In this talk we consider optimal control problems in which there is an infinite number of ex-ante identical agents. The evolution of the idiosyncratic state variables follows a controllable It� process, that is, there exists a vector of controls that allows the planner to modify the individual state of each agent. In addition there are some aggregate states. In this problem, the aim of the planner is to maximize an optimality criterion over the full distribution (across agents) of state variables. The evolution of the state distribution across agents can be characterized by the Kolmogorov forward (KF) equation In this talk we discuss a particular case of interest: the analysis of constrained efficiency in heterogeneous agents economies. The constrained efficient allo- cation is defined as the one of a social planner who maximizes a utilitarian social welfare function (SWF) subject to the same equilibrium budget con-straints and competitive price setting as the individual agents. The planner cannot complete markets or use any transfers between agents. We employ the techniques developed here to compare the solution of this problem with the case of a competitive equilibrium in which each agent maximizes its own dis- counted utility subject to its state dynamics taking the aggregate conditions and the dynamics of the other agents as given. Joint work with B. Moll (Princeton University).