# Fundamental theorems of welfare economics

There are two fundamental theorems of welfare economics. The first states that, under certain idealized conditions, any competitive equilibrium or Walrasian equilibrium leads to a Pareto efficient allocation of resources. The second states the converse, that any efficient allocation can be sustainable by a competitive equilibrium. Because of welfare economics' close ties to social choice theory, Arrow's impossibility theorem is sometimes listed as a third fundamental theorem.

## Quotes

* When I was a student at the University of Chicago, where I was a direct student of Jacob Viner in the classroom, and an indirect student of Frank Knight, I could not learn why price should equal marginal cost. Even when I got to Harvard in 1935, I went around asking everybody: “What is the proof that this is so?” Of course, I did not know the 1892–1893 work of Vilfredo Pareto in which he essentially shows that a perfectly competitive equation system gives you the necessary and sufficient condition, not for ethical optimality—he was always a little slippery on that problem—but for what came to be called Pareto optimality so that there is no avoidable deadweight loss. I think I had most to learn from Abba Lerner, although I, of course, worked it out for myself.
** Paul Samuelson, in Kotaro Suzumura, "An interview with Paul Samuelson: welfare economics, “old” and “new”, and social choice theory", Soc Choice Welfare 25:327–356 (2005).
* If I had had perfect teachers, they would have known the Pareto work; they would have known Enrico Barone and what you might call the fundamental theorems of welfare economics that the conditions for Pareto optimality would be exactly realized by competitive arbitrage. Before Bergson, Lerner–Hicks–Hotelling–Kaldor–Scitovsky insufficiently understood that the full set of Pareto optimality conditions constituted an incomplete set of conditions for ethical maximization. You must ask the right questions and make the right distinctions. All of my teachers believed there was something to Adam Smith’s invisible hand—that each person pursuing their self interest would, by some miraculous action of the invisible hand, be led to contrive in some vague sense the best interest of all. However, none of them could explain properly what the truth and falsity was in that position. I would say that if I had been a bright student in 1894 and read Pareto’s Italian journal article, I would have understood what I now understand to be the germ of truth in the invisible hand argument. All it refers to is the avoidance of deadweight loss. Here is where my association with Abram Bergson becomes relevant.
** Paul Samuelson, in Kotaro Suzumura, "An interview with Paul Samuelson: welfare economics, “old” and “new”, and social choice theory", Soc Choice Welfare 25:327–356 (2005).
* There is little doubt that the observation that quality may depend on price (productivity on wages; default probability on interest rates) has provided a rich mine for economic theorists: A simple modification of the basic assumptions results in a profound alteration of many of the basic conclusions of the standard paradigm. The Law of Supply and Demand has been repealed. The Law of the Single Price has been repealed. The Fundamental Theorem of Welfare Economics has been shown not to be valid. More than that, the theories that we describe here provide the basis of progress toward a unification of macroeconomics and microeconomics. They pro vide an explanation of unemployment and credit rationing, derived from basic microeconomic principles. It is a theory in which the extensive idleness that periodically confronts society's resources, human and capital, is seen as but the most obvious example of market failures that prevasively and persistently distort the allocation of resources.
** Joseph Stiglitz, "The Causes and Consequences of The Dependence of Quality on Price", Journal of Economic Literature, Vol. 25, No. 1 (March 1987).