Regarding the Welfare Theorems included within the chapter 1, I’ve found that they serve as basis of Welfare Economics. What I’m talking about?
“Welfare Economics: The branch of economic thought that deals with economic welfare, including especially various propositions relating competitive general equilibrium to the efficiency and desirability of an allocation.” Deardorffs’ Glossary of International Economics
In other words, its the particular branch of economic theory in which the aggregated well being of an economy is analyzed. For this purpose, it was necessary to establish a function that would be the measure of the social well-being in terms of the aggregate utility. That’s why the central piece of analysis in Welfare Economics is the Social Welfare Function, a function that quantify different elements that affects individual’s utilities and adds them up as as a whole society’s utility function. The analysis of its components leads to interpretations that indicate how does the government should intervene in order to improve social welfare.
This branch of economics –Which has its modern origins in the Social Welfare Function proposed by Samuelson–
in 1947 in the book Foundations of Economic Analysis – has received several critics, being one of the most important the Arrow’s Impossibility Theorem set out by Kenneth Arrow in his doctoral thesis and then published in Social Choice and Individual Values in 1953.
“Kenneth Arrow’s “impossibility” theorem—or “general possibility” theorem, as he called it—answers a very basic question in the theory of collective decision-making. Say there are some alternatives to choose among. They could be policies, public projects, candidates in an election, distributions of income and labour requirements among the members of a society, or just about anything else. There are some people whose preferences will inform this choice, and the question is: which procedures are there for deriving, from what is known or can be found out about their preferences, a collective or “social” ordering of the alternatives from better to worse? The answer is startling. Arrow’s theorem says there are no such procedures whatsoever—none, anyway, that satisfy certain apparently quite reasonable assumptions concerning the autonomy of the people and the rationality of their preferences. The technical framework in which Arrow gave the question of social orderings a precise sense and its rigorous answer is now widely used for studying problems in welfare economics. The impossibility theorem itself set much of the agenda for contemporary social choice theory. Arrow accomplished this while still a graduate student. In 1972, he received the Nobel Prize in economics for his contributions.” The Stanford Encyclopedia of Philosophy
Arrow’s Theorem practically invalidated the existence of the Social Welfare Function under particular conditions, which triggered a controversy between him and Samuelson – translated as a conflict between welfare economics and social choice theory– that lasted almost 50 years. A brief story of this controversy, as well as a deeper explanation of both perspectives is developed by Herrade Igersheim in the very interesting paper The Death of Welfare Economics- History Of a Controversy published by Duke university.
I await your comments regarding this dimension of the Welfare Theorems.
- Arrow, Kenneth J. (1951, 2nd ed., 1963). Social Choice and Individual Values, Yale University Press, New Haven.
- Deardorff, Alan V. (2014), “Welfare economics”, Deardorffs’ Glossary of International Economics (1)
- Igersheim, Herrade, The Death of Welfare Economics: History of a Controversy (January 18, 2017). The Center for the History of Political Economy Working Paper Series, 2017-03. Available at SSRN: https://ssrn.com/abstract=2901574 or http://dx.doi.org/10.2139/ssrn.2901574
- Morreau, Michael, “Arrow’s Theorem”, The Stanford Encyclopedia of Philosophy (Winter 2016 Edition), Edward N. Zalta (ed.), URL = https://plato.stanford.edu/archives/win2016/entries/arrows-theorem/.