By Prof. Dr. Hanjiro Haga (auth.)
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Additional resources for A Disequilibrium-Equilibrium Model with Money and Bonds: A Keynesian-Walrasian Synthesis
Po,n+ l'z) n n+l (j=2,3, ••. , n+l), z ~ 0 and j~lo,j + z I PO,J. > 0 n. 88 Let us consider the k-th firm's individual demand or supply funciton. d), and yEA }, for each PES. " Then, let us investigate the following mapping which associates a set nk(p) in Ak with each vector P on S", that is, k=1,2, ... , (10. ii) We will prove below that the mapping nk is closed. jl. we will show the continuity of the following mapping S" ... iii) k=1,2, ... d) for each given PES". 88. S" contains a vector P (P o ,1,P o ,2' ••.
Max~mum and a .. =n~mum on S. p~ and t J That is, there exist a maximum ex- pected price and a minimum expected price which are both positive. The proof will be established by a successive method. For example, the boundedness of L~(i=1,2, ••• , h) and L~,o(i=1,2, ... i)', making use of the boundedness of the positive expected prices, the lower boundedness of of B! and L~,n+l (i=1,2, Li and Li 2 2,0 D~(i=1,2, ••. 2. 2. By applying the same method i successively to each period after the 2nd period, the boundedness of Lt (t=3, 4, ••• , ,) and Li (t=3,4, ••• , ,-1) can be shown.
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. Also, it is clear, from the continuity of these functions (cf. 3) and from the compactness of S, that the functions t Pkj tak e a . max~mum and a .. =n~mum on S.
A Disequilibrium-Equilibrium Model with Money and Bonds: A Keynesian-Walrasian Synthesis by Prof. Dr. Hanjiro Haga (auth.)