Periodic and Chaotic Programs of Optimal Intertemporal Allocation in an Aggregative Model with Wealth Effects.

We examine a discrete-time aggregative model of discounted dynamic optimization where the felicity function depends on both consumption and capital stock. The need for studying such models has been stressed in the theory of optimal growth and also in the economics of natural resources. We identify conditions under which the optimal program is monotone. In our framework, the optimal program can exhibit cyclic behavior for all discount factors close to one. We also present an example to show that our model can exhibit optimal behavior which is chaotic in both topological and ergodic senses.