The natural projection approach to smooth production economies∗

Smooth economies with private ownership of production of the kind previously considered in the literature are shown to be formally identical to exchange economies with demand functions that are properly adjusted for production. Smooth production economies therefore satisfy the same properties as smooth exchange economies. Some of these properties had resisted extension to production because of their reliance on properties of the no-trade equilibria, a concept specific to the exchange model. The transitivity of consumers’ preferences is not even necessary for those properties to hold true.