ISBN:
0444861270
Content:
This chapter discusses that the mathematical model of a competitive economy conceived as an attempt to explain the state of equilibrium reached by a large number of small agents interacting through markets. Four distinct, but closely related, approaches to the existence problem are recognized. At first, proofs of existence of an economic equilibrium were uniformly obtained by application of a fixed-point theorem of the Brouwer type or Kakutani type or by analogous arguments. This approach, which has remained of central importance to the present, is the subject of the chapter. Second, in the past decade, efficient algorithms of a combinatorial nature for the computation of an approximate economic equilibrium were developed. Third, recently, the theory of the fixed-point index of a map and the degree theory of maps were used to establish the existence of an economic equilibrium, and finally a differential process was proposed whose generic convergence to an economic equilibrium provides an alternative constructive solution of the existence problem.
In:
Handbook of mathematical economics, Amsterdam : North-Holland Pub. Co, 1982, (1982), Seite 697-743, 0444861270
In:
9780444861276
In:
year:1982
In:
pages:697-743
Language:
English
DOI:
10.1016/S1573-4382(82)02010-4
URL:
Volltext
(Deutschlandweit zugänglich)
