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Chapter 2 really began the analysis of public sector economics when it
presented the answer to the distribution question given by the mainstream
normative public sector model in a Wrst-best policy environment: The gov-
ernment should redistribute any one good or factor lump-sum to satisfy the
interpersonal equity conditions of an individualistic social welfare function.
For some good (factor) X
k
, and H individuals, redistribute such that the
social marginal utilities of X are equal for all individuals, or
qW
qU
h
qU
h
qY
hk
h 1, ...,H (4:1)
The interpersonal equity conditions are necessary conditions for a Wrst-best
social welfare maximum, along with the pareto optimal conditions. They are
the entirety of Wrst-best distribution theory in the mainstream model.
Chapter 4 begins Part II on Wrst-best public sector theory with some
common applications of the social welfare function in policy analysis. The
applications are in the spirit of the ``New, New Welfare Economics,'' which
employs Xexible-form social welfare functions to show how ethical judgments
ranging from utilitarian to Rawlsian can instruct public policy. Also, because
the analysis is Wrst-best, the applications generally focus on the question of
distributive justice without worrying about the ineYciencies that actual
redistributions of income give rise to. In other words, they assume that the
pareto optimal conditions are satisWed, unless speciWcally stated otherwise.
SOCIAL WELFARE AND THE DISTRIBUTION OF INCOME: THE
ATKINSON FRAMEWORK
England's Anthony B. Atkinson was a pioneer of the ``New, New Welfare
Economics'' in the early 1970s. He became interested in the possibility of
making social welfare judgments based on the personal income data that
England and other developed capitalist countries were collecting from
surveys of the population. The U.S. survey is the annual Current Population
Survey (CPS), which began in 1947. The CPS surveys approximately 60,000
families and unrelated individuals and is the principal source of the federal
government's published statistics on personal income, poverty, and other
personal characteristics such as family size and education.
Atkinson's desire to meld social welfare and the income data led him to
specify the social welfare function in terms of income. Write each individual's
(family's) utility as a function only of income, Y
h
, and the social welfare
function as:
W W(U
h
(Y
h
)) (4:2)
The relevant margin for the interpersonal equity conditions is the
social marginal utility of income,
qW
qU
h
qU
h
qY
h
; the product of the marginal social
welfare weight,
qW
qU
h
; and the private marginal utility of income,
qU
h
qY
h
.
104 SOCIAL WELFARE AND THE DISTRIBUTION OF INCOME: THE ATKINSON FRAMEWORK
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The Atkinson Assumptions
Atkinson sought a very simple speciWcation of W, one that could easily be
applied to the income data and yet would capture the full range of ethical
judgments from utilitarian to Rawlsian. He achieved this with three highly
simpliWed and heroic assumptions: (1) the social welfare function is utilitar-
ian, (2) everyone has identical tastes, and (3) utility exhibits diminishing
private marginal utility of income. Atkinson's assumptions were widely
adopted in applied social welfare analysis. The assumptions deserve some
comment by way of justiWcation simply because they are so strong.
Utilitarian Social Welfare
Atkinson assumed that social welfare should honor the impersonality
principle, discussed in Chapter 3. The simplest way to incorporate the
principle is to assume that social welfare is utilitarian, with the marginal
social welfare weights always equal to one:
W
P
H
h1
U
h
;
qW
qU
h
1
Other researchers have chosen a less restrictive interpretation of the principle:
Individuals with equal utilities should have the same social welfare weights.
This variation permits Xexible social welfare functions; nonetheless, it retains
the strong results that follow from Atkinson's three assumptions. The imper-
sonality principle is especially compelling in a Wrst-best environment. Such
practices as discrimination, which are used to justify aYrmative action pol-
icies, do not arise in a Wrst-best environment.
Same Preferences
This assumption is clearly false, but it can be justiWed in a modeling
context in one of three ways. The Wrst is to view it simply as an assumption by
default. If we assume that preferences diVer, how should the diVerences be
modeled? No obvious answer comes to mind and, therefore, nothing more
really need be said. Still, the assumption can be somewhat justiWed on other
grounds.
A second possible justiWcation is that diVerences in preferences should
not have any inXuence on policy decisions (so long as tastes are not destruc-
tive). Most people would argue that policy decisions should be based on
diVerences in peoples' circumstances rather than diVerences in their tastes,
especially policies related to the distribution question. How much income
people have is what matters, not what they choose to buy with their incomes.
A Wnal possible justiWcation is that people's preferences may well be quite
similar if viewed from a lifetime perspective. DiV erences in preferences may
be largely determined by diVerent positions in the life-cycle, holding circum-
stances constant. Single 20-year olds have diVerent preferences from married
50-year olds. But the 50-year-old father may have had much the same tastes
4. THE SOCIAL WELFARE FUNCTION IN POLICY ANALYSIS 105
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