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  • 1
    Electronic Resource
    Electronic Resource
    Welfare from a benefit viewpoint (1996)
    Springer
    Economic theory 7 (1996), S. 445-462 
    Details
    ISSN: 1432-0479
    Keywords: D00 ; D60
    Source: Springer Online Journal Archives 1860-2000
    Topics: Economics
    Notes: Summary Individual welfare is most naturally measured in terms of individual utility but this has the well-known disadvantage that utility levels of different consumers cannot be meaningfully compared. This difficulty is traditionally avoided by using various willingness-to-pay measures, such as compensating and equivalent variation. These measures are based on price changes. This paper develops alternative welfare measures using willingness-to-trade concepts as originally proposed by Dupuit (1844). These measures are based directly on commodity bundle changes. These welfare measures can be represented as integrals under certain inverse demand functions. An important property of the proposed welfare measures studied here is that they can be meaningfully aggregated to form overall welfare measures. These measures in turn directly quantify a compensation criterion. It is shown that competitive prices provide a first-order approximation to the welfare measures. Furthermore a second-order approximation can be found by forming a suitable aggregation of the individual second-order effects. Finally, it is shown that the representations for consumer welfare as integrals under inverse demand curves can be extended to the aggregate measures as well. This then provides a complete complement to traditional measures based on price changes.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01213660
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Welfare from a benefit viewpoint (1996)
    Springer
    Economic theory 7 (1996), S. 445-462 
    Details
    ISSN: 1432-0479
    Keywords: JEL Classification Numbers: D00 D60.
    Source: Springer Online Journal Archives 1860-2000
    Topics: Economics
    Notes: Summary.  Individual welfare is most naturally measured in terms of individual utility but this has the well-known disadvantage that utility levels of different consumers cannot be meaningfully compared. This difficulty is traditionally avoided by using various willingness-to-pay measures, such as compensating and equivalent variation. These measures are based on price changes. This paper develops alternative welfare measures using willingness-to-trade concepts as originally proposed by Dupuit (1844). These measures are based directly on commodity bundle changes. These welfare measures can be represented as integrals under certain inverse demand functions. An important property of the proposed welfare measures studied here is that they can be meaningfully aggregated to form overall welfare measures. These measures in turn directly quantify a compensation criterion. It is shown that competitive prices provide a first-order approximation to the welfare measures. Furthermore a second-order approximation can be found by forming a suitable aggregation of the individual second-order effects. Finally, it is shown that the representations for consumer welfare as integrals under inverse demand curves can be extended to the aggregate measures as well. This then provides a complete complement to traditional measures based on price changes.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01213660
    Library Location Call Number Volume/Issue/Year Availability
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    Paper (German National Licenses)
    Fulltext
  • 3
    Electronic Resource
    Electronic Resource
    Convergence rate of a penalty-function scheme (1971)
    Springer
    Journal of optimization theory and applications 7 (1971), S. 39-51 
    Details
    ISSN: 1573-2878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The penalty-function approach is an attractive method for solving constrained nonlinear programming problems, since it brings into play all of the well-developed unconstrained optimization techniques, If, however, the classical steepest-descent method is applied to the standard penalty-function objective, the rate of convergence approaches zero as the penalty coefficient is increased to yield a close approximation to the true solution. In this paper, it is shown that, ifm+1 steps of the conjugate-gradient method are successively repeated (wherem is the number of constraints), the convergence rate when applied to the penalty-function objective conveges at a rate predicted by the second derivative of the Lagrangian. This rate is independent of the penalty coefficient and, hence, the scheme yields reasonable convergence for a first-order method.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00933591
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    Paper (German National Licenses)
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  • 4
    Electronic Resource
    Electronic Resource
    Computing economic equilibria using benefit and surplus functions (1995)
    Springer
    Computational economics 8 (1995), S. 47-64 
    Details
    ISSN: 1572-9974
    Keywords: Equilibria ; Fixed Point Methods ; Surplus ; Benefit
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Economics
    Notes: Abstract This paper suggests some new algorithms for the computation of equilibria for private ownership competitive economies. The algorithms are based on two principles related to economic equilibria termed, respectively, thezero-maximum principle and thezero-minimum principle. These principles relate equilibria to certain optimization problems, and these relations can be used as a basis for actually computing equilibria. The algorithms suggested in this paper employ a standard fixed-point method as a fundamental component, as do other general purpose algorithms for determining equilibria. However, in this paper the fixed-point methods are applied to mappings that are derived from the optimization principles related to equilibria, and these mappings have several attractive features. Especially attractive is the fact that the mappings can be defined either with respect to prices (inm dimensions, wherem is the number of commodities) or with respect to utility levels (inn dimensions, wheren is the number of representative consumers). In applications, typicallyn is much less thanm and hence great efficiency is achieved by using the algorithms that are defined with respect to utility levels. Some computational experience with these algorithms is reported in this paper. This experience confirms the feasibility of using the algorithms and indicates an exceptional degree of reliability and speed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01298497
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    Paper (German National Licenses)
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  • 5
    Book
    Book
    Optimization by vector space methods (1969)
    New York u.a. :Wiley,
    Details
    Title: Optimization by vector space methods
    Author: Luenberger, David G.
    Publisher: New York u.a. :Wiley,
    Year of publication: 1969
    Pages: 326 S.
    Type of Medium: Book
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    ZIB Catalog
    Zuse Institute Berlin get availability status
  • 6
    Book
    Book
    Linear and nonlinear programming (1989)
    Reading, MA u.a. :Addison-Wesley,
    Details
    Title: Linear and nonlinear programming
    Author: Luenberger, David G.
    Publisher: Reading, MA u.a. :Addison-Wesley,
    Year of publication: 1989
    Pages: 491 S.
    Type of Medium: Book
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    ZIB Catalog
    Zuse Institute Berlin get availability status
  • 7
    Book
    Book
    Linear and nonlinear programming /; 116 (2008)
    New York, NY :Springer,
    Details
    Title: Linear and nonlinear programming /; 116
    Author: Luenberger, David G.
    Contributer: Ye, Yinyu
    Edition: 3. ed.
    Publisher: New York, NY :Springer,
    Year of publication: 2008
    Pages: XIII, 546 S. : , Ill., graph. Darst. ; , 235 mm x 155 mm
    Series Statement: International series in operations research & management science 116
    ISBN: 978-0-387-74502-2 , 0-387-74502-5 , 978-0-387-74503-9
    Type of Medium: Book
    Language: English
    URL: http://www.zentralblatt-math.org/zmath/en/advanced/?q=an:pre05308827&format=complete
    URL: Inhaltsverzeichnis
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