Von Neumann models and the oeuvre of Jerzy Łoś
Otto Moeschlin · Banach Center Publications · 2006
There is a line of great and famous Polish mathematicians, well recognized in the international mathematical community, as for instance Alfred Tarski, Stefan Banach, Hugo Steinhaus, Kazimierz Kuratowski, Wacªaw Sierpi«ski and indeed I would also add the name of Jerzy Maria o± to this list.It's an honor for me to have the chance to speak here about the `Von Neumann Models and the Oeuvre of Jerzy o±,' of course understanding this in the sense of `the oeuvre related to von Neumann models.'Jerzy o± has made decisive contributions to this theory as author but also as co author, and he is the editor together with his wife M. W. o± and also A. Wieczorek of three volumes with collected contributions to Mathematical Economics and especially to the theory of von Neumann models.Let me start to explain the von Neumann model of an expanding economy, as introduced in the paper of von Neumann (1937).An economy with m production processes and n commodities is considered.Production in this model is dened by two (m, n)-technology matrices A := (a ij ) i=1,...,m, j=1,...,n , and B := (b ij ) i=1,...,m, j=1,...,n .The i-th production process (a i , b i ) is represented by two row-vectors of A and B, the so-called input bundle and output bundleDuring a production period the input quantity a ij ∈ R + of commodity j is transformed by the i-th process into the output quantity b ij ∈ R + also of commodity j, if this 2000 Mathematics Subject Classication: 91B52, 91B66, 01A60.