Rawls’s maximin and optimal taxation theory

Abstract

The paper analyses the import and appropriation of Rawls’s theory of justice into the emerging field of optimal taxation theory in the 1970s. It focuses first on the pioneer contributions of Atkinson and Phelps to integrate Rawls’s maximin into optimal taxation models, and then on their numerous followers during this decade. It shows that the maximin criterion was quickly accepted and appropriated in optimal taxation theory using “Rawlsian” Social Welfare Functions, which are founded on a welfarist interpretation of the maximin, unfaithful to Rawls. I try to explain why public economists made this choice, insisting on issues of simplicity, tractability, and comparisons with other ethical criteria.

Keywords:

• Optimal taxation theory
• Rawls
• maximin
• public economics
• Atkinson
• social welfare function

JEL codes:

• B2
• B31
• H21

Disclosure statement

No potential conflict of interest was reported by the author.

Correction Statement

This article has been corrected with minor changes. These changes do not impact the academic content of the article.

Notes

1 The reference book is Musgrave (1959).

2 Then TJ.

3 For the story of a misunderstanding between Rawls and Samuelson, see Igersheim (2023). For a more critical take on the encounter between Rawls and public economists, see Guizzo and Paré Ogg (2023).

4 Atkinson had presented his paper at 1972 European Meeting of the Econometric Society which was held between September 5th and 8th in Budapest, and the editor of the Review of Economic Studies underlines his quick answer to Atkinson’s submission.

5 See the letter from the managing editor of the journal, Geoffrey Heal, in Atkinson papers at LSE (ATKINSON/03/20).

6 As a first page footnote in a draft of the « Maximin » paper indicates, it was presented first at the LSE seminar, then in seminars at the Universities of Harvard, Pennsylvania and Yale in Spring 1972, and finally at the European Meeting of the Econometric Society in Budapest (in September 1972, see above).

7 The Atkinson collection of the LSE is made of 124 boxes, transferred in 2014, and spanning the years 1967 to 2011. It contains three files from the 1970s, with multiple items, among which one can find several different versions of “How Progressive Should Income Tax Be?” and “Maximin and Optimal Income Taxation”. These files are referenced as ATKINSON/03/19, untitled “Income Taxation”, ATKINSON/03/20, named “Maximin and Optimal Income Taxation”, and ATKINSON/03/24 untitled “How Progressive Should Income Tax Be?”.

8 ATKINSON/03/20.

9 ATKINSON/03/19.

10 I began working on this paper when Atkinson's Papers at Duke University were not yet available to researchers. While completing the final version of my paper, I finally had access to them (through digital copies). This archive fund also contains some versions of Atkinson's works on maxi-min taxation, and especially two versions - one made of handwritten notes and one typescript - of the first draft from October 1971 as well as different revised versions of 1972, which are all quite similar to the ones found in London (see Anthony B. Atkinson Papers, David M. Rubenstein Rare Book & Manuscript Library, Duke University, Box 64, Folders 1–4). Here too, none of the two versions of the first draft contains any reference to Rawls or to the maximin, while analysing social welfare functions with infinite inequality aversion, maximising the welfare of the least well-off (see Box 64, Folders 3 and 4).

11 ATKINSON/03/19.

12 Arrow’s paper also mentions the burgeoning literature on the application of Rawls’s maximin in optimal taxation theory (Atkinson, Phelps and Sheshinski) and underlines that “the practical implications of this research are as yet dubious, primarily because too little is known about the magnitude of the incentive effects, particularly in the upper brackets.” (Arrow 1973, 259)

13 Atkinson uses this expression for qualifying the maximin case in handwritten notes (ATKINSON/03/19). Just after that he wrote in these notes “get ρ → ∞ maxmin U(n). JET”. Atkinson’s 1970 paper was published in the Journal of Economic Theory. To avoid any confusion, note that Atkinson’s notification changed. In his papers on maximin taxation, he uses ρ to represent the degree of inequality aversion in the society, while he used ε in his 1970 paper.

14 “It appears at first sight that this [formulation of the Social Welfare Function] is identical to the utilitarian approach discussed earlier. It is important to emphasize, however, that H represents the social valuation of income, and that the choice of ρ is based on social values about inequality. The parameter ρ reflects the degree of aversion to inequality in the society.” (Atkinson 1973a, 405–406) In the draft, he also adds that “the social welfare function is defined over observed income (rather than unobservable utilities)” (see ATKINSON/03/24).

15 (ATKINSON/03/20).

16 Mirrlees’s name does not appear on the letter, but it was easy to identify him as his author: it is signed “Jim”, it is written on a headed paper of « Nuffield College, Oxford », and the author refers to his own paper and to Atkinson’s comments on it.

17 There is a draft typescript of Atkinson (1973a) in Atkinson papers with the indication “AUTE 1972” on top of the first page and whose page numbers correspond to Mirrlees’s remarks. See ATKINSON/03/24.

18 “Suppose A(x) is a premise, depending upon a variable x, and it is shown that A(x) implies a conclusion B(x). To demonstrate, in an interesting sense, that the conclusion depends sensitively on x one has to show that, within a range of x that is quite probable, or plausible, B varies significantly. There must therefore be three phases of the argument: (i) derivation of the dependence of B on x, (ii) discussion of the appropriate range for x, (iii) discussion of the significance of variations in B. You only discuss (i) for the income-tax case. In the context, I am not too troubled by the omission of formal discussion of (iii), but in the absence of discussion of (ii), it seems to me that you have established nothing.” (Mirrlees 1972, 1); “You will see that I would reject p. 14 of your paper almost completely. In particular, your suggestion that one should ‘use relatively simple models to identify those considerations which are likely to be important’ is much less plausible than it seems. Considerations can seem important in simple models and not be important in realistic ones. At the same time, to express ones ethical views in terms of a welfare function, one should use even simpler models. I think there is a confusion between the use of sensitivity analysis as a guide to further research and the use of simple models as an aid to the formal specification of objectives.” (Mirrlees 1972, 2)

19 This is similar to Samuelson’s objection to the maximin (Igersheim, 2023).

20 Mirrlees also criticises in the letter his focus on linear tax schedules and his “extreme (and implausible) skill distribution,” a Pareto distribution, whose limitations Atkinson recognizes, noting in the draft that “this assumption is made primarily for its analytical convenience, but it is not clear that it is a significantly worse assumption about the distribution of abilities than normality or lognormality.” In the published version, the sentence becomes: “This assumption is made primarily for its analytical convenience, and is one of the least satisfactory aspects of the model.” (Atkinson 1973a, 395)

21 Atkinson adds in margin: “Fairness.”

22 See his point (ii) in footnote 28. A comparison of the draft and the published version of Atkinson’s paper, though it shows important differences in the structure of the paper, does not suggest that Atkinson made substantial changes in his argumentation.

23 Klevorick and Rawls participated in a special session of the 1973 American Economic Association conference in New York on December, 29 untitled “Concepts of Distributional Equity”, whose proceedings were published the following year in the American Economic Review, Papers and Proceedings (see Klevorick 1974; Rawls 1974b).

24 There is no reference to Phelps’s paper in Atkinson’s papers and vice versa.

25 Sheshinski had attended Rawls and Sen’s joint seminar at Harvard. It gave him the idea to study the implications of the maximin for optimal income taxation, on which he was working at that time (email from Sheshinski to the author, April 26, 2023, see also Sheshinski 1971, 1972a). Interestingly, he also published in 1972 a paper on the relation between a Social Welfare Function and the Gini Index. Inspired by Atkinson’s approach and benefitting from his comments, it mentions Rawls’s view of justice as one in which social welfare depends only on the lower income, which he considers as “a strong egalitarian principle” (Sheshinski 1972b, 99).

26 Phelps discusses his encounter and close relationship with Rawls in his recent autobiography (see Phelps 2023, chapters 3 and 4).

27 “It is the modern-day analogue of Aquinas: Everything for the greater utility of the poor.”; “We are to identify the smallest individual utility in each social state - the utility of the least well-off in that state - and choose the social state where this minimum utility is maximized.” (Phelps 1973, 334)

28 Phelps refers here to Sheshinski (1971), “On the Theory of Optimal Income Taxation," Harvard Institute of Economic Research Discussion Paper No. 172, Feb. 1971, published in 1972 in The Review of Economic Studies (Sheshinski 1972a).

29 On the latter point, see recently Atkinson (2014, 22), Saez & Zucman (2019, chapter 7).

30 Phelps had previously sent a letter to Rawls commenting on Mirrlees’s model and the maximin (see Igersheim 2022b).

31 For other analysis of Rawlsian maximin Social Welfare Functions in the 1970s, see for example Solow (1974), Varian (1974), Meade (1976, chap IV), Hammond (1976), D’Aspremont and Gevers (1977), Phelps and Riley (1978).

32 Atkinson’s papers at the LSE contain several drafts of the Lectures (ATKINSON/03/02 A to N), among which one of a chapter on “The Structure of Income Taxation” dated from January 1974, dealing with Rawlsian maximin Social Welfare Functions and based on materials taken from Atkinson’s 1973 paper. See ATKINSON/03/19. Some will note with interest that the title of this 1974 draft was Lectures on Public Finance rather than Lectures on Public Economics.

33 See Tuomala and Weinzierl (2022) for a similar argument about the importance of the tractability of the maximin case for its use among economists.

34 In their 1977 paper on new developments in Public Finance, dealing with the first results of optimal taxation theory, Stiglitz and Boskin wrote in a section called “The Philosophical Basis of New Public Economics” that: “The utilitarian framework has the advantage of providing a simple, unified, reasonably flexible ethical basis for judging among tax systems. For instance, by positing social welfare functions with different degrees of elasticity of substitution among the utilities of individuals, one can consider, at the one extreme, the Rawlsian criterion of maximizing the utility of the worst-off individual, and at the other, the Benthamite criterion of adding up utilities. The traditional approach has involved ‘listing’ criteria, e.g., horizontal equity, vertical equity, administrative costs, without providing any criterion for trading off among these objectives” (Stiglitz and Boskin 1977, 296)

35 See Sen (1980, 205, section 3; 1984, 318). Igersheim shows that Sen first “assumed some responsibility regarding this ‘Rawlsian’ interpretation of Rawls’s theory and offered a kind of mea culpa” in a 1978 letter to Rawls (Igersheim 2022b).

36 “The question we need to put to Lucas, and indeed all those who refer to the welfare consequences, is how their conclusions would change if Bentham were replaced by Rawls or by Sen. Whatever one thinks of the merits of the views put forward in these two alternatives to utilitarianism, one has to ask when making statements about public policy how adoption of a different view from utilitarianism would affect the conclusions reached. Where people disagree about the desirability of a particular policy reform, is it possible that they do so because they are motivated by a different view of the objectives of society?” (Atkinson 2009, 797).

37 On the complex history of welfare economics, see Backhouse, Baujard, and Nishizawa (2021).