SOME STRUCTURED DYNAMIC PROGRAMS ARISING IN ECONOMICS

We consider stationary discounted deterministic dynamic programs with bounded rewards, and provide sufficient conditions on their data (reward and transition functions) to ensure that the outcome functions (value and optimal policy selections) have some desirable structure. For the value function, the properties of interest are monotonicity, continuity and concavity. For the optimal policies, monotonicity and single-valuedness are investigated. In both cases, monotonicity is the main question, and lattice programming techniques are used. Our results generalize earlier findings reported for specific models of dynamic optimization, including optimal growth theory and resource management.