N.H.Stern,Optimum income taxation 125 or Rawlsian.solution.Some might wish to claim that one is merely specifying he value i dgements of thedecison-maker by g an individual indifference curves together with a me hod by utilities are aggregated.The specification of a particular cardinal numbering for individuals and the form of the social preference relation over utilities may well be difficult,if not impossible,to disentangle,but I find it hard to understand a quantitative comparison between different forms of social welfare function for the same indifference structure(for individuals)if some benchmark of cardinality is not involved eardinality problem is much less severe when a one argument utility function is used- for example,Atkinson(1973a). .One can th nen suppose tha the government defines its values ov er the vectors whose hous hold incomes.However,when supply functions are central to the model 0n argument utility function seems out of place.It then becomes more difficul to wriggle out of the problem of numbering individual indifference curves.It is possible that part of the attraction of maximin objective functions is that the cardinality problem is less troublesome-maximising the lowest utility level will h。 cardinalisation is used when the same monotonic ng tra ation of utilities is applied to all individuals. The abe ove dis and of the literature ha s suppo i that the Be Samuelson social welfare function (no decreas g in each rgument appropriate tool for capturing social values in such analyses.Leaving aside the question of whether it should be used,it is possible that many people have some different underlying notion of welfare or distributional justice when they discuss income taxation.We illustrate the possible phenomenon with a few quotations and argu ents which might be thought plausible and vet imply non-Paretian o6 egin with thre quotations on inequality each of which clearly involves a non-Paretian position Tawney:2 When the press assails them with the sparkling epigram that they desire not merely to make the poor richer but to make the rich poorer,instead of replying,as they should,that,being sensible men,they desire both,since the extremes of both of riches and poverty are degrading and anti-social,they are apt to take refuge in gestures of depreciation. Simons:3 The case for drastic progression in taxation must be rested on the case against inequality-on the ethical or aesthetic judgement that the prevailing distribu- JPE-DN.H. Stern, Optimum income taxation 125 or Rawlsian, solution. Some might wish to claim that one is merely specifying the value judgements of the decision-maker by using an arbitrary numbering of individual indifference curves together with a method by which individual utilities are aggregated. The specification of a particular cardinal numbering for individuals and the form of the social preference relation over utilities may well be difficult, if not impossible, to disentangle, but I find it hard to understand a quantitative comparison between different forms of social welfare function for the same indifference structure (for individuals) if some benchmark of cardinality is not involved. The cardinality problem is much less severe when a one argument utility function is used - see, for example, Atkinson (1973a). One can then suppose that the government defines its values over the vectors whose components are house￾hold incomes. However, when supply functions are central to the model a one￾argument utility function seems out of place. It then becomes more difficult to wriggle out of the problem of numbering individual indifference curves. It is possible that part of the attraction of maximin objective functions is that the cardinality problem is less troublesome - maximising the lowest utility level will give the same policy whichever cardinalisation is used when the same monotonic increasing transformation of utilities is applied to all individuals. The above discussion and most of the literature has supposed that the Bergson￾Samuelson social welfare function (nondecreasing in each argument) is the appropriate tool for capturing social values in such analyses. Leaving aside the question of whether it shouZd be used, it is possible that many people have some different underlying notion of welfare or distributional justice when they discuss income taxation. We illustrate the possible phenomenon with a few quotations and arguments which might be thought plausible and yet imply non-Paretian objectives. We begin with three quotations on inequality each of which clearly involves a non-Paretian position. Tawney : ’ When the press assails them with the sparkling epigram that they desire not merely to make the poor richer but to make the rich poorer, instead of replying, as they should, that, being sensible men, they desire both, since the extremes of both of riches and poverty are degrading and anti-social, they are apt to take refuge in gestures of depreciation. Simons : 3 The case for drastic progression in taxation must be rested on the case against inequality - on the ethical or aesthetic judgement that the prevailing distribu￾Yke Atkinson (1973b, p. 19). I am grateful to Kevin Roberts for drawing my attention to this quote. %ee Simons (1938, p. 15). Kevin Roberts drew my attention to this quote too. JPE- D