Mathematical Appendix

Alfonso Novales, Esther Fernández and Jesus Ruiz

Chapter Chapter 10 in Economic Growth, 2009, pp 495-516 from Springer

Abstract: 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.

Keywords: Spectral Decomposition; Matrix Algebra; Order Differential Equation; Transversality Condition; Shadow Prex (search for similar items in EconPapers)
Date: 2009
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DOI: 10.1007/978-3-540-68669-9_10

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