Balder, Erik
(2008):
*Exact and Useful Optimization Methods for Microeconomics.*
Published in: Springer Lecture Notes in Economics and Mathematical Systems
, Vol. 655, No. New Insights into the Theory of Giffen Goods
(12 October 2011): pp. 21-38.

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## Abstract

This paper points out that the treatment of utility maximization in current textbooks on microeconomic theory is deficient in at least three respects: breadth of coverage, completeness-cum-coherence of solution methods and mathematical correctness. Improvements are suggested in the form of a Kuhn-Tucker type theorem that has been customized for microeconomics. To ensure uniqueness of the optimal solution (if applicable), an apparently new adaptation of the notion of strict quasiconcavity is introduced. The role of the domain of differentiability of the utility function is emphasized. This is not only to repair a widespread error in the microeconomic literature but also to point out that this domain can be chosen sensibly in order to include the maximization of certain nondifferentiable utility functions, such as Leontiev utility functions. To underscore the usefulness of the optimality conditions obtained here, five quite different instances of utility maximization are completely solved by a single coherent method.

Item Type: | MPRA Paper |
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Original Title: | Exact and Useful Optimization Methods for Microeconomics |

Language: | English |

Keywords: | microeconomics, utility maximization, Kuhn-Tucker theorem |

Subjects: | C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C61 - Optimization Techniques ; Programming Models ; Dynamic Analysis D - Microeconomics > D0 - General > D00 - General |

Item ID: | 47080 |

Depositing User: | Professor Erik Balder |

Date Deposited: | 23 May 2013 01:22 |

Last Modified: | 04 Oct 2019 04:51 |

References: | Aliprantis, C.D. (1996). Problems in Equilibrium Theory. New York, NY: Springer. Aliprantis, C.D., D.J. Brown and O. Burkinshaw (1989). Existence and Optimality of Competitive Equilibria. New York, NY: Springer. Bazaraa, M.S., H.D. Sherali and C.M. Shetty (1993). Nonlinear Programming. New York, NY: Wiley. Besanko, D. and D.R. Braeutigam (2005). Microeconomics. New York, NY: Wiley. Crouzeix, J.P. (1980). Conditions for convexity of quasiconvex functions. Mathematics of Operations Research 5, 120–125. Edwards, C.H. (1973). Advanced Calculus of Several Variables. New York, NY: Academic Press. Henderson, J.M. and R.E. Quandt (1980). Microeconomic Theory: a Mathematical Approach. New York, NY: McGraw-Hill. Jehle, G.A. and P.J. Reny (2001). Advanced Microeconomic Theory. New York, NY: Wiley. Luenberger, D.G. (1995). Microeconomic Theory. New York, NY: McGraw-Hill. Mas-Colell, A., M.D. Whinston and J.R. Green (1995). Microeconomic Theory. New York, NY: Oxford University Press. Simon, C.P., and L. Blume (1993). Mathematics for Economists. New York, NY: Norton. Sydsæter, K., P. Hammond, A. Seierstad and A. Strøm (2005). Further Mathematics for Economic Analysis. Harlow, UK: Prentice Hall. Takayama, A. (1996). Mathematical Economics. Cambridge, UK: Cambridge University Press. Varian, H.R. (1992). Microeconomic Analysis. New York, NY: Norton. |

URI: | https://mpra.ub.uni-muenchen.de/id/eprint/47080 |