2002 5 ( ) May 2002 39 3 Journal of Northwest Normal University (Social Sciences) Vol139 No13 (, 730070) [ ],,,, [ ] ; ; [ ] F 0 [ ] A [] 100129162 (2002) 0320052211 1 111 :, A1, 1838,,,,,,,,,, :,,,,,,, E1,, ; ;, ;,,, ;,, ;,,?,,,,,, ;,,,,,,,,,,, :,,,,,,,,,,,,,,,,, 40,,, 70, [] 2002201225 [] (1957 ),,,, 52
, duopoly,,,, 112 19 70,? 19 70, ; 70,,,,,,,, J1 W1 : ;, E1,, ;,,, H1,, : ;,, ;,,, C1,, (Auguste Walras) (Leon Walras), A1 ( ) F1 E1 () V1 ( ),,,,, 2 211, 3,,?, S1, 40,,,,,,,,?,, : =, 0 1 2 3 4 5 6 7 8 9 10,,, =, =, ( ) ( ) ( ),,,,, 0 1, 0 1,,,,,,,, (1) (t 2 - t 1 ), ; (2),, ; (3) = T - 1 gλϖ,,,?,,, gλω 212, C1,,, gλξ, 53
,, (1), (2), 3, (),, (3),,,, () gλψ,,, 1 1, gλζ, ( ) J1 3 4, ( ) ( ) (),,, ( ),, ( Descriptive Statistics ) ( Inferential Statistics) T2 (T2test) (Analysis of Variance ) ( Chi2square Test ) (Correlation) (Regression),, (time series) (event history analysis) (discriminant analysis) (LISREL),,,,,,, ;,,, gλ{ 54,, 4 1) Xd = 0 + 1 P + 2 Y + Ud, Xd, P, Y, 0 1 2, Ud 2) I t = I0 + I1 Y t + I2 Y t- 1 + U It, I t Y t, Y t - 1, I0 I1 I2, U It,?, ( ) ( ),, : (1) ; (2),, ; (3),,,,,,,, gλ,,,,,, R1 :, 20,, gλ}, 20 30, :,,, ;,, gλ,, :,,,, gµυ 213,,,,
,,,, ( ) ( ),,, : (1) n = 1, n 2 ; (2) n 2,, : (1) ; (2),,,,,,,,, ;,,,,,,,, ; ( ),,,,, : = + + = +, +,,, gµϖ,, ( ), ;,, ;,,,,,,,, A1 1) : <,, ;, 2) 2 (1) (2) C 1,2 C 2,1 ; M 1,2 M 2,1 ; C 2,1 = 1/ C 1,2 ; C 1,2 = M 2,1 / M 1,2 C 2,1 = M 1,2 / M 2,1 M 2,1 / M 1,2 M 1,2 / M 2,1-1 < 1,, 3) n (n > 2), (i) (k) C i,k C k,i ; M i,k M k,i ; C k,i = 1/ C i,k, n (n - 1), 1/ 2 [ n (n - 1) ] ; (l), C i,l C l,k ; C i,k = C i,l C l,k,, C i,k = C i,l C l,k : (i) (k) (l) n,, ;,, 4) :, 5), : a. ; b. = : a.,,, ( ) ; b. 6) :, ;, ;,, gµω,,,,,,,,,,,,,,,, 1), 2), xw A = yw B W G W G W G, xw A x A, yw B y B,,, = (xw A = yw B ), = (W G W) =, = ( G W G ) =, G G,,, GG, 55
,, gµξ, 214,, (),, 2,, ;,,,, 3, 3, ( ),, 2 - -, gµψ,, :, ( 3),,,,,,,?,,,,,,,, gµζ : 56 3, :,,, 21,,,,,,, ;
,,,,,,,,,,, = ( ) + ( ) = ( ),,,, 21 20 20 30, 3 311 : 1. 2. T1 +J1 =, J1,,,,,,, gµ{,,? gµ, 19 L1, gµ},, 1993 R 1,,,, :,?, 3 : (1) 1, = GNP - GNP, = ; (2), ; (3) 2,,,, gµ,,,, 312, ( S/ V),, P1 : (SC + SK) / (C - SK) SC SK, C, gνυ, ;,,, J1, : P = (S - U) / C, S, C U, S - U gνϖ :, U, ;,,,, S - U 313, 3 (1) ( diagrammatic), L S ( P/ P e ) Y3 K Y= F ( K, Nf) (2) i, Yit = b (Pit - E (Pt Iit) ) ;, b > 0, (perceived) Pit = Pt + Zit ;, Zit i, Zit = 0 E (Pt Iit) = (1 - ) E (Pt I) + Pit, = p / ( p + z ), Yit = b (1 - ) (Pit - E (Pt It) ), Yt = (Pt - E (Pt It) ), = b (1 - ) (3) (), ( ) ( ) ( 4) : 4 57
, 0, ; 100 %, ; 0 100 %, ; 100 %, ;, 0, ; B 100 %,, gνω,,, 20 50, 1550 1899, FRF ( ), FRF, 60 gνξ,,,,,, gνψ,,, =, - -, =, ( ), ( ) ( ) : (1), ; (2),, 1978 1998, ( ), 1978 1998 1978 1995, : income - 013 %, save - 011 %, price 112 %, interest - 1815 %, expect 7 %, 1995 1998, gνζ,,, 1999, 5195, 1998 1116 % ;, 5 1,,, Hellmann,, 58,,,, -, gν{, 20 90, ( ), 3 : Y= a I K L, Y GDP, I,,, Y= a I K L GDP, : lny= A lni + B lnk+ C lnl, A B C, Y I K L 1980 1992 ( 1980 = 1) GDP, : lny= 01841597 lni + 01255566 lnk + 01697838 lnl - 01032861 R 2 = 0199728 : 1980 1992 GDP, ( 01841597), ( 01697838), ( 01255566),, 1, GDP 01841597, gν 314,,,, (1), 5 5 5 5,, 4,,,,,, Amartya,, (2)
5 5 1),, ;,,,,, :, =,,, ( ) ( ) 2 212 ) = ( ) ( ) 2),, 2 1 ), + = 2 1 =,, I1,, gν} 2 2 ) 2 211 ), ( = = ) ; ( = = ) ;,,, 0 (0 ), > 0,, ( ), > ( ), >,,? 2 213 ), 2 3 ) ( ) ( ) ( ), 2 4 ) 2 411 ) 2 412 ) : T, P ( ) OM ( ) OS ( ) : (1) p 1 p 2 p 3 p 4 (2) OS, O t 3 OS1O t 3, t 1 p 1 (3),, OS ; OS ( OS1t1 t2 t1p1 ),,,, 6 59
3) =, = = =, 3 ;, (3), 20 80 90,, ( ) ;, ( ),, ( ) ; ( ) ( ),,, ( A), ( ) ;, 6 ;, ;, () (4), 5, D1 gν 5 :, 5, ( 7) : 7 5,,,,, ( ) 1 1, = 017 ( ), ( ), (1), ( ) + ( ) = ( ) (2), (3), ;, (4), >, 60 8 8, : 1) A B C D E 2),, E C D C D, C + C, D + D 3) C C 1 C 2 C 3 C 4 4), r, [A] r = [B ] r = [ C 1 + C 3 + C 4-1 + C 4-3 + C ] r ( ) C 2 C 4-2, 5) D + D = (C + C ) + B, (C + C ) + B (D + D ),, K, m ( K ) + (m ) (D + D ) 6) r A, A + (r + A ) A - (r - A ) 7) r,, 8), gου,,,,, ;,, (Microanalysis Simulation Model),?,,
,,,,,, 9), ; ;,,,, 5 ( ),,,, 5,, [ ] gµω [ ] :, 1994, 17 18 38 39 [ ] :, 1981, 316 317 317 372 312 D1C1Coleman, History and the Economic Past. an account of the rise and decline of economic history in Britain, Oxford, 1987. 1890 10,,, 1954 463 [ ] :, 1999 gλϖ [ ] S1, L. :, 1995, 93 42 44 S1 :,, 35 36 gλω S1 :, r t, r = 2 M,, 41 gλξ C. M. Cipolla, Between History and Economics, An Introduction to Economic History, Basil Blackwell Ltd, 1991. gλψ,,,,, gλζ,,,, gλ{ [ ] : 1, 1991, 28 41 gλ,,,, gλ} R. Klein, The Role of Mathematics in Economics. The Mathematical Science. The MLT Press, 1969. gλ,,,,,,,,,,,,,,,,, gµυ K. [ ] A. :, 1989, 161 gµϖ + +,, + +,, + +, ( ),, +?,,,, 61
+,, 0 9 10,, gµξ,, gµψ : L1 20 30,, 19, gµζ [ ] H1 :, 1999, 8 9 gµ{ [ ] J1R1 :, 1962, 64 68 147 166 334 336 gµ, D1,, gµ} L1Cossa, Introduzione studio dellπeconomia politica, Millan, 1892, pp126 281 gµ [ ] J1B1 :, 1981, 24 gνυ P1Erdos, Contributions to the Capitalist Money, Business Fluctuations and Crisis, Budapest 1971. gνϖ J1M1Gillman, The Falling Rate of Profit, London : Dobson, 1957. gνω,,,,,, B gνξ 60 10 (1965 ), gνψ [ ] : 1920, 66 7, 1973 gνζ :, 2000 1 gν{ gν :, 1996 5 gν} [ ] A1 :, 1989, 137 gν [ ] D1 :, 1984 gου,, ( ) ( ),,,,,,, The Key to the Mathematicalization of Theoretical Economics Introduction of Mathematical Thinking CHEN Yong2qing (College of Economy and Management, Northwest Normal University, Lanzhou, Gansu, 730070, PRC) [ Abstract] The mathematicalization of theoretical economics points to revealing relationship from the very beginning. To realize the mathematicalization, one of important prerquisites is to really understand mathematics, only by so doing can mathematical thinking correspondingly come into being. In the process of reflecting on philosophical concepts, and of further comprehending mathematical deductive inference, it can also extend to recognition of the relationship between the three fields of physics, biology and economics. As to how to apply mathematical thinking in the best way, survey and analysis should be made by looking into practical research activities. [ Key words] theoretical economics ; mathematicalization ; mathematical thinking ( g ) 62