By P. Jean-Jacques Herings
Mathematical economics makes use of mathematical instruments and reasoning to explain and clarify monetary truth. on the center of mathematical economics is normal equilibrium conception. Static and Dynamic Aspects of common Disequilibrium Theory describes and analyses quite a few common equilibrium versions, treating idea from an axiomatic viewpoint, which could result in a deeper figuring out of difficulties, can help to prevent wrong reasoning, and should increase conversation in the fiscal technological know-how.
This quantity includes 4 elements, every one of that is self-contained. half I offers with the mathematical and financial preliminaries. half II considers the static points of disequilibrium thought. half III determines cost rigidities endogenously. ultimately, half IV offers with dynamic facets of disequilibrium theory.
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Extra info for Static and Dynamic Aspects of General Disequilibrium Theory
44 CHAPTER 2 Often it is possible to give easy characterizations of lower hemi-continuity. n , and an element ~ of 5 be given. Then the correspondence ep is lower hemi-continuous at ~ if and only if for every sequence (:z:n)nEIN in 5 converging to ~ and for every element y of ep(~) there exists a sequence (yn )nEIN in T such that yn E ep(:z:n), "In EN, and yn -> y. See Hildenbrand (1974), Theorem 2, page 27. The following theorem correspondence. n be given. Let epi : 5 -> T', Vi E ITc, be a lower hemi-continuous correspondence.
A t ' - l q (p(t' = v + EiEIO - 1)) } . = aiq(p(i)) implies :z: AOv + EiEI c, Aip(I+(s) U 1 i i p(Ii-I)) with AO = l-ao, Ai = a - _a , 'Vi E If"-ll and At' = a t '-I. Clearly, EiEIO Ai 1 and Ai ~ 0, 'Vi E Ir" so the point :z: is a convex combination of Notice that :z: t. -1 = " v and t' relative projections of v. 4 (V-triangulation of t::. m - Let a point v of ~m-l and some n E N every p E II', E( s, p) is the collection of tices :z:1, ... , :z:t'+1 E R m satisfying :z:1 = aO, ... ,at '-1 E I~_1 with a t '-1 ::; ...
2 (Glicksberg's fixed point theorem) Let 5 be a non-empty, compact, conve:c subset of a linear topological space X and let ep : 5 -+ 5 be a conve:c-valued correspondence such that the graph of ep is closed in 5 x 5, where the set 5 x 5 is given the topology induced from the product topology on X x X. Then there e:cists an element :z: of 5 such that :z: E ep(:z:). See Glicksberg (1952), Theorem, page 171. 2 is a continuous function, then Tychonoff's fixed point theorem is obtained, see Tychonoff (1935).
Static and Dynamic Aspects of General Disequilibrium Theory by P. Jean-Jacques Herings