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A fundamental concern of welfare economics, as of other evaluative ethical theories, resides in the assessment of the goodness of a given state of affairs. In the context of economic investigation, it is convenient to describe a state of affairs very simply in terms of a given feasible allocation of goods among the individuals constituting the economy under review. In assessing the allocation of goods which comes to pass, some criterion of evaluation must obviously come into play. A criterion that welfare economics has been much concerned with is that of Pareto efficiency—named after the Italian sociologist Vilfredo Pareto.

Before defining Pareto efficiency, it is useful to state what has come to be known as the Pareto principle. The Pareto principle requires that given any two social states (or allocations, in the present context) a and b, if a is Pareto superior to b in the sense that everybody is better off in a than in b, then a is a better state than b. 

Any social state a will be said to be Pareto efficient, if there is no other feasible state b which is Pareto superior to a. We still need to specify what we mean by the term better off, a matter that is aided by the notion of a utility function. 

Each person is assumed to derive some utility from the commodity-bundle assigned to her by each feasible allocation, defined as a collection of commodity-bundles, one bundle for each person in the economy. If the utility she derives from her commodity-bundle under some allocation a is greater than the utility she derives from her commodity-bundle under some other allocation b, then she will be said to be better off with allocation a than with allocation b. And if everybody is better off, in this sense, under allocation a than under allocation b, then a is Pareto-superior to b. 

Welfare economics is also much concerned with the notion of a social welfare function (SWF). Given any feasible allocation a, a SWF associates a number W with a, which is supposed to reflect the aggregate welfare produced by the allocation a. Typically, W would depend on the utility which each person derives from the commodity-bundle assigned to her in the allocation in question. This utility is assumed to be ordinal, that is, imbued only with the property of ranking. Further, individual utilities are assumed to be not interpersonally comparable. Finally, the SWF W is assumed to be Pareto-inclusive, which simply means that other things equal, if any one person’s utility increases, aggregate welfare will also be assumed to increase. In choosing between alternative feasible allocations, welfare economics espouses the cause of that allocation which maximizes a social welfare function of the type just described. It can be easily verified that any allocation which maximizes such a welfare function is also Pareto-efficient. 

Are there any institutional arrangements we know of that are compatible with the emergence of Pareto efficient outcomes? Scholars who have some familiarity with Adam Smith’s “Invisible Hand" account of a market will immediately see a connection between the allocation ordained by a competitive market and Pareto efficiency. Much of welfare economics has been concerned with this connection. 

Indeed, the content of the so-called first theorem of welfare economics is precisely that under certain well-defined conditions, a competitive equilibrium is Pareto efficient. (Lay interpretations of the theorem have led to lazy and inaccurate idealizations of the market as an institution.) But the First Theorem, as Amartya Sen has pointed out, is entirely devoid of the sort of ethical significance one would look for if one had some egalitarian concern for the allocation thrown up by a competitive equilibrium. It is Pareto efficient, but could well be profoundly inegalitarian.

To see this, consider a two-person society in which person 1’s share of the social dividend from an efficient allocation is some fraction x, and person 2’s share is (1-x). If we increase x, then person 1 will be better off, but person 2 will be worse off. If we reduce x, person 2 will be better off, and person 1 worse off. That is, there is no change in x, which can make both persons better off. 

Equivalently, the outcome (x, 1-x) is Pareto-efficient. But this must hold for any and all fractions x. There can thus be an infinite number of Pareto-efficient outcomes (since there are an infinite number of fractions x), and welfare economics offers little normative guidance in choosing between them. We shall investigate this issue in a little greater detail in a subsequent piece, with specific reference to the work of Amartya Sen in this regard. One of Sen’s most distinctive contributions to normative economics has been his critique of the theoretical foundations of welfare economics, a critique which exposes the inability of welfare economics to deal meaningfully with distributional concerns. This, as we shall see later, has much to do with the impoverished and purely utility-based information on the foundations of which welfare economics is erected.

Let me conclude with a reading tip for anyone interested in a deeper exploration of the issues flagged above. A wonderfully lucid treatment of the subject under discussion is available in an essay written, in 1975, by Professor Hal Varian of the University of California at Berkeley, and titled “Distributive Justice, Welfare Economics, And The Theory Of Fairness", which was published in the journal Philosophy And Public Affairs. I have drawn considerably on Varian in writing this account, but there is no substitute for the original, which I strongly commend to the interested reader.

S. Subramanian is an economist.Comments are welcome at theirview@livemint.com

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