Public Finance, 2nd Edition

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

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

h1

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