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Separability and the Existence of Aggregates

  • King-tim Mak
Conference paper

Abstract

If a continuous real-valued function Φ in n variables x1,...,xn has the representation
$$ \Phi ({x_1},...,{x_n}) = F(f({x_{1,...,}}{x_k}),{x_{k + 1}},...,{x_n}) $$
(1.1)
where F and f are continuous real-valued functions, then the function is said to be (continuously) separable in the subset of variables x1,...,xk. The concept of separability is intimately tied with the concept of aggregation and indices: If Φ is a function which gives the interrelationship among n economic quantities x1,...,xn, then a function f may serve as an aggregate for the quantities x1,...,xk when and only when (1.1) holds; moreover, f may qualify as a quantity index for x1,...,xk if it has certain desired properties such as monotonicity (see Eichhorn [4] for a methodological definition of economic indices).

Keywords

Boundary Point Economic Index Dimension Zero Quantity Index General Topological Space 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

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Copyright information

© Springer-Verlag Berlin Heidelberg 1988

Authors and Affiliations

  • King-tim Mak
    • 1
  1. 1.College of Business AdministrationUniversity of Illinois at ChicagoChicagoUSA

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