By S. Kusuoka, A. Yamazaki

Published every year lower than the auspices of the learn heart of Mathematical Economics in Tokyo, this sequence brings jointly mathematicians drawn to monetary theories and economists looking potent mathematical instruments to assist their study. Articles set forth unique effects and distinctive overviews of the issues below dialogue, supplying readers a transparent knowing of either monetary and mathematical theories.

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**Sample text**

Similarly, we derive from (21) that limpi^+oo ^l^^^o ^ ^ ^^^^^^ ^^^^^' ^^^^^ hmp,-^+oo ^|po^+oo ^ ^• Therefore, under (22), there exists PQ > 0 such that Ump^-^+oo ^ > 0 for any Po > PQ- Notice also that ^1 _ ^ 1 _ ^^Q^Q^ /^00^1 A ^^^0 ^24) is an increasing function of po since ^QQPU/P\QPQ\ < 1. Considering that PI e (-1,0) is defined as hmp,_^o ^L_^2 = 0, we derive from (20): «U=„=.. = ' - ( ^ ) ^ ^ > 0 . (25) Therefore, ^|pi=po ^ ^ ^^^ ^^y Po ^ PQConsidering Lemma 5 under (22), we then conclude the following results: (c) (c) for any given po e (PQ , PQ), there exists p^ > max{0, po} such that ^ > 0 for all PI G[0,p2); for any given po > Pg, ^ > 0 for all p\ > 0.

4) and respectively. 4), we obtain {V\ — V2, Jv\ — JV2) = 0. Since J is strictly monotone, it follows that vi = V2. Therefore, {xn} converges weakly to an element of {BJ)~^0. n 58 T. Ibaraki and W. Takahashi We know that the duality mappings J oniP, \ < p < cx) and smooth finite dimensional Banach spaces are weakly sequentially continuous. 2 hold without assuming that J is weakly sequentially continuous. 4. Strong convergence theorem Let £• be a reflexive, strictly convex, and smooth Banach space and let J be the duahty mapping from E into £"*.

When CES technologies are introduced, a much larger set of configurations is compatible with local indeterminacy. In particular, Leontief or Unear technologies for the consumption good sector may be considered. Therefore, we will consider CES technologies in a continuous-time model and provide a complete analysis of the local determinacy properties of equilibria. We will show that, even with asynmietric factor substitutabiUty properties, local indeterminacy is still based on a reversal of factor intensities between the private and social levels, what we call quasi factor intensity.