Lagrange Coefficient

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Emre Kiyak - One of the best experts on this subject based on the ideXlab platform.

  • the optimization of the maximum rentability of an airplane by using Lagrange Coefficient
    ANADOLU UNIVERSITY JOURNAL OF SCIENCE AND TECHNOLOGY –B Theoretical Sciences, 2011
    Co-Authors: Emre Kiyak
    Abstract:

    In this study, the optimization of the maximum rentability of an airplane under various contraints by using Lagrange Coefficients has been realized; so as to, obtain a model of airplane selection for companies. Basically, as an application, the optimum drag polar multiplicative Coefficient has been obtained by using the weights of the main aircraft parts, flight speed, flight altitude, fuel consumption, range, take-off distance, and lift-to-drag ratio.

D. D. Ganji - One of the best experts on this subject based on the ideXlab platform.

  • New approaches to identification of the Lagrange multiplier in the variational iteration method
    Journal of the Brazilian Society of Mechanical Sciences and Engineering, 2015
    Co-Authors: S. S. Samaee, O. Yazdanpanah, D. D. Ganji
    Abstract:

    In this paper, new methods to obtain the Lagrange multiplier are presented. Differential equation consists of linear and nonlinear parts. We have infinite equations that the linear parts of them are different together then any of the equations have different Lagrange multipliers. In this article, steps of the proposed methods are fully described manually. In this paper, we show that the proposed methods attain precisely the Lagrange multipliers. Exact identification of Lagrange multipliers in the VIM is very important for obtaining highly accurate solutions; on the other hand, it is complicate to determine the multipliers for strongly nonlinear equations. Lagrange Coefficient is a parameter that is used in VIM. Therefore, this study introduces a simple and efficient way to solve Lagrange Coefficient. The results show that all three methods obtain the Lagrange Coefficient without any errors and manually are solved easily.

Pablo Cotomillan - One of the best experts on this subject based on the ideXlab platform.

  • utility and production theory and applications
    1999
    Co-Authors: Pablo Cotomillan
    Abstract:

    I: Utility and Consumer Demand Analysis.- 1 Theory of Utility and Consumer Behaviour: A Comprehensive Review of Concepts, Properties and the Most Significant Theorems.- 1.1 Theory of Utility.- 1.2 Preference, Choice and Indifference Concept and Utility Function Existence.- 1.3 Properties of the Utility Function.- 1.3.1 Additivity.- 1.3.2 Homogeneity.- 1.3.3 Homotheticity.- 1.3.4 Weak and Strong Separability.- 1.4 Basic Theory (Primal)* Marshallian (or Walrasian) Demand Functions.- 1.4.1 Properties of the Marshallian (or Walrasian) Demand Functions.- 1.5 Consumer Equilibrium (Dual): Hicksian (or Compensated) Demand Functions.- 1.5.1 Properties of the Hicksian (or Compensated) Demand Functions.- 1.6 Indirect Utility Function.- 1.7 Expenditure Function.- 1.8 Restrictions of the Demand Systems.- 1.8.1 Engel Aggregation Condition.- 1.8.2 Cournot Aggregation Condition.- 1.8.3 Homogeneity Condition.- 1.8.4 Symmetry or Integrability Condition.- 1.8.5 Negativity Condition.- 1.9 Roy's Identity.- 1.10 Hotelling's Theorem (or Shephard's Lemma for Consumers).- 1.11 Relationships between the UMP and the EMP.- 1.12 The Slutsky Equation.- 1.13 Complementary and Substitutive Relationships.- Basic References.- References and Further Reading.- 2 Alternative Theories of Consumer Behaviour.- 2.1 Introduction.- 2.2 Discrete Choice Models.- 2.3 Time Allocation Models.- 2.3.1 Hicks Model.- 2.3.2 Yield-Leisure Model.- 2.3.3 Extended Yield-Leisure Model.- 2.3.4 Goods-Leisure Model with Time Allocation to Goods Consumption.- 2.3.4.1 Becker's Model.- 2.4 Train-McFadden Synthesis Model.- 2.5 Lancaster's Consumption Technology Model.- 2.6 Jara-Diaz Model.- 2.6.1 Jara-Diaz and Farah Model (1987).- 2.6.2 Jara-Diaz Model (1998).- 2.7 Models of Consumer Behaviour with Incomplete Information.- 2.8 Revealed Preference Theory.- References.- 3 Main Forms of Utility Functions.- 3.1 The Cobb-Douglas Utility Function.- 3.1.1 Properties.- 3.1.2 Marshallian or Ordinary Demands (Primal).- 3.1.3 The Indirect Utility Function.- 3.1.4 Hicksian or Compensated Demands (Dual).- 3.1.5 The Expenditure Function.- 3.1.6 Elasticities, Engel Curves and Expenditure Share Functions.- 3.2 The Utility Function of the Constant Elasticity of Substitution (CES).- 3.2.1 Marshallian Demands.- 3.2.2 The Indirect Utility Function.- 3.2.3 Hicksian Demands.- 3.2.4 The Expenditure Function.- 3.2.5 Application to the Particular CES Utility Function.- 3.2.5.1 The Indirect Utility Function.- 3.2.5.2 The Expenditure Function.- 3.2.5.3 Hicksian Demands.- 3.2.5.4 The Own, Cross and Income Elasticity of the CES Demand System.- 3.2.5.5 Restrictions of CES Demand Systems.- 3.3 The Quasi-linear Utility Functions.- 3.3.1 Marshallian Demands.- 3.3.2 The Indirect Utility Function.- 3.3.3 The Expenditure Function.- 3.3.4 Roy's Identity.- 3.3.5 Hotelling's Theorem: Hicksian Demand Functions.- 3.3.6 Application to the Particular Quasi-linear Utility Function.- 3.3.6.1 The Marshallian Demand.- 3.3.6.2 Restrictions of the Quasi-linear Demand System.- Recommended Reading.- 4 Study of the Econometric Applications: Demand Functions and Systems.- 4.1 Demand Functions.- 4.2 Application I for Demand Functions: Walrasian (or Marshallian) Demand Functions for Interurban Passenger Transport.- 4.2.1 Model.- 4.2.2 Data.- 4.2.3 Walrasian (or Marshallian) Demands for Interurban Passenger Transport: Air and Road Transport.- 4.2.3.1 Air Transport Demand.- 4.2.3.2 Road Transport Demand.- 4.2.4 Results of the Empirical Research.- 4.3 Complete Demand Systems.- 4.3.1 Linear Expenditure System (LES).- 4.3.2 Almost Ideal Demand System.- 4.3.3 Diewert Demand Model.- 4.3.4 Translog Demand Model.- 4.4 Application II for Demand Systems: Estimation of an Almost Ideal Demand System (AIDS): Particular Disaggregation for the Main Transport Services.- 4.4.1 Model: Almost Ideal Demand System.- 4.4.2 Data.- 4.4.3 Estimation of the Model.- 4.4.4 Conclusions.- Basic References.- References and Further Reading.- II: Production and Firm Supply Analysis.- 5 Theory of Production, Cost and Behaviour of the Firm: A Comprehensive Reformulation.- 5.1 Theory of the Firm.- 5.2 Production Possibility Set and Existence of Production Function.- 5.3 Properties of Production Function.- 5.3.1 Efficiency.- 5.3.2 Differentiability and Continuity.- 5.3.3 Strict Quasi-concavity.- 5.4 The Firm's Equilibrium: Classic Demand, Profit and Direct Supply Functions.- 5.4.1 Profit Maximisation.- 5.4.2 Properties of Input Classic Demand and Output Direct Supply Functions.- 5.4.2.1 Decreasing.- 5.4.2.2 Existence.- 5.4.2.3 Homogeneity.- 5.4.2.4 Symmetry.- 5.4.2.5 Negativity.- 5.4.2.6 Negative Semi-definite.- 5.4.3 Profit Function.- 5.4.4 Properties of the Profit Function: Hotelling's Theorem.- 5.4.4.1 Non-decreasing.- 5.4.4.2 Homogeneity.- 5.4.4.3 Convexity.- 5.4.4.4 Continuity.- 5.4.4.5 Hotelling's Theorem.- 5.5 The Firm's Equilibrium (Primal A).- 5.6 The Firm's Equilibrium (Primal B): Marshallian Demand and Indirect Supply Functions.- 5.6.1 Output Maximisation.- 5.6.2 Properties of the Input Marshallian Demand and Indirect Supply Functions.- 5.6.2.1 Decreasing.- 5.6.2.2 Existence.- 5.6.2.3 The Lagrange Coefficient P).- 5.6.2.4 Homogeneity.- 5.6.2.5 Negativity.- 5.6.2.6 Symmetry.- 5.6.2.7 Negative Semi-definite.- 5.6.2.8 Roy's Identity.- 5.7 The Firm's Equilibrium: Input Classic Demand and Output Direct Supply Functions.- 5.7.1 Loss Minimisation.- 5.7.2 Properties of Input Classic Demand and Output Direct Supply Functions.- 5.7.3 Loss and Input Classic Demand Functions: Hotelling's Theorem.- 5.8 The Firm's Equilibrium (Dual A).- 5.9 The Firm's Equilibrium (Dual B): Input Conditioned Demand and Cost Functions.- 5.9.1 Cost Minimisation.- 5.9.2 Properties of the Input Conditioned Demand.- 5.9.2.1 Non-decreasing.- 5.9.2.2 Existence.- 5.9.2.3 Homogeneity.- 5.9.2.4 The Lagrange Coefficient ( ).- 5.9.2.5 Negativity.- 5.9.2.6 Symmetry.- 5.9.2.7 Negative Semi-definite.- 5.9.3 Properties of Cost Function: Shephard's Lemma.- 5.9.3.1 Increase.- 5.9.3.2 Homogeneity.- 5.9.3.3 Concavity.- 5.9.3.4 Continuity.- 5.9.3.5 Shephard's Lemma.- 5.10 Diagrammatic Representation of the Main Relationships.- 5.11 Joint Production.- 5.11.1 Income Maximisation.- 5.11.2 Input Minimisation.- 5.12 Short-Run.- 5.12.1 Short-Run and Single Production.- 5.12.2 Short-Run and Joint Production.- 5.13 Reflections on the Main Relationships Designed.- 5.14 The Elasticity of Substitution.- Basic References.- References and Further Reading.- 6 Alternative Theories on Companies.- 6.1 Baumol's Sales Income Maximisation Model.- 6.2 Marri's Production Volume Maximisation Model.- 6.3 Cooperative Company Model.- 6.4 Behavioural Models of the Company.- 6.5 Company Models Based on Transaction Cost Economy.- References.- 7 Main Forms of Production and Cost Functions.- 7.1 The Cobb-Douglas Production Function.- 7.1.1 Characterisation.- 7.1.2 The Marginal Rate of Technical Substitution (MRTS).- 7.1.3 The Elasticity of Substitution.- 7.1.4 Returns to Scale.- 7.1.5 The Profit Function and Input Demand Functions.- 7.1.6 Hotelling's Theorem.- 7.1.7 The Cost Function and Input Conditioned Demand Functions.- 7.1.8 Shephard's Lemma.- 7.1.9 LRAC and LRMC Curves.- 7.1.10 Applying the Duality.- 7.2 The CES Production Function.- 7.2.1 The Marginal Rate of Technical Substitution (MRTS).- 7.2.2 Returns to Scale.- 7.2.3 The Elasticity of Substitution.- 7.2.4 The Output Supply Function and Input Demand Functions.- 7.2.5 The Cost Function and Input Conditioned Demand Functions.- 7.2.6 The LRAC and LRMC.- 7.2.7 Applying the Duality.- Recommended Reading.- 8 Study on Econometric Applications: Production and Cost Functions.- 8.1 Production Functions.- 8.2 Application III for Production Functions: Analysis of the Returns to Scale, Elasticities of Substitution and Behaviour of Shipping Production.- 8.2.1 The Model.- 8.2.2 Data.- 8.2.3 Empirical Results.- 8.3 Cost Function.- 8.4 Other Empirical Functions.- 8.5 Application IV for Cost Functions: Elasticities of Substitution and Behaviour of Shipping Costs.- 8.5.1 Model.- 8.5.2 Data.- 8.5.3 Empirical Results.- 8.5.4 Summary and Conclusions.- Basic References.- References and Further Reading.- III: Uncertainty.- 9 Utility, Production and Uncertainty.- 9.1 Introduction.- 9.2 First Stage in the Development of Utility Theory Under Conditions of Uncertainty: the Principle of Expected Value.- 9.3 Second Stage in the Development of Utility Theory Under Conditions of Uncertainty: the Principle of Expected Utility.- 9.4 Third Stage in the Development of Utility Theory Under Conditions of Uncertainty: Von Neumann-Morgenstern Utility Function.- 9.5 Individuals' Attitudes to Risk.- 9.6 Production and Uncertainty.- 9.7 Critiques of the Theory of Expected Utility and the Theory of Limited Rationality.- 9.7.1 Violation of the Axiom of Independence.- 9.7.2 Violation of the Transitivity Axiom.- References.

S. S. Samaee - One of the best experts on this subject based on the ideXlab platform.

  • New approaches to identification of the Lagrange multiplier in the variational iteration method
    Journal of the Brazilian Society of Mechanical Sciences and Engineering, 2015
    Co-Authors: S. S. Samaee, O. Yazdanpanah, D. D. Ganji
    Abstract:

    In this paper, new methods to obtain the Lagrange multiplier are presented. Differential equation consists of linear and nonlinear parts. We have infinite equations that the linear parts of them are different together then any of the equations have different Lagrange multipliers. In this article, steps of the proposed methods are fully described manually. In this paper, we show that the proposed methods attain precisely the Lagrange multipliers. Exact identification of Lagrange multipliers in the VIM is very important for obtaining highly accurate solutions; on the other hand, it is complicate to determine the multipliers for strongly nonlinear equations. Lagrange Coefficient is a parameter that is used in VIM. Therefore, this study introduces a simple and efficient way to solve Lagrange Coefficient. The results show that all three methods obtain the Lagrange Coefficient without any errors and manually are solved easily.

O. Yazdanpanah - One of the best experts on this subject based on the ideXlab platform.

  • New approaches to identification of the Lagrange multiplier in the variational iteration method
    Journal of the Brazilian Society of Mechanical Sciences and Engineering, 2015
    Co-Authors: S. S. Samaee, O. Yazdanpanah, D. D. Ganji
    Abstract:

    In this paper, new methods to obtain the Lagrange multiplier are presented. Differential equation consists of linear and nonlinear parts. We have infinite equations that the linear parts of them are different together then any of the equations have different Lagrange multipliers. In this article, steps of the proposed methods are fully described manually. In this paper, we show that the proposed methods attain precisely the Lagrange multipliers. Exact identification of Lagrange multipliers in the VIM is very important for obtaining highly accurate solutions; on the other hand, it is complicate to determine the multipliers for strongly nonlinear equations. Lagrange Coefficient is a parameter that is used in VIM. Therefore, this study introduces a simple and efficient way to solve Lagrange Coefficient. The results show that all three methods obtain the Lagrange Coefficient without any errors and manually are solved easily.

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