The Bergson-Samuelson Social Welfare Function

Up till now we’ve defined the social welfare functions over entire allocations (i.e., each person have an opinion about what all other persons get). If we assume that each individual is concerned only with him-/her we can define the social welfare functions only over the individual bundles,

W=W(u₁(x₁), ...,u_n(x_n)).

This type of social welfare function is called a Bergson−Samuelson social welfare function, or an individualistic social welfare function (for obvious reasons). The important point of this function is that it conforms to the (implicit) assumptions that we’ve made in the proof of the first fundamental theorem of welfare economics, that there are no consumption externalities. Remember that the first theorem states that general competitive market equilibrium is Pareto-efficient. Now, if we use the Bergson-Samuelson social welfare function to pick the best point on the utility possibility frontier, this point is associated with competitive market equilibrium, and could be implemented as such given that lump-sum taxes can be used to redistribute initial endowments.

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