Given an economy (consumers, preferences, production sets, endowments), defining a generalized competitive mechanism (assigning under conditions to each consumer an income) and using a weakening of Walras' law, then an application of Kakutani's fixed point theorem delivers an equilibrium. From this connections between competitive equilibria and Pareto efficient allocations are proved (first welfare theorem) and also a decentralization theorem (second welfare theorem). Some interesting remarks are added, so for instance, that convexity in decentralization theorems is needed only to show, that an equilibrium exists, it is not required to show, that the equilibrium occurs at the Pareto efficient allocation.