Diamond-\phi_h dynamics on time scales with an application to economics

Conventional dynamic models in economics are usually expressed in discrete or continuous time. A new modelling technique-time scales calculus-unifies both of these approaches into a general framework. We present and construct a dynamic optimization problem from economics in which the utility function is \phi_{h}-concave and the value function and constraints are on different time scales. The calculus of variations and optimal control are employed, with the aid of the newly introduced diamond-\phi_{h} dynamic calculus by the authors [۱۲] on time scales, to obtain a solution. The Hermite-Hadamard inequality with the diamond-\phi_{h} dynamic integral follows a proof of the new model. The new diamond-\phi_{h} time scale model unifies various related existing models involving general and more complex time domains.

Keywords:

time scales , phi_{h}-concave , diamond-phi_{h} , Hermite-Hadamard , dynamic model