• Corpus ID: 124469594

The Index Number Problem: A Dierential Geometric Approach.

@inproceedings{Malaney1996TheIN,
  title={The Index Number Problem: A Dierential Geometric Approach.},
  author={Pia Malaney},
  year={1996}
}
The first part of this thesis looks at issues in index number theory. By using techniques developed in differential geometry, it is shown that the socalled index number problem can be resolved by the development of a special economic derivative operator constructed for this purpose. This derivative is shown to give rise to a unique differential geometric index number which is then demonstrated to equal the Divisia index. It is then shown in the second chapter (co-authored with Eric Weinstein… 
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References

SHOWING 1-10 OF 35 REFERENCES
Economic Development with Unlimited Supplies of Labour
Written in the classical tradition this essay attempts to determine what can be made of the classical framework in solving problems of distribution accumulation and growth first in a closed and then
INVARIANCE AXIOMS AND ECONOMIC INDEXES
exhibited. We present axiom systems for indexes of several economic variables: inputs, outputs, prices, wages, inflation, and technological change. In addition to conventional smoothness and
A Model for Labor Migration and Urban Unemployment in Less Developed Countries
An economic behavioral model of rural urban migration is formulated which represents a realistic modification and extension of the simple wage differential approach commonly found in the literature
Internal Migration in Mexico: A Test of the Todaro Model
The results of an empirical test of the Todaro model--a model of migration dynamics in which migration is a function of expected income differentials instead of simply wage differentials--using
Tensor Analysis on Manifolds
ing the description in terms of neighborhoods is not a great chore. If f : X -. Y we say that f is continuous at x e X if for every neighborhood V (<--> a neighborhood) of y = fx there is a
Modern geometry--methods and applications
The first € price and the £ and $ price are net prices, subject to local VAT. Prices indicated with * include VAT for books; the €(D) includes 7% for Germany, the €(A) includes 10% for Austria.
The Utility Analysis of Choices Involving Risk
T vHE purpose of this paper is to suggest that an important class of reactions of individuals to risk can be rationalized by a rather simple extension of orthodox utility analysis. Individuals
Migration, Unemployment & Development: A Two-Sector Analysis
This study examines why rural-urban labor migration persists and is even increasing in many developing nations despite the existence of positive marginal products in agriculture and significant
The Welfare Basis of Real Income Comparisons: A Reply
IN PRESENTING his estimates of "la richesse territoriale de France," Antoine Lavoisier [100, 1791] pointed out that the object of such estimation is to furnish "a veritable thermometer of national
...
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