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fixed-point theorem
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Journal Article
History of Political Economy (2016) 48 (4): 635–655.
Published: 01 December 2016
... . Zeuthen Franz . 1933 . “Das Prinzip der Knappheit, technische Kombinationen, und ökonomische Qualität.” Zeitschrift für Nationalökonomie 4 : 1 – 24 . fixed-point theorem general equilibrium theory Vienna Mathematical Colloquium Karl Menger Abraham Wald Copyright 2016 by Duke...
Journal Article
History of Political Economy (2006) 38 (Suppl_1): 213–227.
Published: 01 December 2006
... Equilibria. New Haven, Conn.: Yale University Press. Sonnenschein, H. 1973 . Do Walras' Identity and Continuity Characterize the Class of Community Excess Demand Functions? Journal of Economic Theory 6 : 345 -54. Uzawa, H. 1962 . Walras' Existence Theorem and Brouwer's Fixed Point Theorem...
Journal Article
History of Political Economy (1991) 23 (3): 560–565.
Published: 01 September 1991
... in turn. First is Von Neumann’s approach, using convex
analysis, fixed point theorems, and game theory (257). Second is the line of
inquiry that began with Wald’s work and led to a blind alley in the work of
Kenneth J. Arrow and Frank H. Hahn (258). It is strange to read the authors...
Journal Article
History of Political Economy (2024) 56 (3): 467–488.
Published: 01 June 2024
... (or 1928); see on that Kjeldsen 2001 , but also Weintraub 1983 , which saw the elements of a fixed-point theory already in the 1928 proof, which, although not applying Brouwer’s theorem explicitly, could still be interpreted in that way. 26. Whitney was doing graph theory at that time...
Journal Article
History of Political Economy (2022) 54 (5): 823–858.
Published: 01 October 2022
... to Birkhoff, This is a theorem on inequality systems of linear forms which turns up in the theory of games, and again on a system of equations of production which I published some years ago. I had originally a rather complicated proof, which I connected later with Brouwer's fixed point theorem; that proof...
FIGURES
Journal Article
History of Political Economy (1990) 22 (1): 101–112.
Published: 01 March 1990
... and Political Science. Kakutani , S. 1941 . A generalization of Brouwer's fixed point theorem. Duke Mathematical Journal 8 : 457 -59. Koopmans , T. C. 1951a . Analysis of production as an efficient combination of activities. In Activity analysis of production and allocation , 33 -97...
Journal Article
History of Political Economy (2004) 36 (4): 639–666.
Published: 01 November 2004
... with
convex images, it is possible to apply Kakutani fixed-point theorem to
prove that the mapping has a fixed point, which is the desired equilib-
rium. Hence Nash proves that every n-player finite game played with
mixed strategies admits an equilibrium point. Moreover, for the first time
in game theory he...
Journal Article
History of Political Economy (2020) 52 (4): 799–801.
Published: 01 August 2020
... of Japanese mathematicians such as Shizuo Kakutani s 800 Book Reviews fixed-point theorem). It is striking to learn that as early as 1939 Kazuo Midutani pub- lished in Japanese Comments on Wald s Proof of the Existence of Equilibrium for the Cassel-Schlesinger System of Production (reprinted in his...
Journal Article
History of Political Economy (1975) 7 (4): 530–548.
Published: 01 November 1975
.... Arrow and L. Hurwicz, “On the Stability of a Competitive Equilibrium, I,”
Econometrica, Oct. 1958.
34. The major tool used to solve the existence problem, a fixed point theorem,
was developed in 1941 by S. Kakutani, “A Generalization of Brouwer’s Fixed Point
Theorem,” Duke Mathematical...
Journal Article
History of Political Economy (1995) 27 (1): 195–199.
Published: 01 March 1995
... is the most consistent path
to human dignity.
I find it troubling to think that we should ever lose sight of Marx’s
work. Historians of economics should not restrict themselves to a story
of analytical progress. The economy does not present itself in terms
of fixed point theorems or quasi...
Journal Article
History of Political Economy (2021) 53 (4): 595–631.
Published: 01 August 2021
... to the (structural) parameters of his system, von Neumann offered an analytical treatment. Incidentally, when calculating the roots of the system, von Neumann used a Brouwer s fixed-point theorem. With it, he concluded, There are infinitely many solutions in existence. 51 These notes clearly instantiated...
Journal Article
History of Political Economy (2002) 34 (2): 291–320.
Published: 01 June 2002
...” by Benoit Mandelbrot. Information and Control 4 : 217 -23. ____. 1979 . Rational Decision Making in Business Organizations. American Economic Review 69.4 : 493 -513. ____. 1982a . Accurate Predictions and Fixed Point Theorems: Comments. Social Science Information 21.4-5 : 605 -26...
Journal Article
History of Political Economy (1972) 4 (2): 533–550.
Published: 01 June 1972
...
of a ked point which was his generabtion land a more applicable
fomdation of Brouwer’s theorem. He wrote an article on this
theorerm, “A Generalization of Brouwer’s Fixed Point ‘Theorem” in
19413O from a mathematical point of view, because he is a math-
mabician. I know that in 1935-36 von...
Journal Article
History of Political Economy (1992) 24 (Supplement): 15–27.
Published: 01 December 1992
... Neumann sent Borel a
note on his result, which Borel presented to the Academie des Sciences
in June 1928.
In his 1937 paper, von Neumann gave an entirely topological proof of
the existence of general competitive equilibrium, using Brouwer’s fixed-
point theorem to provide a much clearer...
Journal Article
History of Political Economy (2020) 52 (5): 863–894.
Published: 01 October 2020
... questions depend on one another, and the solution had to use a fixed-point theorem. He assumed, for simplicity, constant returns to scale and supposed an economy that could expand but with an unchanged structure: each of the possible production processes would be used in cer- tain intensities...
Journal Article
History of Political Economy (1975) 7 (2): 174–192.
Published: 01 June 1975
... commentary on the theorem, more than a half-century
later, was a composite of Jevons’ and Marshall’s. Like the former, he
pointed out that capital consisted of nothing more than advances.
Then, altering the latter’s analysis slightly, he noted that the only real
difference between the two...
Journal Article
History of Political Economy (1999) 31 (3): 511–523.
Published: 01 September 1999
... Jr. Robert E. 1988 . On the Mechanics of Economic Development. Journal of Monetary Economics 22 : 3 -42. Marshall , Alfred [1890] 1961 . Principles of Economics . 9th ed. Edited by C. W. Guillebaud. London: Macmillan. Robinson , Joan . 1934 . Euler's Theorem and the Problem...
Journal Article
History of Political Economy (2007) 39 (Suppl_1): 76–95.
Published: 01 December 2007
... René Roy. The Brouwer fixed-point theorem
and the Kakutani fixed-point theorem are so named not just to honor those
who first stated them but also to make it easier to recall which is which.
Long lists of names and subtle distinctions among individual contribu-
tions and points of view...
Journal Article
History of Political Economy (1991) 23 (1): 167–170.
Published: 01 March 1991
... necessitates an increase in the money wage (assume for now that the
commodity wage is fixed at subsistence), which then causes the rate of profit to
fall. As stated, the theorem supports the view of a fixed commodity wage
determined prior to exchange. However, this cannot be the case...
Journal Article
History of Political Economy (2004) 36 (1): 103–129.
Published: 01 March 2004
... simply by appeals to the envelope theorem.4 It is reflected in
the equality of the firm’s marginal cost to the Lagrange multiplier in
the cost minimization problem, and in the fact that short-run and long-
run marginal costs are the same if the fixed factors are at optimal lev-
els before the parameter...
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