( [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
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1 ( ) 1 ( ) 2 ( ) ( ) This work was supported by Grand-in-Aid for Scientific Research (Research No ). 1
2 ( [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.) 2
3 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
4 p 1 = 1 p 2 = 2 p = (1, 2) ( ) u = (+2, 1) A u = (+2, 1) B u = ( 2, +1) u v a 90 u v b 90 0 u p ( ) ( ) (1) (2) ( [5] p.46.) [5] 5 6 4
5 commodity2 a vb +u a p b -u -u va b commodity1 +u 1: 5
6 ( [4] p.367.) ( [4] p.368.) ( ) 6
7 ( ) 4 ( ) ( ) ( ) A 1 B A 1 A 2 u A1 u A2 u A1 u A2 ( 1 ) 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
8 ( ) ( ) ( ) Seller Volume of Offer (sell) Price (Yen) Volume of Bid (buy) Buyer A2 1 5 A B1 1 5 B2 1: 4 ( ) 8
9 commodity2 -ub2 pa1 pb1 -ub1 commodity ua2 +ua1 図 2: 板と交換ベクトル 9
10 ( ) ( ) ( ) 3 ( ) 1 ( ) u 1 2 ( ) u 2 u 1 p 1 2 u 2 p 2 2 +u 1 u u 1 + u 2 1 ( ) 2 ( ) 5 U-Mart ( ) 10
11 commodity2 p1 -u1 -u2 p2 +u1 - u2 commodity1 -u1+u2 +u2 +u1 3: 11
12 ( ) GDP [1].., 1 1., [2] Adam Smith. An Inquiry into the Nature and Causes of the Wealth of Nations ( (1)(2)(3)(4) ). [3].., [4] Ludwig von Mises. Human Action: A Treaties on Economics. Henry Regnery, third edition, Reprinted in Human Action, ed. by Bettina Bien Greaves, Liberty Fund, (, 1991.). [5] Léon Walras. Eléments d économie politique pure ou Théorie de la richesse sociale. Paris et Lausanne, fourth edition, (, 1983.). 12
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