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APPENDIX TO CHAPTER V1
A CRITICISM OF THE VON NEUMANN TYPE oF DyNAMIC MODELS
The vertically-integrated model developed in the present
work — as the reader has by now realised — has taken so
marked a departure from all the dynamic extensions of the
inter-industry system, which have become so widespread in
current economic literature, as to require perhaps some justi-
fication. To this purpose, I may append a critical assessment
of the approach adopted in all the dynamic models which are
currently discussed among mathematical economists.
As is well known, the most outstanding of all of them is
voN NEUMANN’s extension over time of the general equilibrium
system (!). Another model of particular interest to us is,
of course, LEONTIEF’s dynamic version of his static input-
output analysis (?). AII the other works that have followed (3)
(') Jounn von NEUMANN, A Model of General Equilibrium, « The Review
of Economic Studies », 1945-46.
() W.W. LEonTIEF, Dynamic Analysis, Chapter 3 of « Studies in the
Structure of the American Economy », by W.W. LEONTIEF and others,
New York, 1953. This dynamic analysis of LEONTIEF’s has been anticipated
by Davip Hawkins, Some Conditions of Macroeconomic Stabilitv. « Eco-
nometrica », 1948.
(®) See, for example: KEMENY, MORGENSTERN and THompsoN, 4 Generali-
zation of the von Neumann Model of Expanding Economy, in « Econome-
trica », 1956; D. GALE, The Closed Model of Production, in « Linear Inequa-
lities and Related Systems », Annals of Mathematical Study, No. 38, ed.
by H.W. Kuhn and A.W. Tucker, Princeton, 1956; R. DorFMAN, P.A. Sa-
MUELSON, R.M. SoLow, Linear Programming and Economic Analysis, New
York, 1958, chapters 11 and 12; M. MorisHIMA, Prices, Interest and Profits
in a Dynamic System, « Econometrica », 1958; Some Properties of a Dy-
namic Leontief System with a Spectrum of Techniques, « Econometrica »,
1959: Economic Expansion and the Interest Rate in Generalized von Neu-
mann Models « Econometrica ». TroÂ6
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