2015 1 31 1 ( ) 1 ( ) 2 ( ) ( 25380245) This work was supported by Grand-in-Aid for Scientific Research (Research No.25380245). 1
( [2], 1 p.38.) 1. [1] C R n y C u = (u 1,, u n ) α n u i y i > α i=1 n u i x i α, x C i=1 α 1 2 f(x) g(x) f(x) g(x) 1 ( 1 ) A B a b O a O b A B v a v b O a v a C(a) O b v b C(b) C(a) C(b) 0 A B O a O b a b 0 a b 0 O a O b ( ) C(a) C(b) a O a v a O b v b O a O b v a v b C(a) C(b) [1] n 2 1 [3] 6 2 [1](p.81.) http://shiozawa.net/fukuzatsukeikeizaigaku/yoshitoshomei.html#teiri1 2
A a > 0 B b > 0 u A B ( ) ( ) A u + u A u = u + u B A u B u + A u A B a b a = a + u = (a + u + ) u 0 b = b u = (b u + ) + u 0 A B v a v b u u, v b < 0 < u, v a a, v a b, v b a + u, v a = a, v a + u, v a > a, v a b u, v b = b, v b u, v b > b, v b a + u, v a > a, v a b u, v b > b, v b u ( ) p ( ) ( ) n p = (p 1, p 2,, p n ) C(a) C(b) ( ) ( ) A B 2 ( ) (= ) 1 2 p 1 p 2 3
1000 1000 1 2000 1 1000 p 1 = 1 p 2 = 2 p = (1, 2) 1 2000 (1000 2 ) u = (+2, 1) A u = (+2, 1) B u = ( 2, +1) 0 1 1 1 u v a 90 u v b 90 0 u p ( ) ( ) 3 3 60 60 3 60.05 (1)60 60.05 (2)60 60.05 ( [5] p.46.) 60 59.95 60 59.95 2 3 3 [5] 5 6 4
commodity2 a vb +u a p b -u -u va b commodity1 +u 1: 5
( [4] p.367.) ( [4] p.368.) ( ) 6
( ) 4 ( ) ( ) ( ) 5 1 1 A 1 B 1 1 2 A 1 A 2 u A1 u A2 u A1 u A2 ( 1 ) +4 +5 B 1 B 2 u B1 u B2 ( 1 ) 2 1 ( ) 2 ( ) 1 ( ) 2 u A1 p A1 u B1 p B1 p p A1 p B1 1 A 2 ( ) p A1 p B1 2 ( ) 4 (special quote) (opening price) (pre-opening quote) ( ) 5 7
( ) ( ) ( ) Seller Volume of Offer (sell) Price (Yen) Volume of Bid (buy) Buyer A2 1 5 A1 2 4 3 2 2 B1 1 5 B2 1: 4 ( ) 8
commodity2 -ub2 pa1 pb1 -ub1 commodity1 +4 +5-2 -1 +ua2 +ua1 図 2: 板と交換ベクトル 9
( ) ( ) ( ) 3 ( ) 1 ( ) u 1 2 ( ) u 2 u 1 p 1 2 u 2 p 2 2 +u 1 u 2 1 2 2 2 1 1 u 1 + u 2 1 ( ) 2 ( ) 5 U-Mart ( ) 10
commodity2 p1 -u1 -u2 p2 +u1 - u2 commodity1 -u1+u2 +u2 +u1 3: 11
( ) GDP 1980 30 [1].., 1 1., 2004. [2] Adam Smith. An Inquiry into the Nature and Causes of the Wealth of Nations. 1776. ( (1)(2)(3)(4) 2000-01.). [3].., 2011. [4] Ludwig von Mises. Human Action: A Treaties on Economics. Henry Regnery, third edition, 1966. Reprinted in Human Action, ed. by Bettina Bien Greaves, Liberty Fund, 2007. (, 1991.). [5] Léon Walras. Eléments d économie politique pure ou Théorie de la richesse sociale. Paris et Lausanne, fourth edition, 1926. (, 1983.). 12