When do Optima Converge to Optimum?
DOI:
https://doi.org/10.15678/AOC.2018.1902Keywords:
Gamma-convergence, Ramsey model, convergence of optima, stability of optimal pathsAbstract
In this paper we consider the problem of the convergence of optima in approximated problems to the optimum of limiting problem. We recall the concept of Г-convergence, which is crucial in optimisation problems. We show its importance and provide a list of theorems describing its properties. Using described tools we derive the conditions under which an approximation of the parameters of the Ramsey model with vanishing absolute error of approximation gives the explicite formula for the time-varying consumption per capita, which leads to “almost”-maximisation of the CRRA utility functional.
References
Attouch, H. (1984) Variational Convergence for Functions and Operators. London: Pitman.
Barro, R. J. and Sala-i-Martin, X. (2004) Economic Growth. Second edition. The MIT Press.
Dal Maso, G. (1993) An Introduction to Г-Convergence. Boston, MA: Birkhäuser, https://doi.org/10.1007/978-1-4612-0327-8.
De Giorgi, E. (1984) G-operators and Г-convergence. Proceedings of the International Congress of Mathematicians, Warsaw 1983. Amsterdam: North Holland, pp. 1175–91.
Kuratowski, K. (1961) Topologie I et II. Mathematical monograph. Second edition. PWN.
