A Note on the Negishi Approach to Equilibrium

In this note we generalize the Negishi approach to equilibrium. We embed a standard one-period exchange economy into a two-period model, where agents' first-period utility functions can be any strictly increasing and concave functions satisfying the lower Inada condition, and prove the existence of equilibrium by working with the space of agents' first-period consumptions. The celebrated Negishi method is a special case of this approach where agents' first-period utility functions are all assumed to be logarithmic