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EN
The aim of this article is to present trends and tendencies which may be encountered while modelling economic phenomena, processes as well as social interactions, and to illustrate how the above modelling had been shaped over the years. The general theory of mathematical models has its own language which - in the case of economic models - takes its specific, strictly specified form, depending on the nature of described issues.
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Credit Risk Analysis Using Failure Time Models

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EN
Credit granting institutions have to face the risk that some amount of money that has been lent will not be repaid. Therefore banks and other lending institutions are concerned with the issue of measuring the risk of each credit default, which is needed to accept or reject credit applications. The aim of this paper is to present an approach for classifying applicants, based on duration data - survival analysis. Including an extra dimension - time - in the analysis allows the lending institution to take into account the profitability of a loan. Moreover, failure models give an opportunity to include in the model time-varying covariates - regressors that change in time of the repayment. They make it possible to use in the estimation data about the credits that are still being repayed - censored durations. This method is also a useful tool to predict the influence of the particular characteristics on the probability and the expected time of exit to different kinds of states - complete repayment on time, default but also e.g. an early repayment.
EN
In the paper we consider a role which a matrix plays in the educational process of students of economics (as a notion, a symbol of a mathematical operation as well as a numerical tool). We remind that matrices and determinants appear systematically in courses of mathematics and related subjects. They help to model and solve various significant problems of econometrics (wide sense) and operation researches. It is worth noting, howe-ver, that we make use of matrix notation in our lectures on microeconomics and macroeconomics. The paper initiates the series of three 'didactical' articles devoted to matrices. So it also plays a role of some kind of introduction to the subject. The article may be divided, in a natural way, into two parts, different in character. At the beginning we show and shortly discuss - in an informal manner - selected problems in which matrices 'work'. The second part is quite different: it is much more formalized. The examples we describe in that segment are formulated in the mathematical language. Intentionally, we have chosen elementary facts taken from standard programmes of 'math' for students of economics. According to the plan, we collect them and place under unified label 'Matrices'. We also have announced some themes which will be considered in the following articles of the series.
EN
Generalizing from his experience in solving practical problems, Koopmans set about devising a linear model for analysing activity. Surprisingly, he found that economics at that time possessed no uniform, sufficiently exact theory of production or system of concepts for it. He set out in a pioneering study to provide a theoretical framework for a linear model for analysing activity by expressing first the axiomatic bases of production theory, which rest on the concept of technological sets. He is associated with exact definition of the concept of production efficiency and efficiency prices, and confirmation of their relation as mutual postulates within the linear model of activity analysis. Koopmans saw the present, purely technical definition of efficiency as a special case; he aimed to introduce and analyse the concept of economic efficiency. The study uses the duality precepts of linear programming to reconstruct the results for the latter. It is shown first that evidence confirming the duality precepts of linear programming is equal in value, and secondly that efficiency prices are really shadow prices in today's sense. Furthermore, the model for the interpretation of economic efficiency can be seen as a direct predecessor of the Arrow-Debreu-McKenzie models of general equilibrium theory, as it contained almost every essential element and concept of them - equilibrium prices are nothing other than Koopmans' efficiency prices. Finally Koopmans' model is reinterpreted as a necessary tool for microeconomic description of enterprise technology
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