Can a reallocation of initial endowments improve social welfare?

In this paper we show that in a pure exchange economy it is possible to improve the social welfare along an e±cient path. This path will be called the Negishi map. Moving the relative weights of the agent in a social welfare utility function, we obtain an e±cient path of allocations and social weights, such that along this path the social welfare level change. Moving along this path it is possible to reach a maximum social welfare. The e±cient allocation maximizing the social welfare is characterized by the fact that the individual utilities have the same value. This level will be called the Negishi number of the economy. Such allocation is not necessarily an allocation corre- sponding to a walrasian equilibrium so, the participation of a benevolent policy maker can have sense. We introduce a de¯nition of developed economy. Finally, the relations between changes in utilities and changes in social weights is analized.