Optimal and competitive programs in reachable multi sector models

We show that in multi-sector optimal growth models, where the technology satisfies a simple reachability condition, infinite horizon programs which satisfy the competitive conditions are optimal. We provide examples of a variety of production models where the reachability condition is satisfied. An example is also provided where the reachability condition is not satisfied and there are competitive programs which are not optimal. The results of the paper are of interest from the standpoint of decentralization in intertemporal economies.