Table Of ContentWelfare Economics
Towards a More Complete Analysis
Yew-Kwang Ng
Welfare Economics
Towards a More Complete Analysis
Yew-Kwang Ng
Personal Chair in Economics
Monash University
Australia
© Yew-Kwang Ng 2004
Softcover reprint of the hardcover 1st edition 2004978-0–333–97121–5
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Library of Congress Cataloging-in-Publication Data
Ng, Yew-Kwang.
Welfare economics:towards a more complete analysis/Yew-Kwang Ng.
p. cm.
Includes bibliographical references and index.
1. Welfare economics. I. Title.
HB99.3.N449 2003
330.15(cid:1)56—dc21 2003051788
10 9 8 7 6 5 4 3 2 1
13 12 11 10 09 08 07 06 05 04
Contents
Preface ix
List of Abbreviations xii
List of Symbols xiii
1 Introduction 1
1.1 What is welfare economics? 2
1.2 Is welfare economics a positive or normative study? 5
1.3 Welfare versus utility 6
1.4 Utility measurability and interpersonal comparability 16
1.5 The organisation of the book 18
1.6 Summary 19
Appendix 1.1: Basic Value Judgments and Subjective Judgments
of Fact 19
2 Pareto Optimality 26
2.1 The Pareto principle 26
2.2 The conditions for Pareto optimality 28
2.3 The attainment of Pareto optimality 38
2.4 Summary 42
Appendix 2.1: The First-Order Conditions for Pareto Optimality 43
3 The Direction of Welfare Change: Welfare Criteria 47
3.1 The debate on compensation tests 47
3.2 Taking distribution into account: Little’s criterion 52
3.3 The inadequacy of purely distributional rankings 57
3.4 Retreat to purely efficiency comparisons 61
3.5 Quasi-Pareto improvements 62
3.6 Conclusions 64
3.7 Summary 64
4 The Magnitude of Welfare Change: Consumer Surplus 65
4.1 The origin of the concept: Dupuit and Marshall 65
4.2 Hicks’ four measures and the average cost difference 66
4.3 Which measure? 70
4.4 Aggregation over commodities: the issue of path dependency 72
4.5 Aggregation over individuals: the Boadway paradox 76
4.6 The approximate nature of surplus measurement 78
v
vi Contents
4.7 Consumer surplus of diamond goods 80
4.8 Some uses of surplus measurement 82
4.9 Summary 85
Appendix 4.1: CV, EV or Marginal Dollar Equivalent? 86
Appendix 4.2: Acceptability of the Marshallian Measure –
The Benchmark Case of a Cobb–Douglas Utility Function 90
5 Social Choice 92
5.1 Arrow’s impossibility theorem 92
5.2 The impossibility propositions by Kemp–Ng and Parks 98
5.3 Can the paradox of social choice be resolved? 101
5.4 Revealing the intensity of preferences 107
5.5 A dollar is a dollar: a 90 per cent solution to the paradox of
interpersonal cardinal utility 115
5.6 The possibility of a Paretian liberal 119
5.7 Summary 120
Appendix 5.1: The Incompatibility of Individualism and Ordinalism 121
6 The Optimal Distribution of Income 127
6.1 Conceptual determination of optimal distribution 127
6.2 Utility illusion 129
6.3 Theories of optimal income distribution and taxation:
Lerner and Mirrlees 131
6.4 Discussion 135
6.5 Concluding remarks 141
6.6 Summary 143
7 Externality 144
7.1 The concept and classification of externalities 144
7.2 Divergence from optimality and the tax/subsidy solution 147
7.3 Other solutions 152
7.4 The conscience effect 154
7.5 The Coase theorem and liability rules 158
7.6 Summary 162
8 Public Goods 164
8.1 Basic characteristics of public goods 164
8.2 Optimality conditions and the financing of public goods 167
8.3 An incentive-compatible mechanism for preference revelation 174
8.4 Income distribution as a peculiar public good: the paradox
of redistribution 180
8.5 Economic theories of clubs 182
8.6 Summary 183
Appendix 8.1: The Paradox of Redistribution and the Paradox of
Universal Externality 184
Contents vii
9 First, Second or Third Best? 187
9.1 The theory of second best 188
9.2 Softening the blow of second best 193
9.3 A theory of third best 196
9.4 Towards a third-best policy 203
9.5 Summary 208
Appendix 9.1: A Dollar is a Dollar – Efficiency, Equity and
Third-Best Policy 208
10 Beyond Marginal Analysis: Perspectives from an
Inframarginal Analysis of the Division of Labour 230
10.1 Towards a more complete welfare economics 230
10.2 Marginal versus inframarginal analysis 231
10.3 Basic inframarginal analysis of the division of labour 232
10.4 The devastating implications of increasing returns on
some traditional conclusions 234
10.5 The Smith dilemma and its resolution 240
10.6 The Pareto optimality of general equilibrium in the
new framework – the role of entrepreneurs 243
10.7 Welfare economic issues and the division of labour 246
10.8 Implications 250
10.9 Summary 253
Appendix 10.1: A Simple Model of the Yang–Ng Framework of
Specialisation 254
11 From Preference to Happiness 257
11.1 Preference economics or welfare economics? 257
11.2 Developments that have prompted a reconsideration 261
11.3 A simplified analysis of welfare 275
11.4 Implications and concluding remarks 277
11.5 Summary 282
12 Conclusion: Towards an Interdisciplinary
Study of Welfare? 284
12.1 Further considerations 287
12.2 Towards an interdisciplinary study of welfare 293
12.3 Summary 296
Appendix 12.1: Notes and References on Some Advanced and
Applied Topics 297
References and Author Index 306
Subject Index 351
Preface
While it has been called ‘welfare economics’ for nearly a century, traditional
welfare economics actually only analyses preferences. Recently I have been
making a small effort to push the analysis to the level of real welfare, or
happiness. This was the main reason for writing this book. Going deeper from
the level of preference to that of welfare (that is, happiness) is necessary as
preference is not our ultimate objective – happiness is. This extension can
not only lead to new findings in welfare economics but also suggests a need
for reformulation of the welfare foundation of public policy in general and
cost–benefit analysis in particular.
In the last dozen years or so I have worked closely with my colleague
Xiaokai Yang on the analysis of economies of specialisation that arise from
the division of labour and the implications of these on growth, trade and
the evolution of economic organisations. This analysis has included various
welfare economic issues associated with increasing returns and organisa-
tional efficiency. The extension of welfare economic analysis to cover such
issues is also discussed. Despite these extensions, the subtitle of this book
isperhaps a little ambitious and more emphasis should be given to ‘towards’
than to ‘complete’, as it is very far from being a complete analysis.
The intended readers of this book include advanced undergraduates,
graduates and specialists. The conflict that arises from the diversity of the
intended readers is resolved by putting the more technical and advanced
material into appendixes and by using an asterisk to denote material that
the beginner can omit without losing continuity. The expert may, however,
be particularly interested in this material. The same applies to the endnotes,
which mostly contain bibliographical references or technical comments.
Chapter sections marked with two asterisks contain new arguments. An
asterisk after the title of a reference indicates that the work in question is
more advanced, mathematical or touches on a technical point.
It might be thought that the diversity of the intended readers will render
the book inefficient either as a basic textbook or as a treatise, but it is hoped
that the following explanation will largely dispel any such apprehension.
First, a textbook is read not only by students but also by lecturers. The for-
mer will benefit more from the basic discussions in this book and the latter
from the more advanced parts. By getting lecturers actively interested in
reading the book, more effective teaching may result when it is used as a text
(lecturers do not always have the patience to read through basic textbooks).
Meanwhile students who are encountering welfare economics for the first
time may have the very slight inconvenience of having to skip some sections
in the first reading, but will find that they are useful and provide interest for
ix
x Preface
a second reading that will bring a much deeper understanding of welfare
economics. Furthermore they may use this book and the many references
therein as a guide to further study. By the time they reach the end they
may find that the book is worth more than a basic text plus an advanced
treatise (the two usually do not completely cohere with and complement
each other).
Second, as a treatise it is useful for the author to explain the basic concepts
and theories and his own opinions on them before he embarks on his own
argumentation. In this regard experts may find that the basic discussion is
worth reading. While some will find it a little too elementary, they should
have little difficulty deciding which parts to skip. Similarly those readers who
have some elementary training in or understanding of welfare economics
and wish to advance their understanding, (for example graduate students
and economists who do not specialise in welfare economics) may find it
useful to review the basic concepts before going further. An explanation of
the organisation of the book is provided in Section 1.5 and summaries are
provided at the end of each chapter, before the appendices.
Partly because of the semitreatise nature of the book and partly because it
is more efficient to deal with topics with which I am familiar, the selection
of the non-basic topics is admittedly idiosyncratic. However I believe that a
largely unbiased coverage has been achieved for the basic topics. Due to
space limitation I have not been able to include detailed discussions of as
many topics as I would have wished, but Appendix 12.1 is intended to
remedy this. Moreover, due to time limitation and my other commitments
I have not been able to improve the quality of the text as much as I would
have liked. While the discussion may be a little terse in places and some
ambiguities may be present, this has the advantage of provoking inde-
pendent reasoning. In any event, if the reader has the patience to reread the
unclear parts, comprehension should not be difficult to achieve. Beginners
will find lecturers’ instructions and seminar discussions helpful in this
respect. For average beginners, therefore, the book might most profitably
beused under instruction.
To make the book accessible to as large an audience as possible given
the content, the discussion is mainly non-mathematical and relies heavily
on simple two-dimensional illustrations. Mathematics is used only when
essential and appears mainly in appendices. The conceptual discussions start
from the very basic and proceed to the fairly complicated, including some
new arguments. The features of the book that can be found in its previous
incarnation (Ng, 1979/1983) include a methodological argument for a
positive welfare economics (Chapter 1), a proposed rehabilitation of Little’s
welfare criterion (Sections 3.2.2 and 3.3), resolving Arrow’s paradox of
social choice by revealing the intensity of preferences (Section 5.4), the
‘conscience effect’ in externalities (Section 7.4) and above all a theory of
third best (Sections 9.4 and 9.5) with an extension to the equity-efficiency
Preface xi
consideration, reaching the remarkable conclusion that ‘a dollar is a dollar
to whomever it goes’ (Appendix 9.1). New features include a proposed quasi-
Pareto criterion that requires the potential for full compensation within each
income group (Section 3.5), diamond goods (goods valued for their exchange
value) and the havoc they play with the Marshallian measure of consumer
surplus (Section 4.7), resolution of the paradox of interpersonal cardinal
utility (Section 5.5), a reconsideration of the excess costs of financing for
public spending that suggests economists grossly overestimate the costs of
public spending (Section 8.2), and the argument that if economists as
a group were aware of the true relationship of equality versus incentives
they would be in favour of reverse distributional weighting, counting a
dollar to the poor as worth less than a dollar to the rich in all specific cases
(Section A9.1.4). The major new extensions are the two completely new
chapters; Chapter 10, which examines welfare economic issues within the
new Yang–Ng framework for economies of specialisation, and Chapter 11,
which attempts to push the analysis beyond the traditional focus on pre-
ference to the ultimate level of happiness.
Happy reading!
YEW-KWANG NG
List of Abbreviations
AC Average cost
CIC Community indifference contour
CS Compensating surplus
CV Compensating variation
ES Equivalent surplus
EV Equivalent variation
GUFF Grand utility feasibility frontier
IIA Independence of irrelevant alternatives
MC Marginal cost
MDE Marginal dollar equivalent
MRS Marginal rate of substitution
MRT Marginal rate of transformation
MU Marginal utility
MV Marginal valuation
SWF Social welfare function
UPC Utility possibility curve
WMP Weak majority preference
xii
