After the showstopper that is Arrow’s Theorem, we could just throw in the towel.  The motivation for studying social welfare functions was to find a coherent standard by which to judge institutions and to propose policies.  Now we see that there is no coherent standard.  Well students you are not getting away so easily, after all this is only the second week of the course.  We will accept that we must violate one of the axioms.  Which one do we choose?

A lot of normative economic theory is implicitly built upon one of two welfare criteria, either Pareto efficiency or utilitarianism.  While it is standard to formally define Pareto efficiency in an undergraduate micro class, utilitarianism is often invoked without explicit mention.  For example, we are implicitly using some form of utilitarianism when we talk about consumer and producer surplus.  And to argue that a monopoly is inefficient in a partial equilibrium framework is a utilitarian judgment (absent compensating transfers.)

So I make it explicit.  And I take the time to formally define utilitarianism, explain where it applies and what justifies it and I point out its limitations.  In terms of Arrow’s theorem I tell the students that we are dropping the axiom of universal domain (UD.)  That is, we are not requiring our social welfare function to apply in all situations, only in those situations in which there is a valid measure of welfare that can be transferred and/or compared inter-personally.  In this class, that measure of welfare is willingness to pay, and it applies when there are monetary transfers available and all agents value money in equal terms, i.e. quasi-linear utility.

These lectures contain one important formal result.  In the quasi-linear world with monetary transfers utilitarianism coincides with Pareto efficiency.  So these two common welfare standards are the same.  (Any utilitarian improvement can be made into a Pareto improvement with judiciously chosen transfers and any Pareto improvement is a utilitarian improvement.)

Here are the notes.