scholarly journals Intuitive Mathematical Economics Series. Constrained Maximization and the Method of Lagrange Multipliers

2018 ◽  
Author(s):  
Sergio Pernice
Keyword(s):  
Lagrange Multipliers ◽  
Mathematical Economics ◽  
Constrained Maximization ◽  
Method Of Lagrange Multipliers

Applying the Method of Lagrange Multipliers to Derive an Estimator for Unsampled Soil Properties

2014 ◽  
Vol 11 (1) ◽  
pp. 15
Author(s):  
Set Foong Ng ◽  
Pei Eng Ch’ng ◽  
Yee Ming Chew ◽  
Kok Shien Ng
Keyword(s):  
Soil Properties ◽  
Lagrange Multipliers ◽  
Unbiased Estimator ◽  
Soil Property ◽  
Minimum Variance ◽  
Distance Method ◽  
True Value ◽  
A Site ◽  
Method Of Lagrange Multipliers ◽  
Inverse Distance

Soil properties are very crucial for civil engineers to differentiate one type of soil from another and to predict its mechanical behavior. However, it is not practical to measure soil properties at all the locations at a site. In this paper, an estimator is derived to estimate the unknown values for soil properties from locations where soil samples were not collected. The estimator is obtained by combining the concept of the ‘Inverse Distance Method’ into the technique of ‘Kriging’. The method of Lagrange Multipliers is applied in this paper. It is shown that the estimator derived in this paper is an unbiased estimator. The partiality of the estimator with respect to the true value is zero. Hence, the estimated value will be equal to the true value of the soil property. It is also shown that the variance between the estimator and the soil property is minimised. Hence, the distribution of this unbiased estimator with minimum variance spreads the least from the true value. With this characteristic of minimum variance unbiased estimator, a high accuracy estimation of soil property could be obtained.

scholarly journals On Some Aspects of the Examination in Econometrics

2021 ◽  
Vol 8 (3) ◽  
pp. 7-16
Author(s):  
Symon Serbenyuk
Keyword(s):  
Linear Programming ◽  
Nonlinear Programming ◽  
Mathematical Models ◽  
Mathematical Optimization ◽  
Input Output ◽  
High Quality ◽  
Mathematical Economics ◽  
Linear And Nonlinear Programming ◽  
Scientific Results ◽  
Method Of Lagrange Multipliers

Teaching econometrics has been studied by a number of researchers, however, there is little information available on the quality of examination and on simplification of tests for demonstration the high-quality knowledge by students in concrete topics of econometrics or mathematical economics.One can note the following main goals of studying the basics of mathematical economics or econometrics by students: forming the notions of mathematical model and of modeling economic processes and phenomena; understanding a role of using mathematical models for economics research and obtaining scientific results; formatting skills for constructing mathematical models in economics, for solving economics problems by mathematical modeling.The main goal of this paper is to simplify test tasks, is to help to students to demonstrate the high-quality knowledge in certain areas of mathematical economics, and also is to construct a system of testing tasks, in which the emphasis was placed on the knowledge and understanding of an algorithm of solving the problem.In the present paper, to quality examine the student knowledge in the basics of mathematical economics, a certain system of tests was constructed and is considered. The main attention is also given to algorithms and techniques of solving some tasks (problems) of mathematical economics. The following topics of mathematical economics are viewed: constructing mathematical models of linear programming, the input-output model, the Monge-Kantorovich transportation problem, the simplex method of linear programming, the graphic method of linear and nonlinear programming, the method of Lagrange multipliers in mathematical optimization. Some primary basic results of studying linear programming, nonlinear programming, and the input-output model are noted.A new system of tests that satisfies the aim of this paper is modeled. The described tests require less time for solving than usual tasks. Here we do not focus on the repetition of auxiliary mathematical knowledge and arithmetic skills. These tests are simplified versions of standard tasks and help students to demonstrate knowledge in the mentioned topics of mathematical economics. The tasks are focused only on the knowledge of basic formulas, techniques, and connections between mathematical objects, economic systems, and their elements.

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