Economic growth with heterogenous space and population: an optimal control model of PDEs
Fausto Gozzi
Luiss University, Roma Italy
Co-Author(s): Raouf Boucekkine, Giorgio Fabbri, Salvatore Federico
Abstract:
A series of pretty recent works have merged the spatial dimension with
growth theory models using the framework coming from
classical geographical economy.
In such papers the underlying mathematical model is an optimal control problem
where the state equation is a second order PDE.
In this talk we briefly describe such models and their motivation.
Then we provide the main results, obtained with the Dynamic Programming approach:
- the existence of an explicit solutions of the associated HJB equation;
- the existence of optimal strategies in feedback form.
We present some economic consequences of such results
and discuss possible generalization of them when explicit solutions are not availeble.