By S. Kusuoka, A. Yamazaki

ISBN-10: 4431727337

ISBN-13: 9784431727330

Loads of financial difficulties can formulated as restricted optimizations and equilibration in their strategies. a variety of mathematical theories were providing economists with necessary machineries for those difficulties bobbing up in fiscal thought. Conversely, mathematicians were motivated by way of quite a few mathematical problems raised through monetary theories. The sequence is designed to assemble these mathematicians who have been heavily drawn to getting new not easy stimuli from fiscal theories with these economists who're looking for potent mathematical instruments for his or her researchers.

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**Extra resources for Advances in Mathematical Economics. Vol, 10**

**Example text**

Gamier et al. Proposition 3. Let Assumption 1 hold. The steady state is locally indeterminate if and only if the consumption good is capital intensive from the private perspective, but quasi labor intensive from the social perspective. To get indeterminacy in a framework with constant returns to scale at the social level, we need a mechanism that nuUify the duahty between the Rybczynski and Stolper-Samuelson effects. 1, the Rybczynski effect is given by the input coefficients from the private perspective while the StolperSamuelson effect is given by the quasi-input coefficients from the social perspective.

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 £"*. Then J~^ is also single valued, one-to-one, and surjective, and it is the duaUty mapping from E* into E. 1) for 2i\lx e E and jc* e E*. In other words, Vi (jc, jc*) = V (jc, J~^ (jc*)) for all X e E and JC* G £"*. For each x* e £*, the mapping g(x) = V\{x, x*) for all JC € £" is a continuous and convex function from E into R.

We can write g{p\) as follows: g(p\) = exp Pi - Po , ^^^p[Tfk^-(fe)]-^^i -In Pi(l + Po) I Po\ = exp{/(pi)}. Capital-labor substitution and indeterminacy 45 If / ( p i ) is monotone increasing, so is g(p\). Wethen conclude from all this that for any given po > Po, there exists p\ e [p\, 0) such that g(p\) is a monotone increasing function for all p\ > p\. u It clearly appears from Proposition 2 that under the conditions of Lemma 5, h and b are monotone decreasing functions of p\. We may now prove Proposition 4: in the first part of the proof we consider positive values of p\ only.

### Advances in Mathematical Economics. Vol, 10 by S. Kusuoka, A. Yamazaki

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