In subsistence economies with general convex technology and rational optimising agents, a new, axiomatic approach is developed, which allows an explicit analysis of the core positive and normative intuitions behind the concept of exploitation. Three main new axioms, called Labour Exploitation in Subsistence Economies, Relational Exploitation, and Feasibility of Non-Exploitation, are presented and it is proved that they uniquely characterise a definition of exploitation conceptually related to the so-called New-Interpretation (Duménil, 1980; Foley, 1982; Duménil at el., 2009), which focuses on the unequal distribution of (and control over) social labour, and on individual well-being freedom and the self-realisation of men. Then, the main results of Roemer's (1982, 1988) classical approach and all the crucial insights of exploitation theory are generalised, proving that every agent's class and exploitation status emerges in the competitive equilibrium, that there is a correspondence between an agent's class and exploitation status, and that the existence of exploitation is inherently linked to the existence of positive profits.