In this work we study the problem of characterizing efficient, price efficient and optimal allocations in a very general economic model with a continuum of agents and an infinite-dimensional commodity space. We do that using the theory of concave normal integrands and Clarke’s theory of generalized gradients, as well as certain results from geometric functional analysis. We also consider approximations of those notions and study their properties using the theory of $\varepsilon $-subdiflerentiation and Ekeland’s variational principal. Then we examine those concepts in the context of a particular sector of the enonomy using single valued and multivalued conditional expectations and martingale theory. Finally we study stability questions using the Kuratowski–Mosco convergence of sets and the epi-convergence ($\tau $-convergence) of closed functions.