Abstract In this paper we investigate incentive aspects of the Linear Cost Share Equilibrium principle by designing mechanisms whose Nash allocations coincide with Linear Cost Share equilibrium allocations. The mechanisms presented here allow not only preferences but also initial indowments to be privately observed, a feature missing from much recent work in implementation theory. We give mechanisms for both cases of withholding and destruction of endowments. If one reinterprets the commodity space, our mechanisms also implements Walransian allocations to economics with purely private goods. Thus, our mechanisms are sufficiently general to cover Walrasian equilibria, Lindahl equilibria, and cost share equilibria. In other words, the mechanisms in this paper appear to represent "generic" mechanisms to implement competitive-type allocations in private and public goods economies. Journal of Economic Literature Classification Numbers: C72, D61, D78.