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Mathematical Appendix

In: Economic Growth

Author

Listed:
  • Alfonso Novales

    (Complutense University of Madrid)

  • Esther Fernández

    (Complutense University of Madrid)

  • Jesús Ruiz

    (Complutense University of Madrid)

Abstract

Let us consider the dynamic optimization problem, $$\displaystyle{\mathop{\mathit{Max}}\limits_{v_{t}}\text{ }\int _{0}^{T}f(x_{ t},v_{t},t)\mathit{dt}}$$ subject to the constraint, $$\displaystyle\begin{array}{rcl} \dot{x}_{t}& =& h(x_{t},v_{t},t) {}\\ & & \mathrm{and\ given}\ \ x_{0} {}\\ \end{array}$$ where v t is known as the control variable, x t being the state variable. The constraint is in the form of a differential equation describing the time evolution of the state variable, as a function of the decision taken at each point in time, i.e., of the value of the control variable. Control and state could be vector variables, in which case we would have several restrictions like the one above, one for each state variable.

Suggested Citation

  • Alfonso Novales & Esther Fernández & Jesús Ruiz, 2014. "Mathematical Appendix," Springer Texts in Business and Economics, in: Economic Growth, edition 2, chapter 0, pages 525-548, Springer.
  • Handle: RePEc:spr:sptchp:978-3-642-54950-2_10
    DOI: 10.1007/978-3-642-54950-2_10
    as

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