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ï²£ă AbstractA theoretical consistency between the value structure of “average social capital” (illustrated in “Capital: Volume III”, “Chapter IX and Chapter X”) and that of two departments of reproduction (illustrated in “Capital: Volume II”, “Chapter XX. Simple Reproduction” and “Chapter XXI. Accumulation and Reproduction on an Extended Scale”) is examined.
For comparing these two value structure, the number of circulation of each capital in reproduction is assumed to be the same i.e. 1. Furthermore, a specific capital segments all capitals into two departments of reproduction, and the ratio of the first year of reproduction is used for this comparing.
The conclusion is that the Marx’s reproduction scheme is not always compatible with the spectrum of capitals including average social capital. This work does not show a general proof, but means that Marx’s numerical example contains the counter example in itself, and this conclusion is contradictory to his own description.
I. HN69
ÞĘ06ťŅÞľğ 3 µ 9 ĝ¹÷þ1Āānãť10 ĝ Ğ_4@CVİć÷þ5Ġ ¶ nã1¶ nrņŏ÷ example contains the counter example in itself, and this conclusion is con- tradictory to his own description.
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< ௗ , ܿ െ ܽ < ݀ െ ܾ, 0 < ݔ < 1͐͐ (3,1) ࡇࡢ㸪◚⥺MJ ࡣ♫ⓗᖹᆒ㈨ᮏ࠾ࡅࡿ㈝⏝౯᱁㒊ศࢆ㸪◚⥺ JE ࡣྠ㈨ᮏࡢಶู₶㒊ศࢆ♧ࡍࠋ ࠸ࡲ㸪㒊㛛I㸪㒊㛛 II ࡀ⏕⏘㒊㠃 SpȘࡼࡗ࡚༊ศࡉࢀࡿ㸪 㒊㛛I ᒓࡍࡿ⏕⏘㒊㠃ࡢ㈨ᮏᵓᡂࡀࡍ࡚㒊㛛 II ࡢࡑࢀࡼࡾ ࡶ㧗ࡃ࡞ࡿࠋࡼࡗ࡚㸪᭦௨ୗࡢࡼ࠺ᐃࡵ㸪⏕⏘᮲௳ࡢ㛵ಀ ࢆ୍⯡ⓗ᳨ウࡍࡿࡇࡋࡼ࠺ࠋ Ic : Iv= ܴூூ௩: 1 㸦ࡓࡔࡋܴூூ௩> 0㸧 IIc : IIv = ܴூூூூ௩: 1 㸦ࡓࡔࡋ ܴூூூூ௩> 0㸧 Ic㸸IIc= ܴூூூ: 1 㸦ࡓࡔࡋܴூூூ> 0㸧 వ౯್⋡= 100ܴ㸣㸦ࡓࡔࡋ ܴ> 0㸧 (3,2) 㒊㠃⏕⏘≀⥲౯᱁䠄⥲౯್䠅 㒊㠃⏕⏘≀⥲౯᱁䠄⥲౯್䠅 㒊㠃⏕⏘≀⥲౯᱁䠄⥲౯್䠅 㻽 㻽 㻽 㻴㻝 㻴㻝 㻴㻝 㻰㻝 㻿 㻗㻝 㻗㻝␒┠䛾⏕⏘㒊㠃 㻰㻝 㻿㼜 㼚㻗㻝㻦 㼚㻗㻝␒┠䛾⏕⏘㒊㠃 㻰㻝 㻿㼜㻌㼚㻗㻝㻦㻌㼚㻗㻝␒┠䛾⏕⏘㒊㠃 㻔䛯䛰䛧㼚䛿ṇ䛾ᩚᩘ䠅 㻔䛯䛰䛧㼚䛿ṇ䛾ᩚᩘ䠅 㻔䛯䛰䛧 䛿ṇ䛾ᩚᩘ䠅 㻯㻝 వ౯್⋡ 㻾 㻳㻵㻛㻵㻭 䠄 㻝㻜㻜 䠂䠅 㻯㻝 వ౯್⋡䠙㻾㼙䠙㻳㻵㻛㻵㻭 䠄㽢㻝㻜㻜䠙䠂䠅 㻯㻝 వ౯್⋡䠙㻾㼙䠙㻳㻵㻛㻵㻭㻌䠄㽢㻝㻜㻜䠙䠂䠅 㻱 㻮㻝 ᖹᆒ₶⋡䠄 ⯡ⓗ₶⋡䠅䠙㻴㻝㻯㻝㻛㻯㻝㻺 㻱 㻮㻝 ᖹᆒ₶⋡䠄୍⯡ⓗ₶⋡䠅䠙㻴㻝㻯㻝㻛㻯㻝㻺 㻱 㻮㻝 ᖹᆒ₶⋡䠄 ⯡ⓗ₶⋡䠅 㻴㻝㻯㻝㻛㻯㻝㻺 㻰㻞 㻰㻞 㻵㼙 䕕㻮㻞㻺㻞㻺㻮㻝䠙㻵㼏 㻰㻞 㻵㼙 䕕㻮㻞㻺㻞㻺㻮㻝䠙㻵㼏 㻵 䕕㻯㻞㻮㻞㻮㻝㻯㻝 㻵 㻵㼢 䕕㻯㻞㻮㻞㻮㻝㻯㻝䠙㻵㼢 㻵㼢 䕕㻯㻞㻮㻞㻮㻝㻯㻝䠙㻵㼢 㻴㻞 㻶 䕕㻰㻞㻯㻞㻯㻝㻰㻝䠙㻵㼙 㻴㻞 㻶 䕕㻰㻞㻯㻞㻯㻝㻰㻝䠙㻵㼙 㻴㻞 㻶 䕕㻰㻞㻯㻞㻯㻝㻰㻝 㻵㼙 㻳 䕕㻭㻜㻺㻞㻮㻞䠙㻵㻵㼏 㻳 䕕㻭㻜㻺㻞㻮㻞䠙㻵㻵㼏 㻵㻵 㻯㻞 㻷 䕕㻵㻭㻮㻞㻯㻞 㻵㻵 㻵㻵㼙 㻯㻞 㻷 䕕㻵㻭㻮㻞㻯㻞䠙㻵㻵㼢 㻵㻵㼙 㻯㻞 㻷 䕕㻵㻭㻮㻞㻯㻞䠙㻵㻵㼢 㼐 㼏 䕕㻳㻵㻯㻞㻰㻞䠙㻵㻵㼙 㼐 㼏 䕕㻳㻵㻯㻞㻰㻞䠙㻵㻵㼙 㼐 㼏 䕕㻳㻵㻯㻞㻰㻞 㻵㻵㼙 㻵㻵㼢 㻮㻞 㻵㻵㼢 㻮㻞 㻵 㻵 㻵 㻵㼏 㻵 㻵㼏 㼍 㻵㻵㼏 㼍 㻵㻵㼏 㻭 㼤 㻝 㻭 㼤 㻝㻙㼤 㻭 㼤 㻝 㼤 㼎㼎 㻺㻞 㻹 㻺 㒊㠃ᩘ 㻺㻞 㻹 㻺 㒊㠃ᩘ 㻺㻞 㻹 㻺 㒊㠃ᩘ 㻔㒊㠃ྡ㻕 㻾 㻜 㻔㻿㼜 㻝㻕 㻿㼜䃐 㻔㻿㼜 㼚㻗㻝㻕 㻔㻿㼜 㻞㼚㻗㻝㻕 㻔㒊㠃ྡ㻕 㻾 㻜 㻔㻿㼜㻌㻝㻕 㻿㼜䃐 㻔㻿㼜㻌㼚㻗㻝㻕 㻔㻿㼜㻌㻞㼚㻗㻝㻕 㻔㒊㠃ྡ㻕 㻾 㻜 㻔㻿㼜㻌㻝㻕 㻿㼜䃐 㻔㻿㼜㻌㼚 㻝㻕 㻔㻿㼜㻌㻞㼚 㻝㻕 㒊㛛 㻵㻵 㒊㛛 㻵 㒊㛛 㻵㻵 㒊㛛 㻵 㒊㛛㻌㻵㻵 㒊㛛㻌㻵 㻝㻝 ᅗ㻟 ≉ᐃ䛾⏕⏘㒊㠃䛷㒊㛛䛜ศ䛥䜜䜛ሙྜ䐠 ᅗ㻟 ≉ᐃ䛾⏕⏘㒊㠃䛷㒊㛛䛜ศ䛥䜜䜛ሙྜ䐠 ᅗ㻟䚷≉ᐃ䛾⏕⏘㒊㠃䛷㒊㛛䛜ศ䛥䜜䜛ሙྜ䐠
- 4/ťyĀāĴ½ö*%ße6ťé5(1)A(4)0C (1) IcŨIvŪB2N2NB1 5śęŨC2B2B1C1 5śęŪ @ Bť Ĩ{ B2N2 5Œ"Ū Ĩ{ C2B2 5Œ"ŪĨ{ C2N2 5Œ"– Ĩ{ B2N2 5Œ" Ū +Ať (2,1)@B +Ať!DGÔÿ%C1ť (3,3) (i) 5oÓ4./ Ð(3,1),(3,2)@B +Ať 5oÓ ū0 @-/ť (3,4) (ii) 13Cße6ť ³ŊG¢¿%C1ť @-/ (3,5) (iii) 13Cße6ť
!DGÔÿ%C1ť +A (3,6) @-/(3,5) (3,6)5 (3,4)6 13C (2) IIc IIvŪ @Bť (3,1)@B +Ať!DGÔÿ%C1ť (3,7) (i) 5oÓ4./ Ð(3,1),(3,2)@B +Ať 5oÓ @-/ť (3,8) (a) 13Cße6ť @-/ (3,9) (b) 13Cße6ť !DGÔÿ%C1ť (3,10) @-/(3,9) (3,10)5 (3,8)6 13C
(3) IcŨIIcŪB2N2NB 5śęŨA0N2B2 5śęŪ @Bť (3,1)@B +Ať!DGÔÿ%C1ť 5}~½6ť Ð(3,1),(3,2)@B @-/ 6é5 2 .5¬ÓķGÍ. ##Ð(3,1),(3,2)@Bť{í +Ať 13C56ť (3,11) 5 4ŗADC !5Ùť (i) 13Cße6ť +Ať [Ŋ6êÓ+A(D)D2 ^#/Ôÿ%C1ť !D6Ð(3,1),(3,2)@B¸4ÉBĜ. (ii) 13Cße6ť +Ať
!DGÔÿ%C1ť [Ŋ6êÓ+A(D)D2 ^#/Ôÿ%C1ť Ð(3,1),(3,2)@B +Ať !D6¸4ÉBĜ. @-/ťÐ(3,1),(3,2)5X0ť(3,11)Ē% 6ť 13C (4) IIcŪIv+Im @Bť+ IIc = A0N2B2 5śę (3,12) ;*ťIv+Im = Iv =C2B2B1C1 5śę Ţ ĀāŐś5knrþŪš+Ať ţ @-/ť Iv +Im = (3,13) (3,12) = (3,13)+Ať (2,14)@B +A!DGÔÿ%C1ť (3,14) (i) 5oÓ4./ Ð(3,1),(3,2)@B + Ať (ii) 5oÓ 5 ť
!DG¢¿%C1 (3,15) !5Ù(3,14)@Bť @-/ť (3,16) Ð(3,1),(3,2)@B{í +Ať (a) 13C56ť (3,16)5{¨ !D6Ð(3,1),(3,2)@B¸4ÉĜ%C (b) 13C56ť @-/ (3,17) (3,15)G(3,17)4ct%C1ť !DGÔÿ%C1ť Ð(3,1),(3,2)@B +Ať !D6¸4ÉĜ%C @-/ťÐ(3,1),(3,2)5?10ť(3,16)6¸4 Gö*% (iii) 5oÓ 5 ť b
1ĩ1ť !5ÙťÐ(3,1),(3,2)@Bť (3,18) (3,19) (3,20) (3,21) 13C56ť @-/ťŕÓ5ŝø5 ¼è6ť (3,22) (a) (3,14)5 5oÓê5 ť +Ať @-/!D6ť 5 ť 5 ť (3,23)
ሙྜศࡅࡉࢀࡿࠋ ๓ᥦ(3,1),(3,2)ࡼࡾ െܽ < 0 < ܴ(ܽ െ ܾ) ࡔࡽ㸪 㛵ᩘ݂(ݔ)ࡢ㡬Ⅼࡢ ݔ ᗙᶆ= െܽെܴ݉(ܽെܾ) (െܽ+ܿ)+ܴ݉(െܽ+ܾ+ܿെ݀)< 0 ࡇࢀ(3,18),(3,19),(3,20),(3,21)ࡼࡾ㸪㛵ᩘ݂(ݔ)ࡣᅗ ♧ࡉࢀࡿࠋ ࡇࡢ݂(ݔ) ࡣ 0 < ݔ < 1 ゎࢆ 1 ࡘᣢࡘࠋࡲࡓ㸪 ݔ = ିଶ{ାோ(ି)}ାට൛ଶ{ାோ(ି)}ൟ మିସ{(ିା)(ଵାோ )ା(ିௗ)ோ}{ି(ଵାோ)(ିାିௗ)} ଶ{(ିା)(ଵାோ)ା(ିௗ)ோ} ͐͐ (3,24) (b) (3,14)ࡢ ݔଶ ࡢಀᩘࡀ㈇ࡢሙྜ㸪 (െܽ + ܿ)(1 + ܴ) + (ܾ െ ݀)ܴ< 0 ࡔࡽ㸪 െܽ + ܿ + ܴ(െܽ + ܾ + ܿ െ ݀) < 0 㡬Ⅼ䛾 ᗙᶆ 㻜 㻝 㻜 㻝 㡬Ⅼ䛾 ᗙᶆ ᅗ㻠 䛾ಀᩘ䛜ṇ䛾ሙྜ ᅗ㻡 䛾ಀᩘ䛜㈇䛾ሙྜ
@-/!D6ť 5 ť 5 ť 1 { "DC Ð(3,1),(3,2)@B +Ať ŕÓ5ŝø5 ¼è Ú4ť 13C56ť 5 0Bť!D6Ð (3,1),(3,2)5?10¸4ÉBĜ. @-/ť!D1(3,18),(3,19),(3,20),(3,21)@Bťŕ Ó6- 4Ē"Dť 6 4ķG 1 .Í.!5Ùť 13Bť 5oÓê5 5â143C (5) ēgć¹ŅÞ5q~÷þŪ¹÷þ@B ēgć¹ŅÞ5q~÷þ ĐĨ 5Œ" ĐĨ 5Œ" (3,26) ¹÷þ (3,25)
(3,27) Ic+IIcB2N2NB1+A0N2B2 5śę5śę Iv+IIvIAB2C2 5śę+C2B2B1C1 5śę @-/Ð(3,1),(3,2)@B +Ať (3,26)=(3,27)6¸4ÉBĜ.@-/ťÐ (3,1),(3,2)4 /ēgć¹ŅÞ5q~÷þ¹÷þ6 16ùŕo4ÉBĜ. (6) ¯ó !D;05ĥáG;1>C1ťÐ(3,1),(3,2)5?10 13C56ť (1)@Bť 5ße6ť (3,5) . (3,6) !5 4ť (3,4)
(2)@Bť 5ße6ť (3,9) . (3,10) !5 4ť (3,8) (3)@Bť (3,11) Ţ!5Ù 6¸4 ţ (4)@Bť 5oÓ 5 6ť (3,15) !5 4ť (3,16) C6ť 5oÓ 5 6ť (3,24) (5)@BťÐ(3,1),(3,2)5X0 6 5u/5rG1BC
(7) ;Ð(3,1)Gö*%Ór1#/ťÚ4 (3,28) 1%C ēgć¹ŅÞ1yĀāĴ½4 CyĀāGĮ4 %CŅÞ{·¸4[Ĝ%C3Aťēgć46ÊZ0 C!DA5r5X0?ťWĹ5ĿŕoGö*%ŅÞ{·6 ¸4ÉBĜ*3 D73A36&0C (!0!D;0ÂAD*Ŀŕo4!DAGct%C1ť (i) (4)5 5oÓ 5 6ť (a) (3,15)@Bť +A (b) (3,16)@Bť (c) (3,28),(3,29)Gť 4ġße53(3,11)4c t%C1ť !DGÔÿ%C1ť 4./}~½5rGð>C1ť @-/ 6¬ÓķGÍ.ť C6 13BťÐ(3.1)5 4%C (3,29)
@-/ 5oÓ 5 ť 5ģ'6©#3 (ii) (4)5 5oÓ 5 ť (a) 5oÓ 5 @-/ 1!E(3,28)@B +Ať!5 ť ÐGö*% 5ģ'6© #3 (b) 5oÓ 5 @-/ ;*ť +Ať(3,23)@Bť @-/(3,25)@B 6ÉĜ%C!10 C !5Ùť (3,30) 13BťÐ(3,1)5 ?ö*"DC @-/(3,28)6ť(4)5 5oÓ 5 4Ä#*Ó rm0C!1FC (!0ť 5oÓ 5 4Ä#*Órm0C (3,28)5 4 5Ŕ425@3ŕo ÉĜ%C5Gé4đļ%C!14#@ (8) 5ŕo
@-/ť (3,31) (3,31)4(3,28),;*(3,30)@B 1#/ct%C1ť @-/ť (3,32) (9) (3,28), (3,32)5?10ť(1),(2)0Ē"D* 5ßeÚ 4 Cŗ« (i) (1)5(3,5)1(3,6)4/ť !DGÔÿ%C1 3 +Ať 3 >0 (3,32)@B
@-/(1)1(2)6°31?é5 4ÉBĜ. (3,33) (ii) (2)5(3,9)1(3,10)4/ť !DGÔÿ%C1 +Aťç4ť @-/(1)1(2)6°31?é5 4ÉBĜ. (3,34) (10) !DA(3,33),(3,34)5X0ÉBĜ.ŕoG;1>ť(D4 (3,28)5ÓrGct#/ 5Ŕ5ŕoGð >C (i) (3,4)(3,8)@Bť (3,28)5ÓrGct#/ť (3,35) (ii) (3,8)(3,11)@Bť
(3,28)5ÓrGct#/ť (3,36) (iii) (3,8)(3,24)@Bť (3,28)5ÓrGct#/ť (3,37) (iv) (3,33)@Bť (3,28)5ÓrGct#/ (3,38) (v) (3,34)@Bť (3,28)5ÓrGct#/ (3,39) (11) !DA(3,32),(3,35),(3,36),(3,37),(3,38),(3,39)@8Ð (3,2)5ŕoGĒ%C !DA5ŕoGĴ#*?5- 0C - A6ť ¸4©%C56ť]¦ 5 3 śÙ4a´%C 1 ø4ŗADC!1{C 1!E0ť!5- 5]¦53 śÙ4a´%C 1 ø 4C A®DC 6 0
C!1×4đļ"D/C @-/ťÐ(3,1)Gö*%(3,28)5 46ťÐ(3,2)G ö*% ©#ť(DA5Ór5X0 13Cvō5 ©%C!143Cť ©#ÂC56å>/ŗAD* 0C !1ť!50Ē"DC!143C dWÞĘ06ťÌ¤yĀā zĆĴ½ğ1 mPLRť%3F,ť ¤ŐœwŐ5c:v î¤ŐœŔ0ą3C 4./ťü«5Őś ŅÞ4@BŐśĿŅÞ ¤ŐœŔ4{DC 5äĸGij-* äĸ4ř#/6ťēgć¹ŅÞ5Ĵ%ħŅÞ5{·ýÈ1yĀ āĴ½4 CŅÞ{·GîʼnĮ3¿4¢Ñ%C*>4ťyĀā 4 CŅÞ5ňÓG 1%CÐGĩ* äĸ5ĥáťĀāŐś5ħĀāû4 Cc+v 5nrťÁ-/ ħńĂnãťĠ´G3% ťēgć¹ŅÞG©"'CŅÞ {·1yĀāĴ½5yĀāGĮ4%CŅÞ{·16ťå>/ŗA D* 4#[Ĝ'&ť ŢŞţ(1)A(5)5ŕoťÐ(3,1)Gö*%fÇ5ŦŦŦ 5 ?10ťÐ(3,1)Gö*%fÇ5ŦŦŦ 4/ ÉĜ%C 6ÉBĜ*3!1ĥľ1#/ÂAD* ÞĘyĀā4 CŅÞ5ňÓG 1%CÐGÍ.!1 AťÞĘ5ĥľGĊ,4Vİ %C!1603##ťÞĘ 5ĥľ6ťNRHJ5Órmįj4NRHJįŇ5ŋ1ĎČ%C m;DC!1GĒ#/C éĘ06ťì"D*ĽŞOHN P"OHN P5äĸ4Ŏ=!14# @
ூூூ ㍈ ோೡ ିଵ ଵǤହାǤସோ ೡ ൌ ିǤହሺோ ାଵሻା ඥ ሺோ ାଵሻሺǤଶହோ ାସሻ ଵǤହሺோ ାଵ ሻ Ⅼ ூ ூ௩ ㍈ ூூூூ௩ ㍈ ூ ூ௩ ூ ூ௩ ூூூூ௩ ᅗ ࡢሙྜ㸪 ࡽ ࢆྠᡂ❧ࡉࡏࡿ ூ ூ௩ ǡ ூூூூ௩ ூூூ ࡢ⤌ྜࡏ ூ ூ௩ ூூூூ௩ ூூூ ܴூூூூ௩ െͳ ͳǤͷ ͲǤͶܴ ூூூூ௩ ൌ െ͵ ξͳʹǤ͵ ͳǤͶ ͲǤܴ ூூ௩ െ ʹǤͷ ͳǤͷ ͲǤͶܴ ூூ௩ ൌ ܴூூூூ௩ െͳ ͲǤͷ ͲǤͶܴ ூூூூ௩ ூூூூ௩
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NRHJťK.(1885/1985)ŅÞľ ğ 2 µ ğ 3 {xēgĕªďĚ ÊĈpTŅÞľīϧgĻťğ 7 {xťÕØÞzúē ŬMarx, Karl. Das Kapital: Kritik der politischen Ökonomie. Zweiter Band, Buch II: Der Cirkulationsprocess des Kapitals. Herausgegëben von Friedrich Engels. Hamburg: Verlag von Otto Meissner, 1885. Herausgegeben von Institut für
Marxismus-Leninismus beim ZK der SED. Band 24 der Werke von Marx und Engels. Berlin : Diez Verlag, 1969.ŭ
(1894/1987)ŅÞľ ğ 3 µēgĕªďĚÊĈpT
ŅÞľīϧgĻťğ9 {xťÕØÞzúē
ŬMarx, Karl. Das Kapital: Kritik der politischen Ökonomie. Dritter Band, Hamburg: Verlag von Otto Meissner, 1894.Herausgegeben von Institut für
Marxismus-Leninismus beim ZK der SED. Band 25 der Werke von Marx und Engels. Berlin : Diez Verlag, 1976.ŭ
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