• Corpus ID: 124469594

The Index Number Problem: A Dierential Geometric Approach.

  title={The Index Number Problem: A Dierential Geometric Approach.},
  author={Pia Malaney},
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… 
Divisia price and quantity indices: 80 years after
This paper reviews and extends the theory of price and quantity indices which are defined as line integrals, the two types being those of Divisia and Montgomery. The properties of these indices are
Gauge Invariance, Geometry and Arbitrage
In this work, we identify the most general measure of arbitrage for any market model governed by It\^o processes. We show that our arbitrage measure is invariant under changes of num\'{e}raire and
Geometric Arbitrage Theory and Market Dynamics Reloaded
We have embedded the classical theory of stochastic finance into a differential geometric framework called Geometric Arbitrage Theory and show that it is possible to: --Write arbitrage as curvature
Geometric Arbitrage Theory and Market Dynamics
We have embedded the classical theory of stochastic finance into a differential geometric framework called Geometric Arbitrage Theory and show that it is possible to: --Write arbitrage as curvature
Time and symmetry in models of economic markets
These notes discuss several topics in neoclassical economics and alternatives, with an aim of reviewing fundamental issues in modeling economic markets. I start with a brief, non-rigorous summary of
The Black-Scholes Equation in Presence of Arbitrage
We apply Geometric Arbitrage Theory to obtain results in Mathematical Finance, which do not need stochastic differential geometry in their formulation. First, for a generic market dynamics given
Tracking Changes in Bilateral Trading Patterns in the Absence of PPP
When the ‘law of one price’ fails to hold between trading partners, they may find it difficult to measure the balance of trade due to the inherent currency discrepancy. This may be of particular
Scale Invariance, Bounded Rationality and Non-Equilibrium Economics
We study a class of heterogeneous agent-based models which are based on a basic set of principles, and the most fundamental operations of an economic system: trade and product transformations. A
Can You Hear the Shape of a Market? Geometric Arbitrage and Spectral Theory
Utilizing gauge symmetries, the Geometric Arbitrage Theory reformulates any asset model, allowing for arbitrage by means of a stochastic principal fibre bundle with a connection whose curvature


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
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