By Shigeo Kusuoka, Toru Maruyama
The sequence is designed to collect these mathematicians who're heavily attracted to getting new hard stimuli from monetary theories with these economists who're looking powerful mathematical instruments for his or her study. loads of monetary difficulties could be formulated as limited optimizations and equilibration in their strategies. quite a few mathematical theories were delivering economists with critical machineries for those difficulties coming up in financial concept. Conversely, mathematicians were inspired through numerous mathematical problems raised through financial theories
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Extra resources for Advances in mathematical economics. Vol.19
Fk /k also converges to %f with respect to the closed convergence topology. gk /k is a sequence of inverse demand functions that converges to g uniformly on any compact set, then the corresponding sequence of preference relations converges with respect to the closed convergence topology. The reason the topology of the demand function must be finer than that of the inverse demand function is very complicated. We discuss this further in the remarks on our theorems. We obtain results for the consumption space RnCC .
Furthermore, we show a similar relation for the estimate error of the inverse demand function with respect to the local uniform topology. These results hold when the consumption space is the positive orthant, but are not valid in the nonnegative orthant. Keywords Demand function • Inverse demand function • Integrability theory • Closed convergence topology • Uniform convergence topology • C 1 convergence topology Article type: Research Article Received: January 9, 2014 Revised: November 14, 2014 JEL Classification: D11.
1. c/ D tan. c/ " 1 if c " 1. x; y/ of this equation is unique. x; y/ is C 1 -class. x; y/ is increasing in both x and y. c/ 1C c g; 1 1 1 44 Y. t; m qpt /. t// is negative if % m=p t is sufficiently small. Therefore, we have f is a single-valued C 1 -class mapping from R2CC RCC onto R2CC , that is, f % 2 F \ F . c/. This indicates that there is no continuous and transitive extension of % on R2C . In fact, if % is such an extension, we have 1 1 . 0; 1/ . 14 but c. 14 ; 14 / < c. 23=2 Figure 1 illustrates the above example.
Advances in mathematical economics. Vol.19 by Shigeo Kusuoka, Toru Maruyama