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Introduction to Calculus of Variations

In: Economic Dynamics and Distributions

Author

Listed:
  • Paulo B. Brito

    (University of Lisbon, Lisbon School of Economics and Management)

Abstract

Calculus of variations problems coinsist in the maximization of functionals over variations in which the objective criterium depends on derivatives. Instead of the maximization of an aggregate, as in the problems studied in chapter 8, the local variation of the state function also contributes to the maximized value of the objective functional. Therefore, their solutions take the form curves traced out by functions of time or of another type of independent variable endowed with an order structure. When the independent variable is not time, the solution to a calculus of variations problem is an optimum distribution profile, as in optimal taxation problems, and when the independent variable is time the solution is an optimal trajectory, as in the resource depletion, intertemporal household, or firm pricing under menu costs problems, as is shown in this chapter.

Suggested Citation

  • Paulo B. Brito, 2026. "Introduction to Calculus of Variations," Dynamic Modeling and Econometrics in Economics and Finance, in: Economic Dynamics and Distributions, chapter 0, pages 303-322, Springer.
    • Handle: RePEc:spr:dymchp:978-3-031-94717-9_9
    DOI: 10.1007/978-3-031-94717-9_9
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