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Mathematical Appendix

In: Economic Growth

Author

Listed:
  • Alfonso Novales

    (Universidad Complutense)

  • Esther Fernández

    (Universidad Complutense)

  • Jesús Ruiz

    (Universidad Complutense)

Abstract

Let us consider the dynamic optimization problem, 1 $$\mathop {Max}\limits_{v_t } \int_0^T {f\left( {x_t, v_t, t} \right)}dt$$ subject to the constraint, 2 $$\begin{array}{rl}\mathop {x_t }\limits^. = h(x_t, v_t, t)\\ {\rm and\ given}\ x_{0}\end{array}$$ 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, 2009. "Mathematical Appendix," Springer Books, in: Economic Growth, chapter 0, pages 495-516, Springer.
    • Handle: RePEc:spr:sprchp:978-3-540-68669-9_10
    DOI: 10.1007/978-3-540-68669-9_10
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