By Prof. Dr. Hanjiro Haga (auth.)
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Extra info for A Disequilibrium-Equilibrium Model with Money and Bonds: A Keynesian-Walrasian Synthesis
40. This assumption is important to enSure that the supply of bonds is bounded from below. This boundedness, in turn, plays a crucial role in our existence proof. It has often been asserted that the supply of bonds cannot be infinite, because there are limitations on the ability of economic units to redeem bonds. , the budget constraints on the maximization behaviour of household and firm. i k i k For example, suppose that xt,n+l (or Yt,n+l) and xt,o (or Yt,o) can be - 00 and 00 respectively, when Pt,n+l is equal to one.
60 Now, the set of inequalities (6) is less restrictive than (4). Ai ELi xo,n+l o,n+l' ~i E Li o If there exists 0' and Now, we will state the properties of these sets. LeIlUlla 1. For each i and each k, a) Li,Li Li Tk Tk and Tk are non-empty sets. b) Li Li Li Tk Tk and Tk are convex sets. c) Li,Li ,L i ,T k Tk and Tk are bounded sets. o 0' o o,n+l' o,n+l' o,n+l 0,0' 0,0' 0,0 0' 0' 0' o,n+l' 0,0 o,n+l' 0,0 o,n+l' 0,0 Proof. 61 The non-emptiness of sets Li0 and Tk is easily shown. a) 0 non-emptiness of the sets Li Tk o,n+l' o,n+l' Li 0,0' and Tk 0,0 Also, the is easily shown.
3 and the compactness of S. 85. The boundedness of net output and net input is proved in Appendi~ I. Z. T ... , t) . Also. let VO denote the interior of V. i) VO :> Li. Z. ii) Mi :> Li. Z. , t. Then: t. •• T). form an n-dimensional compact ball Et • with center zero. large enough to include Tkt within its interior EOt· This is k possible because of the boundedness of Tt • Also. • T. • T-l. Let E denote the Cartesian product Eo x Eo x EI x EI x EZ x EZ x and let Nk denote the Cartesian product Qk x RI x RI x Qk x RI x RI x QkZ x RI x RI x o + I + + Qk x ••••• x Qk.
A Disequilibrium-Equilibrium Model with Money and Bonds: A Keynesian-Walrasian Synthesis by Prof. Dr. Hanjiro Haga (auth.)