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By Kenneth J. Arrow

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0 by the commodity bundles he gets under each. Let a commodity bundle be designated by (a, b)} where a is the amount of the first commodity in the bundle and b the amount of the second commodity. 9. 2. It can easily be seen that there are indifference maps having the indicated properties in which the indifference curves are continuous, convex, and downward-doping. In state y, each individual is better off or not worse off than in state x, so that it is trivial to say that there exists a redistribution of the goods in state y which will make everybody no worse off than in state x.

IV the different commodities commensurable; and usually such a standard of value must depend on the distribution of income. In other words, there is no meaning to total output independent of distribution. " n This argument fits well into our formal framework. The Kaldor compensation principle is being proposed as a social welfare function in the sense of Definition 4. " For a given set of individual orderings, let R be the corresponding social ordering, P the corresponding social (strict) preference relation (see Definition 1), and Q the unanimity quasi-ordering introduced in the last section.

Op. , pp. 318-320. The Fundamental Value Propositions of Individual Preference are not, strictly speaking, implied by Conditions 2 and 4 (in conjunction with Conditions 1 and 3), though something very similar to them is so implied; see Consequence 3 in Chapter V, Section 3. A slightly stronger form of Condition 2 than that stated here would suffice to yield the desired implication. * See E. , 1941,305 pp. SEC. 6] THE SUMMATION OF UTILITIES 31 value judgments and could be called into question; taken together they express the doctrines of citizens' sovereignty and rationality in a veiy general form, with the citizens being allowed to have a wide range of values.

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