Mathematical Appendix

Alfonso Novales, Esther Fernández and Jesus Ruiz

Chapter Chapter 10 in Economic Growth, 2014, pp 525-548 from Springer

Abstract: 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.

Keywords: Optimal Control Problem; Spectral Decomposition; Order Differential Equation; Transversality Condition; Shadow Prex (search for similar items in EconPapers)
Date: 2014
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
Chapter: Mathematical Appendix (2022)
Chapter: Mathematical Appendix (2009)
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sptchp:978-3-642-54950-2_10

Ordering information: This item can be ordered from
http://www.springer.com/9783642549502

DOI: 10.1007/978-3-642-54950-2_10

Access Statistics for this chapter

More chapters in Springer Texts in Business and Economics from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().