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• Article details

Przegląd Statystyczny

2005 | 52 | 2 | 23-39

THE TANGENT LINES AND LOCAL PROPERTY

PL

Abstracts

EN
In this paper the local property of economic processes is considered. The economic-process is said a real function and its shape is global property of economic process. The local property of !he processes is an algebraic expression. Each expression contains: the derivative of the function, and alternatively the value of the function, or the value of the argument of the function; it is represented by an tangent line to the process. For example: marginal value of the process is a coefficient of proportionality for expansion of the function; 'dy' and expansion of the argument: 'dx', so it is the classic linear derivative of the process: 'y' . The marginal value is represented by linear function tangent to the process. Logarithmic derivative of the process as well as its elasticity are also presented in the mathematical form. The paper presents an universal construction of tangent lines. First, the construction is made in the language of the theory of sets. The local property is said a function tangent to the process. Later the universal model is filled up with the theory of group. For the construction of tangent function two elements are needed: a principle of tangent and advisable class of functions. The class is correlated with the principle. Each function of the advisable class is not tangent to the other function of the class. Principle of tangent is a relation of equivalent. The advisable class of the function is said a class of derivatives. Derivative of any function is a function of the advisable class. Any function has got one derivative or no derivative. In the construction of derivative in language of the theory of group the mapping from a topological group into any group is considered. The principle of tangent is defined by the local topology of the Cartesian product of the groups. These constructions include classic calculus and parallel calculus with mappings:linear, exponential, power and logarithmic

EN

23-39

ARTICLE

Contributors

author
• T. Janaszak, Akademia Ekonomiczna we Wroclawiu, ul. Komandorska 118/120, 53-345 Wroclaw, Poland

Identifiers

CEJSH db identifier
05PLAAAA0038926