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Public Finance and Public Policy
Responsibilities and Limitations of Government: Second Edition
This book is the second edition of Public Finance and Public Policy (2003). The
second edition retains the first edition’s themes of investigation of responsibilities
and limitations of government but has been rewritten and restructured. Publicchoice and political-economy concepts and political and bureaucratic principal–
agent problems that are the sources of limitations on government are introduced
at the beginning for application to later topics. Concepts of behavioral economics
and experimental results are integrated throughout this edition. Asymmetric information is a recurring theme. The book begins with the efficiency case for the
competitive market and the minimal responsibility of government to ensure the
rule of law. Subsequent chapters address questions concerning institutions and
governance, public goods, taxation and bond financing of public spending, market
corrections (externalities and paternalist public policies), voting, social justice,
entitlements, and choice of the structure of taxation and the tax base. The final
chapter summarizes evidence on and reasons for the growth of government and
considers how trust or social capital affects the need for government. The purpose
of the book is to provide an accessible introduction to the choice between relying
only on personal decisions in markets and the use of public finance and public

policy by governments to improve on market outcomes.
Arye L. Hillman is William Gittes Professor of Economics at Bar-Ilan University
in Israel. He has taught at Princeton University, the University of California in
Los Angeles, and Australian National University and has been an invited lecturer
at universities in various countries. Professor Hillman received his Ph.D. in economics from the University of Pennsylvania. His professional research includes
studies under the auspices of the International Monetary Fund and the World
Bank. He is a former president of the European Public Choice Society. Professor
Hillman was jointly awarded the Max Planck Prize in Economics for his contributions to political economy.


ADDITIONAL PRAISE FOR PUBLIC FINANCE AND PUBLIC POLICY,
Second Edition
“This book provides a comprehensive and accessible account of the core issues
in public finance and public policy. Although designed as a textbook, the book
is also an organizing guide for practitioners and policymakers, who will find particularly useful the application of concepts to issues in income support and work
incentives, education, health care, and the choice between tax financing and user
prices.”
– Sanjeev Gupta, Fiscal Affairs Department,
International Monetary Fund, Washington, DC
“This fascinating book provides a clear account of the role of government
through public finance and public policy. It gives a balanced and insightful analysis of the scope and limits of what government can and should do. Students will
like the clear exposition, and researchers will benefit from the book as a reference
volume.”
– Kai Konrad, Max Planck Institute for Intellectual
Property, Competition and Tax Law, Munich
“This book is a gem. It brings alive the topics of public finance. The book is an
extraordinary piece of work that enables students to achieve a balanced overview
of market failures and government failures and thereby gain mature insight into
desirable interactions between the market and the state. Teachers and students
will benefit from this major achievement for years to come, making this book a
classic.”
– Dennis Snower, Kiel Institute for the World Economy and
Christian-Albrechts University, Kiel


Public Finance and Public Policy
Responsibilities and Limitations of
Government: Second Edition

Arye L. Hillman


Bar-Ilan University, Israel


CAMBRIDGE UNIVERSITY PRESS

Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore,
São Paulo, Delhi, Dubai, Tokyo
Cambridge University Press
The Edinburgh Building, Cambridge CB2 8RU, UK
Published in the United States of America by Cambridge University Press, New York
www.cambridge.org
Information on this title: www.cambridge.org/9780521494267
© Arye L. Hillman 2009
This publication is in copyright. Subject to statutory exception and to the
provision of relevant collective licensing agreements, no reproduction of any part
may take place without the written permission of Cambridge University Press.
First published in print format 2009
ISBN-13

978-0-511-64127-5

eBook (NetLibrary)

ISBN-13

978-0-521-49426-7

Hardback

ISBN-13

978-0-521-73805-7

Paperback

Cambridge University Press has no responsibility for the persistence or accuracy
of urls for external or third-party internet websites referred to in this publication,
and does not guarantee that any content on such websites is, or will remain,
accurate or appropriate.


For Jeannette

Tamara and Yitzi; Ilana and Hovav; Nachman Eliyahu and Galit,
Benjamin and Yael

Dafna, Yishai, Mayan, Ya’ara, Dov, Ze’ev, Shani, Lior, Hallel, Harel, Raphael,
Michal, Eyal, Ronni, Eliashiv, Eitan, and Libbi, and the others

In memory of my parents, for whom good government allowed a new beginning.
In memory of my brothers and my sister and all the other children.


From Sayings of the Fathers
The Individual and Social Justice
If I am not for myself, then who will be for me?
And if I am only for myself, then what am I?
And if not now, when?
Hillel, 110 BCE – 20 CE∗

The Individual and the Dilemma of Government
Pray for the peace of the government; for, except for the fear of that, we
should have swallowed each other alive.
R. Hanina, born around the year 20 CE
Be cautious with the government, for they do not make advances to a man
except for their own need. They seem like friends in the hour of their advantage, but they do not stand by a man in his hour of adversity.
Rabban Gamliel, around the year 230 CE



BCE and CE are universal ways of indicating dates. BCE indicates before the Common Era of
counting and CE indicates the Common Era.


Contents

Preface to the Second Edition

1. MARKETS AND GOVERNMENTS

page ix

1

1.1 The Prima Facie Case for the Market
1.2 Efficiency and Social Justice
1.3 The Rule of Law

4
24
36

2. INSTITUTIONS AND GOVERNANCE

71

2.1 The Political Principal–Agent Problem
2.2 Government Bureaucracy
2.3 Life without Markets and Private Property

73
101
107

3. PUBLIC GOODS
3.1 Types of Public Goods
3.2 Information and Public Goods
3.3 Cost-Benefit Analysis

4. PUBLIC FINANCE FOR PUBLIC GOODS
4.1 Taxation
4.2 Tax Evasion and the Shadow Economy
4.3 Government Borrowing

5. MARKET CORRECTIONS
5.1 Externalities and Private Resolution
5.2 Public Policies and Externalities
5.3 Paternalistic Public Policies

6. VOTING
6.1 The Median Voter and Majority Voting
6.2 Political Competition
6.3 Voting on Income Redistribution

135
138
178
209
243
246
279
288
307
309
334
367
405
409
437
461

vii


viii

Contents

7. SOCIAL JUSTICE
7.1 Social Justice and Insurance
7.2 Moral Hazard
7.3 Social Justice without Government

8. ENTITLEMENTS
8.1 The Attributes and Consequences of Entitlements
8.2 The Entitlement to Income during Old Age
8.3 The Entitlement to Health Care and Health Insurance

9. CHOICE OF TAXATION
9.1 Optimal Taxation
9.2 Capital and Other Tax Bases
9.3 Fiscal Federalism

10. THE NEED FOR GOVERNMENT
10.1 Growth of Government and the Need for Government
10.2 Cooperation, Trust, and the Need for Government
10.3 Views on the Need for Government

489
492
527
543
587
589
627
645
665
667
694
709
739
741
763
771

TOPICS FOR DISCUSSION

787

Author Index
Subject Index

825
831


Preface to the Second Edition

This book, a treatise on markets and governments, is presented as a text on public
finance and public policy. The exposition incorporates concepts of public choice
and political economy (which are, in large part, equivalent), as well as concepts
and evidence from behavioral economics. Elements of moral philosophy are
present, beginning with Adam Smith’s description of virtue through personal
behavior in markets and how perceptions of human nature affect views on the
need for government. The book covers the basic topics of a course in public
finance or public economics, or a course in the political economy of markets and
governments.
The focus of the book is the achievement, whether through markets or the
public finance and public policy of governments, of the social objectives of efficiency and social justice. There are objective criteria for efficiency. Social justice can be defined in different ways, as the natural right of possession, equality
of opportunity, or ex-post equality of incomes after redistribution. Ideology can
influence choice of the definition of social justice.
The book describes feasible policies. In particular, governments do not use
lump-sum taxes. From the outset societies are shown to confront choices between
the objectives of efficiency and equality.
This second edition retains the themes of the first edition. Although the
themes are the same, the book has been rewritten and restructured. The objective retained from the first edition is to make ideas accessible. Economics can
explain and enlighten. Yet, it is a curiosity of contemporary academic economic
writings that an idea is often given more applause when the presentation is made
arcane and inaccessible. This book presents in an accessible way the topics that
arise when governments are called on to improve market outcomes. The book
is the product of an ongoing inquiry – proceeding beyond the first edition –
into the political economy of markets and government. The line of inquiry in
this book has origins in my previous investigations focusing on the political economy of protection: the investigation of why governments prevent free trade is a
beginning for the broader questions about markets and governments that are the
topics of this book.
A course in intermediate microeconomics or price theory is a helpful prerequisite for using this book as a text, although an introductory course in economics
is sufficient for many of the topics. A course in macroeconomics is not required.
Questions to motivate discussion of the topics in each chapter are provided at
ix


x

Preface to the Second Edition

the end of the book. For graduate students and professional readers, a guide to
elaboration and more technical exposition of topics in the literature is provided
at the end of each chapter.
Other than in setting out the historical perspective on the growth of government, the book does not present data on the composition of government budgets
or the sources of government revenue. Such data differ, of course, among countries and also among states, cities, and localities that in fiscal-federal systems levy
taxes, engage in public spending, and decide on public policies. The data, which
change over time, are readily available from official sources. Issues involving data
on government spending and sources of government revenue have been placed
inside the topics for discussion. The topics may involve comparisons between
government jurisdictions or may ask for contemporary descriptions of taxation,
public spending, or public policy. The focus of the book is on ideas and concepts
that will outlive the data applicable for any time – or for any place.
I thank Scott Parris of Cambridge University Press in New York for his confidence that a treatise on the need for and consequences of government could
be an accessible textbook covering traditional topics of public finance and public
policy.
I am thankful to the professors and instructors who chose the first edition of
this book as the means for introducing students to the choice between markets
and governments and for the support that took the first edition into three printings. The first edition was translated into Chinese by Wang Guohua and into
Russian by Mark Levin. Toshihiro Ihori headed the team that translated the first
edition into Japanese and provided insights that were incorporated into the second edition. Michael Brooks, Gene Gotwalt, and Heinrich Ursprung read the
manuscript of the second edition and provided helpful suggestions. In preparing
the second edition, I also benefited from helpful comments from Joel Guttman,
Wolfgang Mayer, and Warren Young.


1
MARKETS AND
GOVERNMENTS
1.1 The Prima Facie Case for the Market
A. Self-interest with virtue
B. Efficiency and competitive markets
C. Reasons why markets fail to achieve efficiency
D. Information and spontaneous order

1.2 Efficiency and Social Justice
A. Pareto efficiency and compensation
B. Are competitive markets socially just?
C. Social justice as equality
D. The choice between efficiency and equality

1.3 The Rule of Law
A. Benefits of the rule of law
B. Anarchy with strong and weak
C. Anarchy and ethics
D. Imperfections in the rule of law

Supplement S1
S1A. Market efficiency in general equilibrium
S1B. The competitive market-adjustment mechanism
S1C. Monopoly profits and social justice

Summary
Literature Notes

1



Markets and Governments

T

3

he most important question in the study of economics is:

When should a society forgo the economic freedom of markets and rely on
the public finance and public policy of government?

This is a normative question. A normative question asks what ideally should
be done or what ideally should happen. Normative questions are distinct from
positive questions, the answers to which are predictions and explanations. The
primary positive question that we shall ask is:
What do we predict will be the outcome when voters and taxpayers delegate
responsibilities to governments through public finance and public policy?
These normative and positive questions, asked in different circumstances, are the
focus of this book. We shall take care to distinguish between normative and positive questions. A clear distinction is required because we do not wish to confuse
what governments ideally ought to do with what governments actually do. The
two can coincide but need not.
We shall not study any one particular government – federal or central, state or
provincial, or local. Descriptions of a particular government’s budget and public
policies become outdated when the government and the policies change. Today’s
government budget is not necessarily tomorrow’s, nor are today’s public policies necessarily the policies that will be appropriate or in place in the future.
Studying the details of a particular government’s budget and public policies,
therefore, does not provide useful, long-lasting knowledge. Lasting knowledge
requires identification of general principles that remain applicable anywhere at
any time. We shall seek to identify such general principles. Our quest is for general principles that apply to societies and governments in high-income democracies; however, occasionally comparisons will be made with other types of societies
and governments.
Whether through outcomes in markets or the decisions of government, we
shall seek the two objectives of efficiency and social justice. These are social
objectives. A social objective is an objective that in principle is expected to be
sought by consensus. Efficiency as a first approximation requires maximizing the
total income of a society. Social justice is multifaceted and involves redistribution
of income, equality of opportunity, and protection of rights to life and property.
There are three social objectives sought through public finance and public policy. After efficiency and social justice, the third social objective is macroeconomic
stability, expressed in avoiding inflation and unemployment and maintaining stability of the banking and financial system. We shall not study macroeconomics.
Our scope will extend beyond the narrow definition of economics as choice
when resources are limited. We shall encounter political economy, which is the
interface between economics and politics and studies the economic consequences
of political decisions. We shall draw extensively on concepts of the school of public choice, which is the source of political economy in the modern economics literature; a characteristic of the public-choice approach to economic analysis is that


4

Markets and Governments

all individuals, whether making decisions outside of or within government, are
viewed as seeking their self-interest. We shall study outcomes of collective decisions made by voting. We shall also encounter the influence of ideology on social
objectives; an ideology may give preeminence either to efficiency or social justice.
The emotions and feelings that underlie views on fairness and social justice will
take us to the intersection between economics and psychology known as behavioral economics. We also encounter moral philosophy and ethics – which is where
we now begin.

1.1
The Prima Facie Case for the Market
If the social objectives of efficiency and social justice cannot be achieved through
markets, governments can be asked to use public finance and public policy to
attempt to improve on market outcomes. Before we consider responsibilities for
governments, however, we look at outcomes of markets alone. Market outcomes
provide the benchmark on which we ask governments to improve.

A. Self-interest with virtue
In markets, buyers and sellers pursue personal self-interest. Buyers maximize
utility (or personal benefit) and sellers maximize profits. The decisions of buyers and sellers in markets are personal (rather than collective) and voluntary
(rather than coerced). Individuals cannot lose from a personal voluntary market
decision; people who perceive that they will not benefit simply can decide not to
buy or sell. Buyers and sellers both gain from their personal voluntary decisions:
Does the mutual benefit to buyers and sellers then imply that personal decisions
in markets achieve the two social objectives of efficiency and social justice?
Adam Smith (1723–90), who is regarded as the founder of modern economics,
proposed that when people seek personal benefit in markets, the ensuing market
outcomes benefit society at large. Adam Smith first studied at Glasgow University
in Scotland and then at Oxford University in England. After leaving Oxford (he
did not receive a degree because he had been found to have read the then-banned
author, David Hume), he returned to Glasgow University, where he was first a
professor of logic and then subsequently a professor of moral philosophy.
It is significant that Adam Smith was a professor of moral philosophy. Moral
philosophy studies ethical behavior. In his writings, Adam Smith referred to an
invisible hand that is the source of social benefit in markets. The invisible hand
transforms the quest for private benefit in markets into social benefit.1
1

The “invisible hand” appeared in the books The Theory of Moral Sentiments published in 1759 and
An Enquiry into the Causes of the Wealth of Nations first published in 1776.


The Prima Facie Case for the Market

5

People do not intend that their personal market decisions result in social benefit. The social benefit is unintentional: people intend only to benefit themselves.
Nonetheless, the invisible hand ensures that personally decided self-interested
outcomes are for the good of society.
The invisible hand thereby reconciles self-interest and virtue. People need not
have guilt feelings about pursuing their own self-interest in markets and not altruistically caring about consequences of their market decisions for others.
The invisible hand also eliminates hypocrisy from market behavior. There is
no reason for people to claim that they are seeking social benefit by doing favors
in markets. Adam Smith observed, “I have never known much good done by
those who affected to trade for the public good” (1776/1937, p. 423).2

B. Efficiency and competitive markets
Adam Smith viewed the invisible hand as maximizing total income for a society.
Maximized total income is associated with the social objective of efficiency. The
invisible hand is, of course, a metaphor. In the time that has passed since Adam
Smith’s writings, the need for the metaphor has been surpassed and formal proofs
have confirmed that markets – in particular, competitive markets – achieve efficiency. The formal proofs differ in complexity and scope. The simplest proof,
with which we now proceed, considers a single competitive market.

Social benefit and efficiency
We first define social benefit. With B indicating total benefit and C indicating total
cost, social benefit is:
W = (B − C).

(1.1)

The benefit W is social because the personal benefits and costs of everyone in
society are included in evaluating B and C. Next we define efficiency.
An outcome is efficient when social benefit W = (B − C) is maximized.
Achieving efficiency thus requires that marginal benefit be equal to marginal
cost:3
MB = MC.

(1.2)

Efficiency does not depend on who in a population benefits and incurs costs.
Questions about the distribution of benefits and costs among people involve
2

3

The saying “do not look a gift horse in the mouth” suggests that we should not examine too closely
the quality of a gift (the teeth reveal the age and health of the horse). The invisible hand suggests,
however, that we should be wary of favors offered in markets.
Expression (1.2) is the first-order condition for maximum W. The second-order condition for a
maximum requires that:
∂ MB
∂ MC
<
.
∂Q
∂Q


6

Markets and Governments
W=B − C
Maximum W
where MB = MC

MB > MC

0

MB < MC

QE

Quantity Q

Figure 1.1. The efficient quantity that maximizes W = (B – C) is QE .

social justice. Efficiency requires only the largest possible social benefit, independently of how benefits and costs are distributed among a population.
The definitions of social benefit and efficiency in general apply to any source
of benefit or cost. We are in particular interested in benefits and costs associated
with markets. When W refers to social benefit provided through a market, B is
the total benefit of all buyers in the market and C is the total cost of all sellers.
Figure 1.1 shows social benefit W as depending on the total quantity of output
Q supplied in a market. The efficient quantity that maximizes W is QE , determined in accord with expression (1.2) where MB = MC.4

Proof of the efficiency of a competitive market
In a competitive market, individual buyers and sellers do not influence price and
are free to enter and leave the market. A proof of the efficiency of a competitive
market has three components. The proof requires showing that:
(1) The market assigns goods among different buyers to achieve maximized total benefit, which we denote as B max .
(2) The market assigns supply among different sellers to achieve minimized total costs, which we denote as C min .
(3) With B max and C min achieved, the market also chooses a quantity such
as QE in figure 1.1 that maximizes W = B max − C min .
We begin with buyers.
Buyers
Competitive markets have many buyers. Figure 1.2a shows two representative
buyers with personal marginal benefits MB1 and MB2 from consumption. The
4

In figure 1.1, the second-order condition also is satisfied at output QE . When Q = 0, also W = 0.
When Q is sufficiently great, W = B − C becomes negative because total costs exceed total benefits.


The Prima Facie Case for the Market

7
Price

Price

ΣMC
MC1

Equal MB at
price PB = MBmax

MC2

PS

PB
MB2

MB1

ΣMB

Equal
MC at
price
PS = MC min

Market
demand

O

Market
supply

qb1

qb2

QB

Quantity

(a)

O

qs1

qs2

QS

Quantity

(b)

max

Figure 1.2. (a) B
achieved through self-interested buyers’ decisions. (b) C min achieved
through self-interested sellers’ decisions.

MB functions indicate individual demands, expressed as marginal willingness to
pay for additional output. Marginal willingness to pay is an amount of money.
MB is therefore measured in terms of money – which can therefore be compared
with marginal cost MC, which is also measured in terms of money.5
We now regard benefit from consumption as exclusively private or personal for
each buyer. Only the buyer benefits and no one else. We shall presently define
public goods from which a number of people can benefit simultaneously. In figure 1.2a, MB1 and MB2 decline with the quantity consumed, thereby indicating
diminishing marginal benefit (or utility) from consumption.6
Total benefit of buyers is
B = B1 + B2 ,

(1.3)

which is maximized when
MB1 = MB2 .

(1.4)

Expression (1.4) is a technical requirement (the first-order condition) for attaining maximal total benefit B max . To prove that the market outcome for buyers is
efficient, we need to show that self-interested market behavior of buyers replicates the technical requirement (1.4).
In figure 1.2a, total market demand at the price PB confronting buyers is
QB = (qb1 + qb2 ). The personal quantities, qb1 and qb2 , are determined by buyers maximizing utility according to:
PB = MB1 , PB = MB2 .
5

6

(1.5)

Marginal utility is not measured in money but rather in terms of utility. Utility is ordinal and
expresses rankings of outcomes according to preferences. Marginal willingness to pay expressed
in MB is cardinally measurable in money terms. We shall refer to utility in some circumstances; for
example, we describe people as making decisions to maximize utility. In general, we shall use the
terms benefit and utility interchangeably.
Linearity of marginal benefit is only for exposition.


8

Markets and Governments

It follows from expression (1.5) that self-interested utility-maximizing behavior
of buyers results in:
MB1 = PB = MB2 .

(1.6)

The competitive market outcome (1.6) thus replicates the condition for efficiency (1.4). Therefore:
A competitive market efficiently assigns goods among buyers to maximize
buyers’ total benefit.
The “assignment” of goods among buyers in a competitive market is selfassignment through personal choice. In figure 1.2a, buyers voluntarily choose the
personal quantities qb1 and qb2 that maximize buyers’ total benefit.
Sellers
A proof similar to that of the case of buyers shows that self-interested profitmaximizing behavior of sellers minimizes total cost of market supply. In figure 1.2b, MC1 and MC2 are marginal costs of two among many competitive
sellers. The total cost of supply of the two sellers is
C = C1 + C2 ,

(1.7)

which is minimized when
MC1 = MC2 .

(1.8)

Expression (1.8) is the technical requirement for achieving minimum total cost
C min . We now look at self-interested market behavior of sellers. In figure 1.2b,
total market supply offered at price PS confronting sellers is QS = (qs1 + qs2 ).
Individual sellers’ profits are maximized when the sellers supply the quantities
qs1 and qs2 , determined by
PS = MC1 , PS = MC2 .

(1.9)

Therefore, self-interested market behavior of sellers results in:
MC1 = PS = MC2 .

(1.10)

The technical requirement (the first-order condition) for achieving minimized
total cost of supply C min as given by expression (1.8) is equivalent to expression
(1.10), which is the consequence of self-interested market behavior of sellers.
Therefore:
A competitive market efficiently assigns supply of goods among sellers to
achieve minimized total cost.
The assignment of supply to individual sellers is again through voluntary market
decisions. That is, the assignment of supply is self-assignment through decisions
freely made in response to the market selling price.


The Prima Facie Case for the Market

9

Price
A
SUPPLY

PB = PE = PS

E

MBmax = MC min

DEMAND
O

QB = QE = QS

MC with C min

MB with Bmax

Quantity

Figure 1.3. The maximum value of W = B max − C min is indicated by the shaded area AEO.

The market equilibrium
The third and final condition for efficiency of market outcomes is satisfied if a
competitive market maximizes:
W = B max − C min .

(1.11)

The technical requirement is:
MB max = MC min .

(1.12)

In the market shown in figure 1.3, the technical requirement (1.12) is satisfied at
point E. We now need to show that self-interested market decisions replicate the
technical requirement for efficiency (1.12).
The initial two steps of our proof of the efficiency of a competitive market
indicated that, respectively, total benefit from consumption is maximized for any
total quantity of output QB on a market demand function, while total cost of supply is minimized for any quantity of output QS on a market supply function. We
therefore associate quantities on a market demand function with maximized total
benefit to buyers B max and quantities on a market supply function with minimized
total cost of suppliers C min . Correspondingly, as in figure 1.3, the market demand
function indicates marginal benefit MB max from additional consumption and the
market supply function indicates marginal cost MC min of additional supply.
Returning to figure 1.2a, we see that for buyers:
PB = MB1 = MB2 ≡ {MB max }.

(1.13)

Similarly, figure 1.2b shows that for sellers:
PS = MC1 = MC2 ≡ {MC min }.

(1.14)


10

Markets and Governments

In figure 1.3, the output supplied at point E is QE and the price is PE , where:
QB = QE = QS ,

PB = PE = PS .

(1.15)

Combining expressions (1.13), (1.14), and (1.15) shows that, at point E:
MB max = PE = MC min .

(1.16)

The outcome of self-interested behavior of buyers and sellers as described
by expression (1.16) thus replicates the technical requirement (1.12) for maximized W.
At any quantity in figure 1.3, the area under the demand function measures
maximized total benefit B max . The area under the supply function measures minimized total cost C min . The difference between the areas under the demand and
supply functions is therefore W = (B max − C min ), which we have indicated is
maximized at point E. The maximized value of W is shown in figure 1.3 by the
shaded area AEO.7
The competitive market-adjustment mechanism
Although we have shown that the market outcome at point E in figure 1.3 is
efficient, the question remains:
How do we know that a competitive market will be at the efficient point E?
A competitive market-adjustment mechanism ensures that the market will be at
point E. The point E is indeed the equilibrium of a competitive market.
At the quantity Q1 < QE in figure 1.4:
PS = MC < PB.

(1.17)

Sellers thus know that buyers’ willingness to pay for additional output, given by
PB , exceeds the MC of supply. Sellers therefore increase supply beyond Q1 . At
the efficient quantity QE at point E, buyers’ willingness to pay PB is precisely
equal to suppliers’ MC. Suppliers therefore no longer have an incentive to expand
output.8
Alternatively, at a quantity such as Q2 > QE :
PS = MC > PB.
7

8

(1.18)

The shaded area above the price PE is known as consumer surplus. The shaded area below the
price PE is known as producer surplus. In using MB to represent demand and using the area under
the demand function to represent total benefit B, we rely on the substitution effect of relative price
changes. There is also an income effect. For any one good, the income effect is, in general, small and
the substitution effect is therefore the basis for a good approximation to total benefit (see Willig,
1976). Income effects will be introduced and explained where income effects have consequences
that we wish to emphasize. When income effects are introduced, all goods will be regarded as normal goods (for which demand increases when income increases).
In general, after we proceed beyond the proof of the efficiency of competitive markets, we shall use
MB and MC without adding the respective superscripts max and min. We then take for granted that
MB refers to the equal marginal benefit of buyers that has maximized total benefit B and that MC
indicates the equal marginal cost of suppliers that has minimized total cost C.


The Prima Facie Case for the Market

11

Price
SUPPLY (PS )
H

G
E

PS > PB

PB = PE = PS
PB > PS

A
F

O

Q1

DEMAND (PB)

QE

Q2

Quantity

Figure 1.4. The competitive market-adjustment mechanism.

Buyers are therefore willing to pay less than sellers’ MC of supply and the output supplied falls. The fall in output again ceases at the efficient quantity QE at
point E.
If quantity Q1 were supplied in figure 1.4, there would be an efficiency loss
equal to the area HEF. If the quantity Q2 were supplied, the efficiency loss would
be GEA.9 The competitive market-adjustment mechanism does not allow such
efficiency losses to persist because the market will not remain at inefficient disequilibrium outputs such as Q1 or Q2 but will move to the efficient, stable equilibrium output QE .
We therefore conclude:
A competitive market-adjustment mechanism ensures that the market
moves to and remains at the efficient market equilibrium.
How do prices in competitive markets change?
If individual buyers and sellers cannot influence the market price, how do prices
in a competitive market change? The inability of individual buyers and sellers
to influence price in a competitive market applies only at the equilibrium output
QE . In figure 1.4, at Q1 < QE , sellers are approached by buyers who offer to pay
PB > PS = MC. Sellers therefore can increase the price PS at which they sell,
knowing that buyers will pay. As the price PS increases, so does the quantity
supplied, until the equilibrium quantity QE is reached. At QE , because PS = PB,
a seller cannot increase price and find buyers willing to buy. Alternatively, at
9

In figure 1.4, the area HEQE Q1 is the total benefit from supply of the additional output
(QE – Q1 ) that is required to reach the equilibrium output QE . The area FEQE Q1 is the total
cost of supplying this additional output. The difference is HEF, which therefore is the net gain from
supply of the efficient output QE rather than Q1 . By similar reasoning, EGA is the net gain from
supply of QE rather than Q2 .


12

Markets and Governments

Q2 > QE in figure 1.4, sellers approach buyers and offer to sell at PS = MC > PB.
However, the selling price is too high for buyers to be prepared to buy. That
is, the selling price exceeds buyers’ marginal willingness to pay. To find buyers,
sellers need to reduce their selling price PS . The reduction in the selling price
takes place and the output supplied falls until the equilibrium price PE is attained
where buyers are willing to pay the price at which sellers offer to supply.
Confirmation of the social benefit of the invisible hand
We have now confirmed that the three conditions necessary for efficiency are
satisfied in a competitive market equilibrium. Figure 1.5 shows the simultaneous
fulfillment of the following three conditions.
(1) Self-interested market behavior of buyers has resulted in maximized
total benefit B max for any quantity Q demanded in the market. The
slope of B max is MB max .
(2) Self-interested market behavior of sellers has resulted in minimized
total cost C min for any quantity Q supplied. The slope of C min is
MC min .
(3) W = B max − C min is maximized at the equilibrium market quantity
QE , where QB = QS . At the equilibrium market quantity QE , buyers
and sellers face the common equilibrium price PE . We see that PE =
MB max and PE = MC min and, therefore, that W is maximized because
MB max = MC min .10

Total benefit B
Total cost C

Minimized
total cost C min
Maximized
total benefit B max

PE = MB max

Maximum W = B max – C min

PE = MC min
0

QB=QE=Q S

Quantity Q

Figure 1.5. A competitive market achieves B max and C min and maximizes W = B max − C min .

10

In figure 1.5, MB (the slope of B max ) is declining and MC (the slope of C min ) is increasing, indicating that the second-order condition for a maximum of W is satisfied.


The Prima Facie Case for the Market

13

We conclude that, as Adam Smith predicted using the metaphor of the invisible hand:
Buyers and sellers making self-interested decisions in a competitive market
achieve efficiency.
Normative and positive questions about competitive markets
We have asked and answered a normative and a positive question about competitive markets. The normative question has been:
Is the equilibrium outcome of a competitive market efficient?
The positive question has been:
Can we predict that a competitive market will be at the efficient outcome?
We have affirmative answers to both questions.
Supplement S1A: Market efficiency in general equilibrium
Our proof of market efficiency is based on a single competitive market. A view
of a single market is called partial-equilibrium analysis because of the partial
single-market picture of economic activity. General-equilibrium analysis, in
contrast, includes all markets in an economy as well as international trade.
Supplement S1A presents a general-equilibrium picture of an economy and
demonstrates the efficiency of a competitive market economy – and shows that
efficiency also requires free international trade. A general-equilibrium proof
of the efficiency of a competitive market economy requires a supplementary
definition of efficiency (Pareto efficiency), which will be introduced presently.

The concepts of supply and demand
Adam Smith used the metaphor of the invisible hand and did not express his
ideas in terms of the demand and supply functions of a market. Demand and
supply functions were introduced later by Alfred Marshall (1842–1924), who was
professor of political economy at Cambridge University in England. Marshall
ended a debate about whether the value of a good is caused by the cost of
production or is caused by the willingness of buyers to pay. The water–diamond
paradox (which Adam Smith had also noted) is that although it is impossible
to survive without water, nonetheless water generally has a low market value
(a low price), whereas diamonds, which are unnecessary for life, have a high market value. William Stanley Jevons (1835–82) resolved the water–diamond paradox by observing that people’s valuations of goods are determined by marginal
benefit, not total benefit. The total benefit from having water exceeds the total
benefit from having diamonds. Diamonds, however, are usually more highly valued


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