, duopoly,,,, ,? 19 70, ; 70,,,,,,,, J1 W1 : ;, E1,, ;,,, H1,, : ;,, ;,,, C1,, (Auguste Walras) (Leon Walras), A1 ( ) F1 E1 () V1 ( ),,,,, 2

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1 ( ) May Journal of Northwest Normal University (Social Sciences) Vol139 No13 (, ) [ ],,,, [ ] ; ; [ ] F 0 [ ] A [] (2002) :, A1, 1838,,,,,,,,,, :,,,,,,, E1,, ; ;, ;,,, ;,, ;,,?,,,,,, ;,,,,,,,,,,, :,,,,,,,,,,,,,,,,, 40,,, 70, [] [] (1957 ),,,, 52

2 , duopoly,,,, ,? 19 70, ; 70,,,,,,,, J1 W1 : ;, E1,, ;,,, H1,, : ;,, ;,,, C1,, (Auguste Walras) (Leon Walras), A1 ( ) F1 E1 () V1 ( ),,,,, 2 211, 3,,?, S1, 40,,,,,,,,?,, : =, ,,, =, =, ( ) ( ) ( ),,,,, 0 1, 0 1,,,,,,,, (1) (t 2 - t 1 ), ; (2),, ; (3) = T - 1 gλϖ,,,?,,, gλω 212, C1,,, gλξ, 53

3 ,, (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 = 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,,,,

4 ,,,, ( ) ( ),,, : (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

5 ,, gµξ, 214,, (),, 2,, ;,,,, 3, 3, ( ),, 2 - -, gµψ,, :, ( 3),,,,,,,?,,,,,,,, gµζ : 56 3, :,,, 21,,,,,,, ;

6 ,,,,,,,,,,, = ( ) + ( ) = ( ),,,, , : 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

7 , 0, ; 100 %, ; %, ; 100 %, ;, 0, ; B 100 %,, gνω,,, 20 50, , FRF ( ), FRF, 60 gνξ,,,,,, gνψ,,, =, - -, =, ( ), ( ) ( ) : (1), ; (2),, , ( ), , : income %, save %, price 112 %, interest %, expect 7 %, , gνζ,,, 1999, 5195, % ;, 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 = 1) GDP, : lny= lni lnk lnl R 2 = : GDP, ( ), ( ), ( ),, 1, GDP , gν 314,,,, (1), ,, 4,,,,,, Amartya,, (2)

8 5 5 1),, ;,,,,, :, =,,, ( ) ( ) ) = ( ) ( ) 2),, 2 1 ), + = 2 1 =,, I1,, gν} 2 2 ) ), ( = = ) ; ( = = ) ;,,, 0 (0 ), > 0,, ( ), > ( ), >,,? ), 2 3 ) ( ) ( ) ( ), 2 4 ) ) ) : 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

9 3) =, = = =, 3 ;, (3), ,, ( ) ;, ( ),, ( ) ; ( ) ( ),,, ( A), ( ) ;, 6 ;, ;, () (4), 5, D1 gν 5 :, 5, ( 7) : 7 5,,,,, ( ) 1 1, = 017 ( ), ( ), (1), ( ) + ( ) = ( ) (2), (3), ;, (4), >, , : 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 C 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),?,,

10 ,,,,,, 9), ; ;,,,, 5 ( ),,,, 5,, [ ] gµω [ ] :, 1994, [ ] :, 1981, D1C1Coleman, History and the Economic Past. an account of the rise and decline of economic history in Britain, Oxford, ,,, [ ] :, 1999 gλϖ [ ] S1, L. :, 1995, S1 :,, gλω S1 :, r t, r = 2 M,, 41 gλξ C. M. Cipolla, Between History and Economics, An Introduction to Economic History, Basil Blackwell Ltd, gλψ,,,,, gλζ,,,, gλ{ [ ] : 1, 1991, gλ,,,, gλ} R. Klein, The Role of Mathematics in Economics. The Mathematical Science. The MLT Press, gλ,,,,,,,,,,,,,,,,, gµυ K. [ ] A. :, 1989, 161 gµϖ + +,, + +,, + +, ( ),, +?,,,, 61

11 +,, ,, gµξ,, gµψ : L ,, 19, gµζ [ ] H1 :, 1999, 8 9 gµ{ [ ] J1R1 :, 1962, gµ, D1,, gµ} L1Cossa, Introduzione studio dellπeconomia politica, Millan, 1892, pp gµ [ ] J1B1 :, 1981, 24 gνυ P1Erdos, Contributions to the Capitalist Money, Business Fluctuations and Crisis, Budapest gνϖ J1M1Gillman, The Falling Rate of Profit, London : Dobson, gνω,,,,,, B gνξ (1965 ), gνψ [ ] : 1920, 66 7, 1973 gνζ :, gν{ gν :, 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, , 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

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