˜ÚËÚÂθÌ˚ı ‰Îfl ÔÓÚð·ËÚÂÎfl i ‚ ð‡Ï͇ı „Ó
·˛‰ÊÂÚÌÓ„Ó Ó„ð‡Ì˘ÂÌËfl ÔðË ˆÂ̇ı p:

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