By Prof. Dr. Hanjiro Haga (auth.)
Read or Download A Disequilibrium-Equilibrium Model with Money and Bonds: A Keynesian-Walrasian Synthesis PDF
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Extra info for A Disequilibrium-Equilibrium Model with Money and Bonds: A Keynesian-Walrasian Synthesis
If we let Ak denote the Carte~ian product Ak x Ak x Ak x Ak x Ak x Ak x ••••• x o 0 1 122 Ak then by definition. for each k. i) If we let Bi denote the Cartesian product Bi x iii x Bi x iii x Bi x iii x ••••• x o 0 1 1 2 2 Bi T' then by definition. 2 ••••• I). ii) Remark III. Ak is non-empty, compact, and convex, for each k. ~). •• , t. Proof. The non-emptiness of Bi and Ak is easily verified as follows •. For each i(i=1,2, ••• , ~), and each k, take (n+2)T + n-dimensional zero vectors of the i-th household and the k-t~ firm simultaneously.
We will take steps similar to those taken for households (labourers and rentiers). Now. for each firm k and each period t. let Tk(P) denote the set of all yk,s t t y~) which has the following properties: for each given PES. (i) Let this vector satisfies (3)'. a)'. b). c). d). and T~ denote T~(S). es: YkZ,Yk2 ,n+l'Y k2 ,o' •••• YT for each given PES, (i) Let Tk k t,n+l denote Tt,n+l (S). 82. a)'. c). d), and Ak. o k k k In order to show that Tt(S) is bounded, we need only impose (Yo,n+l'Y o • o ) The reason for this formulation is that yk must be restricted within Ak as a step of our proof.
Yk) which has the following properties: T for each given P E 5. (i) this vector satisfies (3)'. a)'. b). c). d). and Let Tk denote Tk (5). o . o and Tk • t o Lemma II. For each i and each k. Li and Tk are bounded sets. 2 ••••• T. Li and Tk are bounded sets. n+l Li and Tk are bounded sets. •••• T-l. 2 ••••• T-l. Proof. b) for each labourer i. b) for each rentier i. B! b) for each firm k. o ii kandTk Next. o are shown as follows. l. for each i and each k. and 53 P~(P) > 0 for any PES, pk. t,J t J t=l,2, ••• , '; j=l,2, ••• , n.
A Disequilibrium-Equilibrium Model with Money and Bonds: A Keynesian-Walrasian Synthesis by Prof. Dr. Hanjiro Haga (auth.)