Introduction to Calculus of Variations

Paulo Brito

Chapter Chapter 9 in Economic Dynamics and Distributions, 2026, pp 303-322 from Springer

Abstract: 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.

Date: 2026
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DOI: 10.1007/978-3-031-94717-9_9

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