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THE PRICE THEORY OF VALUE
IN PUBLIC FINANCE

by Donald R. Escarraz

UNIVERSITY OF FLORIDA PRESS / GAINESVILLE, FLORIDA, 1966

EDITORIAL COMMITTEE

Social Sciences Monographs

MARVIN E. SHAW, Chairman
Professor of Psychology

RALPH H. BLODGETT
Professor of Economics

ARTHUR W. COMBS
Professor of Education

MANNING J. DAUER
Professor of Political Science

T. LYNN SMITH
Professor of Sociology

GEORGE D. WINIUS
Professor of History

3 oS

c, 6a

COPYRIGHT @ 1966 BY THE BOARD OF
COMMISSIONERS OF STATE INSTITUTIONS
OF FLORIDA

LIBRARY OF CONGRESS
CATALOG CARD No. 66-64915

PRINTED BY THE PARAMOUNT PRESS
JACKSONVILLE, FLORIDA

CONTENTS

1. Introduction .................... 1
2. Graphical Models ... ............. 4
3. Revealed Preferences ............. 23
4. A Suggested Approach ............ 35
5. Taxes and the Political Process..... 48
6. Applications of the
Suggested Approach .............. 59
7. Other Applications
of the Theory ................... 66
Selected Bibliography ............... 76

UNIVERSITY OF FLORIDA MONOGRAPHS

Social Sciences

1. The Whigs of Florida, 1845-1854,
by H. J. Doherty, Jr.
2. Austrian Catholics and the Social
Question, 1918-1933, by A. Diamant.
3. The Siege of St. Augustine in 1702,
by C. W. Arnade
4. New Light on Early and Medieval
Japanese Historiography, by J. A.
Harrison
5. The Swiss Press and Foreign Af-
fairs in World War II, by F. H.
Hartmann
6. The American Militia: Decade of
Decision, 1789-1800, by J. K. Mahon
7. The Foundation of Jacques Mari-
tain's Political Philosophy, by H. Y.
Jung
8. Latin American Population Studies,
by T. L. Smith
9. Jacksonian Democracy on the Flori-
da Frontier, by A. W. Thompson
10. Holman Versus Hughes: Extension
of Australian Commonwealth Pow-
ers, by C. Joyner
11. Welfare Economics and Subsidy
Programs, by M. Z. Kafoglis
12. Tribune of the Slavophiles: Kon-
stantin Aksakov, by E. Chmielewski
13. City Managers in Politics: An
Analysis of Manager Tenure and
Termination, by G. M. Kammerer,
C. D. Farris, J. M. DeGrove, and
A. B. Clubok
14. Recent Southern Economic Develop-
ment as Revealed by the Changing
Structure of Employment, by E. S.
Dunn, Jr.
15. Sea Power and Chilean Independ-
ence, by D. E. Worcester
16. The Sherman Antitrust Act and
Foreign Trade, by A. Simmons

17. The Origins of Hamilton's Fiscal
Policies, by D. F. Swanson
18. Criminal Asylum in Anglo-Saxon
Law, by C. H. Riggs, Jr.
19. Colonia Baron Hirsch, A Jewish
Agricultural Colony in Argentina,
by M. D. Winsberg
20. Time Deposits in Present-day Com-
mercial Banking, by L. L. Crum
21. The Eastern Greenland Case in
Historical Perspective, by 0. Svar-
lien
22. Jacksonian Democracy and the His-
torians, by A. A. Cave
23. The Rise of the American Chemistry
Profession, 1850-1900, by E. H.
Beardsley
24. Aymara Communities and the
Bolivian Agrarian Reform, by W. E.
Carter
25. Conservatives in the Progressive
Era: The Taft Republicans of 1912,
by N. M. Wilensky
26. The Anglo-Norwegian Fisheries
Case of 1951 and the Changing Law
of the Territorial Sea, by T. Koba-
yashi
27. The Liquidity Structure of Firms
and Monetary Economics, by W. J.
Frazer, Jr.
28. Russo-Persian Commercial Rela-
tions, 1828-1914, by M. L. Entner
29. The Imperial Policy of Sir Robert
Borden, by H. A. Wilson
30. The Association of Income and Ed-
ucational Achievement, by R. L. Las-
siter, Jr.
31. The Relation of the People to the
Land in Southern Iraq, by F. Baali
32. The Price Theory of Value in Pub-
lic Finance, by D. R. Escarraz

PREFACE

The voluntary exchange or price theory of pub-
lic finance has a history which is as long as
the history of the price theory of private goods, if
the number of years is the basis for the length of his-
tory. However, very few economists have attempted
to develop the theory further as an explanation of
political or economic behavior or to apply it as a
criterion for policy decisions of government. The
theory has not reached the degree of acceptability
which the price theory of private goods has reached.
This difference in acceptability can be explained
in part by the existence of certain criticisms of the
price theory of public finance which are not rele-
vant to, or at least have never been raised with re-
spect to, the price theory of private goods. Another
part of the difference may be explained by the ab-
sence of the development of a general framework
in the price theory of public finance which could
be used for a wide range of problems and which
could be used to indicate the relationship of the two
theories.
This monograph attempts to approach both of
the above factors which have to some extent limited
the acceptability of the price theory of public fi-
nance among economists. The final chapter il-

lustrates some of the uses of the theory in the past
and the prospects of its acceptance by more eco-
nomists in the future.
There is no doubt that the critique of criticisms
of the theory presented here is incomplete. Indeed,
there may exist errors in interpretation and analysis
both with respect to the critique of criticisms and
with respect to the suggested approach. However, if
more issues are clarified by the presentation than
are confused, the author will consider that he has
achieved the purpose of the monograph. The field is
currently confused, and yet it is one which may have
a tremendous potential. Therefore, the monograph
may have value even if it does not clarify issues
but does cause other economists to reconsider the
field, and they as a result clarify the issues.
My indebtedness is acknowledged to Dr. Ansel M.
Sharp who started me into the study of the price
theory of public finance and led me through a dis-
sertation on the subject at Oklahoma State Univer-
sity. I am also indebted to Dr. Milton Z. Kafoglis
of the University of Florida for his encouragement.
It was Dr. Kafoglis who originally suggested that my
dissertation should be published and then urged me
on to incorporate in it my latest work in the field.
The result is that less than half of the original dis-
sertation is contained in this monograph.
I also wish to express my thanks to the editors
and readers for the Social Sciences Monograph Se-
ries for their comments and suggestions, and to the
typing pool of the College of Business Administra-
tion for their prompt and efficient service. Finally,
but not least, I wish to thank my wife and three
children for putting up with me during the many
months of writing, rewriting, and waiting that have
gone into this monograph. The author of any orig-
inal work goes through much but his family un-
doubtedly suffer more.
DONALD RAY ESCARRAZ

1. INTRODUCTION

The voluntary exchange or price theory of public finance had its
origin in the benefit approach to taxation, but it never has had
the widespread acceptance enjoyed by that approach in the eighteenth
and nineteenth centuries. The causes of this lack of acceptance are the
primary theme of this monograph. More specifically, an attempt is made
to show that the criticisms of the theory are not a sufficient reason to
completely reject it. In the process of analyzing the major criticisms,
suggested approaches to the theory and applications to the political
process are presented.
There are many aspects to the voluntary exchange approach to pub-
lic finance, but its essence can be understood by simply considering it to
be the application of the whole body of price theory to the problem of
the supply of goods and services by the government. This view of public
finance requires that the revenues of the government (taxes) be consid-
ered together with the expenditures of the government. The expenditures
must be considered as costs of producing public goods and services. The
government is, thus, a producer or firm in the economy, similar to pri-
vate firms. Economists have not generally accepted this concept. In fact,
economists have often discussed the expenditure activities of the govern-
ment in terms of its being a consumer. The notion of the government as
a consumer may have been an outgrowth of Adam Smith's belief that
some of the expenditures of the sovereign are for unproductive labor.
The unproductive-labor concept has dropped out of economic literature,
but not the concept that the government consumes goods and services
when it makes expenditures. The non-acceptance of the concept of the
government as a producer enters the discussion throughout this mono-
graph.
The most important theoretical concepts which must be accepted with
the price theory of public finance are related to the revealing of pref-
erences for public goods. The theory implies that public goods do pro-
vide satisfaction to the individual and that the individual associates the
satisfaction with the quantity of the public goods available to him. It
also implies that the individual will reveal his preferences for public
goods if given the opportunity. The non-acceptance of these concepts is
discussed in the first part of Chapter 3.
Richard A. Musgrave has placed importance on the determination of
1

THE PRICE THEORY OF VALUE IN PUBLIC FINANCE
a single best solution in the allocation of resources when public goods
are involved. This determination is treated in the last part of Chapter
3 and in Chapter 4. The latter chapter also suggests an approach to
the price theory of public finance. A model is developed which attempts
to show a single best solution analogous to the Pareto optimum.
The price theory of public finance does require that taxes be viewed
as a price paid for goods and services. The taxpayer is a taxpayer-
buyer. If the political organization is taken into consideration, the tax-
payer can be considered a voter-buyer, since he indicates the quantity
of goods and services he desires through his vote rather than through
the taxes paid. Taxes are the prices paid for the goods and services
actually supplied, but the determination of what quantities of goods
and services should be supplied is based on the taxpayers' voting in
the political process. Therefore, the determination of the individual's
taxes constitutes the allocation of the value or costs of the goods and
services. Economists have not generally accepted this concept of taxes
as a price or as an allocation of value or costs. In fact, taxes are often
considered to be little more than a form of coercive activity of gov-
ernment which is inherent in the nature of the state. These problems
are discussed in Chapter 5.
That the taxpayer is a voter-buyer may thus be implied by the price
theory of public finance. In any case, the concept of the voter-buyer
does imply the existence of a particular type of political mechanism.
The voter-buyer not only must want to reveal his preferences for public
goods, he must have a means by which to do so. Therefore, the political
mechanism cannot be ignored by an economist accepting the price
theory of public finance. The effect of the political mechanism upon
the degree of coercion in taxation is discussed in the last part of Chap-
ter 5.
The suggested approach of Chapter 4 and the approach adopted to
analyze the criticisms in Chapter 5 become the basis for possible appli-
cations of the price theory of public finance in Chapter 6. Chapter 7
backs up to take a look at some existing applications of the theory by
economists and to look at the prospects for further applications by
other economists.
Richard A. Musgrave and Alan T. Peacock, Classics in the Theory of
Public Finance, is a minimum requirement to place the arguments
presented here in proper historical perspective. Musgrave, The Theory
of Public Finance, is necessary background for the specific criticisms
that are discussed here, and for seeing the basis upon which the sug-

INTRODUCTION
gested approach was developed. An attempt has been made to present
Musgrave's criticisms and his adaptation of Paul A. Samuelson's model,
but these are not a substitute for reading Musgrave's original work,
since his criticisms are lifted out of the context in which they were
presented.

2. GRAPHICAL MODELS

The development of the voluntary exchange theory of public finance
since the turn of the century has centered around three graphical
models and Knut Wicksell's concept of unanimity. To be sure, other
writings since the turn of the century are directly or indirectly related
to the voluntary exchange or price theory in public finance, but the
graphical models with Wicksell's unanimity principle sufficiently bring
out the main points of the approach. Therefore in this chapter there
is an attempt made to restate three of the geometric models and to
state the unanimity principle in graphical form, so that the main points
of the theory can be understood and the interrelationships among the
presentations can be recognized. Musgrave's criticisms of the Lindahl
model are also considered in this chapter because they have been a
stumbling block to the general understanding and acceptance of the
approach in the United States.
ERIK LINDAHL AND KNUT WICKSELL
In 1919 Erik Lindahl, a Swedish economist,1 presented a simple
graphical model which attempted to establish the total expenditure on
a public good and the relative tax shares of two classes of society. Class
A (the relatively well-to-do) are represented by legislators A and class
B (the relatively poor) are represented by legislators B. It is assumed
that there is an even distribution of political power between the two
groups. It is also assumed that all economically related public services
are lumped together so that the total cost is the total cost of a group
of services rather than a single service.
Figure 1 shows on the abscissa the relative share of the total cost of
providing a given public good. Reading from left to right is the rela-
tive share of A, and reading from right to left is the relative share of
B. Various levels of total cost (V through Z) are shown along the ordi-
nate. The curve AR indicates the total expenditure on the public serv-
ice at various relative cost shares to which legislators A would agree.
Logically, A legislators are willing to have a greater total expenditure
made, if class A of society can pay a smaller percentage of the total
1. See Musgrave and Peacock, pp. 168-76, for a translated chapter from Lin-
dahl, Die Gerechtigkeit der Besteuerung. (Full information on cited works is in
the Bibliography.)
4

GRAPHICAL MODELS

cost. The curve BS indicates the total expenditure on the public service
at various relative cost shares to which legislators B would agree. At X
level of total expenditure, group A would agree only if group B would
pay 60 per cent of the total cost, while group B would agree only if
group A would pay 72 per cent of the total cost.
The equilibrium solution is clearly at the intersection of the two curves
at P. The total expenditure to be made on the group of public services
is Y. A agrees to pay 60 per cent of Y, while B agrees to pay 40 per
cent of Y.

Total Cost of Total Cost of
Public Service Public Service

A B
V -----. ---V---------------------V------ V

W ----------------W---------

X X

Y --Y

z ----- _- _-------- z

A-- 0 10 20 30 40 50 60 70 80 90 100
100 90 80 70 60 50 40 30 20 10 04-B
Figure 1.

The fact that the Lindahl model emphasizes the political process in
the determination of how much should be supplied and who should pay
for the service in a manner consistent with the political principles laid
down by Knut Wicksell has been recognized.2 However, a presentation
of the Lindahl model in terms of Wicksell's unanimity principle3 may
be useful before evaluating the criticisms of the Lindahl model.
In Figure 2 the Lindahl model is traced by the dashed curves AR

2. Musgrave, "Voluntary Exchange Theory of Public Finance," p. 215; Mus-
grave, Theory of Public Finance, p. 74.
3. See Musgrave and Peacock, pp. 72-118, for a translation of Wicksell's state-
ment of the principle; see Uhr, Economic Doctrines of Knut Wicksell, pp. 164-80,
and B. Seligman, Main Currents in Modern Economics, pp. 559-60, for interpre-
tations.

5

THE PRICE THEORY OF VALUE IN PUBLIC FINANCE

and BS, with main bill A representing a total expenditure of V, amend-
ment A', a total expenditure of W, etc. Reading the graph in terms of
Wicksell's unanimity principle, the abscissa reading right to left meas-
ures the percentage of group B who would vote for various expendi-
ture bills with various tax plans. Tax plan a favors group B while tax

Figure 2.

plan i favors group A. These tax plans can be converted into the ter-
minology of the Lindahl model with the following schedule.
Tax Plan A B

90% of
80% "
70% "
60%"
50% "
40% "
30% "
20% "
10% "

total
"9
9v

VP
"9
99
"

"
"

cost
"9
"9
"9
"9

"9

10%
20%
30%
40%
50%
60%
70%
80%
90%

of total cost
99 901 19
If 99 19

99 99 99

99 99 99
99 99, 99

99 99 9

The curve DQ connecting all of the a' points indicates the percent-
age of A legislators who would vote for the various expenditure pro-
posals with tax plan a (i.e., class A of society to pay 90 per cent of the
total cost). The curve EO connecting all of the a points indicates the
percentage of B legislators who would vote for the various expenditure
proposals with tax plan a (i.e., class B of society to pay 10 per cent

6

GRAPHICAL MODELS

of the total cost). The only proposal which can obtain perfect una-
nimity is Amendment A'" with tax plan d. In terms of the Lindahl
model it is the Y level of total cost with class A paying 60 per cent of
Y and class B paying 40 per cent of Y. On Amendment A" with tax
plan g, none of the B legislators and only 65 per cent of the A legis-
lators would vote for the proposal. On Amendment A" with tax plan
c only 15 per cent of the A legislators and 75 per cent of the B legis-
lators would vote for the proposal.4
Both Wicksell and Lindahl, however, recognized the practical limita-
tion that the legislature probably would never be restricted by a perfect
unanimity rule. Therefore, Wicksell accepted the concept of approxi-
mate unanimity, and Lindahl discussed the effects of dropping the as-
sumption of equal political power. The result of either of these practi-
cal considerations may be that equilibrium can be achieved in an area
around point P, depending upon which bill and tax plan approximating
Amendment A'" with tax plan d is voted on first or which group
in society has an advantage in political power.
More specifically using just the Wicksell model, the equilibrium level
of expenditure and tax plan can be seen to depend upon the level of
unanimity required and the order in which the proposals are voted
upon. Assuming 100 legislators in group A and 100 in group B, and
assuming that the majority rule is accepted as approximate unanimity,
equilibrium can take place for Amendment A"" with any tax plan,
because all of the tax plans will get 100 per cent of the vote of the
B legislators and enough of the vote of the A legislators to make a
majority vote. Tax plan a or b would also be accepted as an equi-
librium proposal with Amendment A". With Amendment A'" any
of the tax plans, b, c, d, e, f, or g, will be accepted under the majority
rule concept of approximate unanimity. The exact combination of bill
and tax plan to be accepted would depend entirely on which one was
first presented for a vote.5
According to Lindahl, if unequal political power exists, the solution
will lie on SPR of the Lindahl model in Figure 1. BPS is the total

4. With the Wicksell-Lindahl model, the question of what goods should be
supplied by the government is also determined because only those goods which
are capable of receiving perfect unanimity should be supplied.
5. Wicksell suggests that, in the case of approximate unanimity, all proposals
should be voted on and the one with the greatest total vote be accepted. This
requirement would limit the equilibrium solutions to Amendment A"' with tax
plan d and Amendment A"" with any of the tax plans, since these are the pro-
posals which would receive a 100 per cent yes vote of one group or the other.

7

THE PRICE THEORY OF VALUE IN PUBLIC FINANCE
expenditure which the B legislators would desire at varying tax sharing
plans and APR is the total expenditure which the A legislators would
desire at varying tax sharing plans. PS is the segment of BPS which
is capable of obtaining perfect unanimity and PR is the segment of
APR which is capable of obtaining perfect unanimity. Therefore, with
Lindahl's concept of unequal political power, which is in terms of one
group's ability to force its desires upon the other group, the solution will
lie on PS if B has the greater political power and on PR if A has the
greater political power. However, if unequal political power is accepted
as being any solution reached by compromise other than the optimum
solution which can be reached with perfect unanimity, the equilibrium
can be a large number of solutions around the point P in Figure 2.
No matter what political conditions exist or which concept of political
power is accepted, the combined Wicksell-Lindahl model would appear
to be useful in explaining the results of the political process. Equilib-
rium will take place around point P in any case, and all that would
remain is to accurately evaluate the political process in order to de-
termine the actual equilibrium which will take place.
In February, 1939, Musgrave published an article with an interpre-
tation of Lindahl's model, but Musgrave's conclusions were the opposite
of those arrived at in the foregoing interpretation of the Wicksell-
Lindahl model. "To summarize: as an interpretation of the actual ex-
penditure process, the voluntary exchange theory was found unaccept-
able because of the unrealistic nature of the voluntary exchange
assumption in general and of the competitive pricing assumption in
particular. As a solution to the theory of tax justice it was found strictly
dependent upon the premise of competitive pricing; the definition of
the justice problem employed, moreover, appeared excessively narrow.
As standards of reference for analysis and appraisal of actual revenue-
expenditure policies, the voluntary exchange model and its corollary,
the neutral revenue-expenditure process, were found unacceptable."6
Musgrave's rejection of the theory in general because of the unreal-
istic nature of the voluntary exchange assumption is based on the fact
that "direct compulsion prevails in the legal enforcement of individual
tax contributions, independently of the individual's willingness to share
a part of the burden.'7 However, one answer to this criticism is that the
6. "Voluntary Exchange Theory," p. 231. The voluntary exchange theory as
a standard of reference for analysis and for the meaning and importance of the
neutral revenue-expenditure process is the primary concern of the monograph; see
especially Chapters 5 and 6.
7. Taxes as a form of coercion will be considered in more detail in Chapter 5.

8

GRAPHICAL MODELS
situation in the private economy cannot be said to be very different.
In the private economy, an individual is assumed to have a demand for
any particular good which relates the quantities of the good which the
individual would want to purchase to various prices. Once the indi-
vidual has expressed his demand by making the purchase, laws of
society, generally, protect the seller from the buyer's changing his
mind. In the voluntary exchange model the individual is assumed to
have a similar type of demand for each type of public good. The in-
dividual, however, permits his representative in the legislature to in-
terpret this demand schedule. Once the legislator has expressed this
demand by accepting a particular level of expenditure and tax plan,
the purchase has been made. The laws of society, as in the case of the
private good, protect the seller from the buyer's changing his mind.
Once the demand is expressed by purchase or by the legislators' voting
favorably for the providing of a product or service with a particular
tax plan, the transaction is completed and laws protect the parties of
the sale from changes in the individual's subjective evaluation of the
quantity he wants at the price agreed upon.
The problem which Musgrave seems to have discussed under the head-
ing of the compulsive nature of the political process is just the oppo-
site of compulsion.8 The problem lies in whether or not the fact that
compulsion exists affects the individual's expressed demand. In the
private economy it is assumed that it does not.9 In the political process
it may be more questionable, but, in the opinion of this writer, Mus-
grave has not given a sufficient reason for the rejection of the theory
in general.
Musgrave's rejection of the theory because of the competitive pric-
ing assumption in particular is just a further statement of his rejec-
tion of the theory in general. Musgrave did not recognize the oneness
of his two bases for rejection. He did not consider that compulsion ex-
ists only after a demand is expressed and that this compulsion is not
very dissimilar to the compulsion that exists with a private good once
demand has been expressed through a legal purchase of the good. The
effects of bargaining power or political power which Musgrave con-
siders are merely an analysis based on an assumption that the exist-
8. It is the opposite of compulsion in that it revolves around the individual's
being free to express his demand without compulsion and even to recontract if
an equilibrium solution is not determined which is consistent with the demand
expressed.
9. There is little or no literature on the economic effects of a private firm giv-
ing an absolute guarantee of satisfaction or your money back.

9

THE PRICE THEORY OF VALUE IN PUBLIC FINANCE
ence of compulsion, after a quantity at a price has been expressed,
affects the quantity which would be expressed.
Musgrave's analysis, however, is primarily in terms of the individ-
ual's realizing that his expressed demand will affect the price. This
analysis is based on Lindahl's statement of the model (i.e., that one in-
dividual's demand curve is the other individual's supply curve). Part
of the problem, however, seems to be that Musgrave switches his analy-
sis to the individual from the political process.10 In his analysis the
individual recognizes that his expressed demand is going to affect his
cost and, therefore, he will not express his true demand.11 However, if
it is remembered that the voluntary exchange model takes place in a
political setting, at least part of Musgrave's criticism can be dropped.
The individual is not directly bargaining with another individual for the
exchange of two goods. Two groups of legislators are attempting to ob-
tain the quantity of a good which the individuals, whom the legislator
represents, would want at a price consistent with that quantity. The leg-
islator does not have to obtain the lowest possible price for various
quantities to satisfy the individuals he represents. All that the legislator
must obtain is a quantity and price relationship which the individuals
that he represents consider satisfactory. Therefore, it cannot be as-
sumed that the demand curves will be affected by the fact that the
price is affected by the demand expressed by the legislator. Price can-
not be removed from its relationship to quantity just because the good
under consideration is a public good. If the legislator is attempting to
maximize the satisfaction of those individuals whom he represents, he
must express a demand which relates quantity and price and it must
be a quantity and price relationship indicated by the demand curve in
the Lindahl model because this curve by definition is the schedule of
quantities which the individuals would want at various prices. To ex-
press any other quantity-price relationship would put the legislator in
the position of not truly representing the individuals that put him in
office. This situation may well exist, but this is not the question. In other

10. This criticism is of particular importance when Musgrave considers the
effects of large numbers. If the model is restricted to the political mechanism, the
problem of large numbers does not exist in the form stated by Musgrave. The vot-
ing on specific expenditure-tax proposals is done by a limited number of legis-
lators representing taxpayer consumers and not by the taxpayer consumers them-
selves. The problem of the legislator representing a large number of taxpayer
consumers is a different problem, and is treated in Chapter 6.
11. The theoretical aspects of the problem of unrevealed preferences are dis-
cussed in detail in Chapter 3.

10

GRAPHICAL MODELS
words, Musgrave's criticism although stated in terms of a theoretical
criticism is more akin to a practical criticism that politicians do not
perfectly represent those who put them in office.12
Musgrave in 1959 reconsidered his rejection of the voluntary ex-
change model and came up with the same conclusions.13 This time, how-
ever, his analysis was more specifically in terms of a Cournot duopoly
situation. This analysis can be rejected simply because each individual
is not a producer trying to obtain a favorable price for the goods he
has to sell. The comments about Musgrave's earlier rejection of the the-
ory still apply, but it may be good to consider further what the Cournot
duopoly analysis would imply. An analogy can be made for this pur-
pose. In the private economy, it would have to be assumed that a
stockholder of a large company tries to get management to set its price
so that the stockholder acting as a consumer can purchase a larger quan-
tity of the good produced by the firm. The stockholder and consumer
may be one person, but this does not mean that as a stockholder the
individual tries to bargain with other individuals (stockholders) just
because by so doing he can affect the price he has to pay for the good
as a consumer. In the public economy the individual is a voter and a
consumer. This fact, however, does not mean that the individual as a
voter will bargain with other voters to affect the price he has to pay for
the good as a consumer. The only concern of the individual is that he
can purchase a quantity of the good at a price which maximizes his
satisfaction. In the case of a private good this is accomplished by merely
seeing to it that the quantity he purchases has a particular relationship
to the price determined by the market or by the management. In the
case of the public good this is accomplished by seeing to it that the leg-
islator who represents the individual expresses a quantity and price
relationship that maximizes the individual's satisfaction.
Under the consideration of the voluntary exchange theory as a so-
lution to the theory of tax justice, Musgrave rejects the theory because
of the non-competitive nature of the political process and because of the
assumption that original distribution of wealth is a "just" distribution.
The former cause for rejection has been discussed and only accepted
as a practical limitation to the extent that politicians do not and need

12. The theoretical issue involved in the problem is whether or not individuals
do consider public goods in terms of a quantity and price relationship which
maximizes satisfaction and which they expect their legislators to abide by. This
issue is taken up in Chapter 3.
13. Theory of Public Finance, pp. 78-80
11

THE PRICE THEORY OF VALUE IN PUBLIC FINANCE

not abide by the desires of the individuals whom they represent. The
latter cause for rejection is much more complex and will not be treated
here.14

HOWARD R. BOWEN
In 1943 Howard R. Bowen presented another formulation of the vol-
untary exchange or price theory of public finance, which was in terms
of an individual voting process rather than a political voting process,
and which was presented more along the lines of accepted price theory
analysis.15
Figure 3 presents the determination of the ideal output and cost dis-
tribution in terms of real goods. The vertical axis measures the quan-
tity of all other goods which the individuals would be willing to give
up to obtain social goods, and the horizontal axis measures the quan-
tity of the social good desired. The individual curves of marginal
substitution are individual demand curves with prices stated in terms
of the quantity of all other goods that the individual is willing to give
up to obtain various quantities of social goods.16 The TMS curve is the
total demand curve. Because social goods are defined as those for which
the demand (supply)17 cannot be individually held, the total demand
curve is obtained by vertically adding the individual demand curves
(MS a MSb and MS.) rather than by horizontally adding them. The
intersection of the marginal cost curve (MC)18 and the total demand
curve at point P determines the "ideal" output. The individual cost

14. The nature of the state and the nature of man are important factors in the
question of tax justice, but will not be discussed here. For one interpretation of
the effect of the nature of the state on the acceptance or non-acceptance of the
voluntary exchange theory, see Buchanan, "Pure Theory of Government Finance."
15. "Interpretation of Voting in the Allocation of Economic Resources."
16. Bowen's use of marginal substitution curves instead of regularly defined
demand curves is regrettable because it may have contributed to the later use
of indifference curves. The adoption of indifference curves by Samuelson and Mus-
grave has led to considerable confusion and a continued rejection of the theory.
The problems developing from Musgrave's analysis are treated at length in Chap-
ter 4.
17. Bowen speaks of divisibility of demand, yet speaks of social goods not be-
ing divisible into units that can be the unique possession of individuals. The
possession of individuals refers to the consumption of a supply of goods, so that
it is actually the indivisibility of supply rather than demand.
18. Bowen uses the concept that the ideal output exists when MC equals de-
mand if the product has constant or decreasing costs but when AC equals demand
if the product has increasing costs. Bowen explains the methodology in the latter
case as well as the first two cases, but no attempt is made to present the AC de-
termination since MC determination is still the more widely held concept.

12

GRAPHICAL MODELS

shares are determined by the intersection of the vertical line at the
"ideal" output and the individual demand curves.19
Bowen also shows that the average total demand (TMS/N) and aver-
age marginal cost (MC/N) would determine the same "ideal" output
(P). The slope of the TMS curve and the TMS/N curve would not be

Figure 3.
the same, but the point of intersection would be the same because at
this point TMS equals MC and equal numbers divided by the same num-
ber are equal. The importance of this concept can be seen in Figure 4
where Bowen assumes that the individual demand curves will fall
into a normal pattern of distribution. Assuming a normal distribution,
19. Individual cost shares can be determined in this manner only if it is a
constant cost product, because in the other cases the revenue would not equal
the total cost.

13

THE PRICE THEORY OF VALUE IN PUBLIC FINANCE
the average equals the mode. Therefore, the modal demand curve is
the same as the average demand curve and its use results in the deter-
mination of the same "ideal" output as does the use of the total de-
mand curve.
The assumption of the normal distribution is also important in the
interpretation of the voting process made by Bowen, because if each
individual votes on the quantity of the service he would desire, the

$

AC/N (MC/N)

TMS/N (Modal Curve)

0 X Social Good

Figure 4.
"ideal" output is both the output which gets exactly one-half of the
votes and that which gets more votes than any other quantity. In the
case of voting on various increments or decrements to a given quan-
tity of a social good, the "ideal" output is the one which gets exactly
one half of the votes yes and one half no. Smaller quantities will
receive a greater number of yes votes than the "ideal" output.
Three assumptions which are explicitly made by Bowen, and were
implicit in the presentation, are important: (1) the income dis-
tribution is "correct" (i.e., the income distribution has been accepted

14

GRAPHICAL MODELS
by society; this is the necessary assumption in order to use price theory
of private goods for a policy recommendation); (2) the product will
be available equally to all individuals so that the differences in de-
mand represent differences in tastes and preferences rather than just
differences in benefits (a normal curve of distribution cannot be assumed
if benefits are different to each individual voter); and (3) the cost of
producing the product in various quantities is known to the voters and
will be divided equally among the voters. This means that the voter
automatically knows his cost (AC/N). In other words, the voter knows
his relative share of the total expenditure of the social good.
The second and third assumptions can be modified by assuming that
those receiving different benefits can be grouped into classes so that
the members of each class do receive the same benefit20 and that the
costs will be distributed according to the modal demand for each class
but that the individual and classes of individuals are not affected in
their expressed demand by the fact that their demand affects their own
relative cost share. Figure 5 presents Bowen's model.21
The relationship between the Lindahl model and the Bowen model
is both interesting and important. Figure 6 presents another Bowen
model like Figure 3 and another Lindahl model like Figure 1. The
curves of the Lindahl model have been determined by the curves in the
Bowen model. The total expenditure is computed by multiplying the
quantity by the average cost (AC). The percentage of the total expendi-
ture which each individual is willing to pay is computed by dividing
the individual's demand by the total cost at each possible output. The
output determined by both models is the same. The assumption that av-
erage cost is constant is essential to the reconciliation of the two models
because the equilibrium of the Lindahl model will occur at the output de-
termined by the intersections of average cost and the total demand curve
in the Bowen model. Another assumption which is necessary in the rec-
onciliation of the two models is that the AR and BS curves of Figure 1
must be taken as demand curves of two individuals rather than of two
groups of legislators. This is the interpretation of the Lindahl model
used by Musgrave, but it ignores Lindahl's consideration of output being

20. An example can be made of education where one class of people have no
children and the other classes can be listed by the number of children per family.
Under these conditions, each classification of people can be assumed to have the
same benefit and, therefore, it can reasonably be assumed that within each classi-
fication, tastes and preferences will vary in accordance with a normal distribution.
21. Bowen's model does not determine the tax-price. It is given by the MC/N
curve assumed for each class.

15

THE PRICE THEORY OF VALUE IN PUBLIC FINANCE
determined in parliament. If the Lindahl model is interpreted to be two
groups of legislators representing two classes of individuals in society,
it would be necessary to assume that all individuals in each class have
the same demand function or that all individual demands are vertically
added and the individual cost shares are determined by the modal or
average demand of the particular classes of society. The modal curves
as developed by Bowen in Figure 5 cannot be used to reconcile the two

Figure 5.

models because Bowen has started with a given per-unit cost for each
class of society. To look at it another way, the reconciliation requires
two assumptions: (1) the individual demand curves are not affected
by the fact that the expressed demand affects the relative cost shares of
the individuals; and (2) the legislators have perfectly measured the
total demand function of all individuals of society or the modal demand
function of the individuals which the particular group of legislators
represent.
Bowen's article also brings to light several other points of interest to
the price theory of public finance. One point relates to the quantitative

16

$

0

.Class I

(I)

Social Good

GRAPHICAL MODELS

measurement of social goods. Bowen makes the point that some social
goods like education cannot be measured in simple physical units of
volume, time, or weight. Education consists of buildings, equipment,
number of teachers, quality of teachers, etc.22 Each of these components

Figure 6.
22. Lindahl's concept of voting on all economically related goods at one time
may be interpreted to mean the same thing, or it may be taken to mean goods
related by tastes and preferences. In either case, Musgrave's criticisms of Lindahl,
based on the concept that all goods which are capable of being determined by
the benefit principle are lumped together in one vote, are not valid.

17

THE PRICE THEORY OF VALUE IN PUBLIC FINANCE
of education can be measured as separate goods and the theory applied
to each. This, however, would only be realistic for a large item like
buildings. However, to Bowen this does not rule out the use of the theory
for education as a whole. Quantity can be measured by total expendi-
tures on education if it is assumed that the voters have knowledge of
an existing list of priorities.23 In other words, if the voters know, or
beforehand establish, the order in which expenditures will be made on
the component parts of education, the quantity of education can be
measured in terms of the total expenditure to be made on education.
These considerations of education made by Bowen point out the prob-
lem of not carrying out the concept of the price theory of public finance
to its logical conclusions. Buildings, teachers, equipment, etc., are re-
sources used to produce a product-education. The allocation of these
resources should be based upon the least-cost distribution of resources
and not the demand of individuals. Education must be measured in
terms of levels of knowledge attained. In other words, the quantity of
education which individuals compare with their cost in attempting to
maximize their satisfaction is a quantity in terms of the level of
education (eighth grade, high school, college degree, etc.) which indi-
viduals want the government to supply. It is clear that levels of educa-
tion and levels of knowledge are not the same thing, even if the function
of education is to provide knowledge, but it is reasonable to assume that
individuals in our society do measure education in terms of levels of
education.
Another important concept discussed by Bowen is the alternatives to
voting. Recognizing that the individual voting process is not practical
for any unit of government larger than that which can operate on a
town-meeting basis, Bowen suggests the use by public officials of polls
of random samples of society. "If a poll is based on a representative
sample of the population and if the questions are put in the same way
as if the entire citizenry were voting, the results could be interpreted
in exactly the same way [as the vote of all the people].'"24 Bowen is
quick to add that it would be necessary that those polled be well in-
formed on the issue and be responsible citizens with a knowledge that
their choices will influence policy. These two conditions might be dif-
ficult to meet and still have a representative sample of the entire voting

23. The concept and importance of establishing a list of priorities in expendi-
tures was developed by Emil Sax; see Musgrave and Peacock, pp. 177-89, for
translation of a part of Sax, Die Wertungstheorie der Steuer (1929).
24. Bowen, p. 43.

18

GRAPHICAL MODELS

public, but it is a start in the direction of finding a means by which
the political process (that in all modern societies must make the ulti-
mate decision as to what and how much of social goods are to be pro-
duced by the government) can ascertain the individual demand for
social goods.25

MILTON Z. KAFOGLIS
In 1962 Milton Z. Kafoglis26 added to the stock of theoretical mod-
els which were related back to the original Lindahl model.27 Kafoglis'
formulation makes use of a derivation of net demand curves for each
individual based on the individual's recognition that the consumption
of the social goods by other individuals gives him a "windfall" of sat-
isfaction.
Kafoglis relates his net demand curve model to the concept of "cost
of service pricing" and the Bowen vertical summation of demand curve
model28 to the concept of "value of service pricing."29 To Kafoglis the
"cost of service" concept involves a horizontal summation of adjusted
(net) demand curves to arrive at the collective demand. The per-unit
tax-price paid is the same to all individuals, as in the case of private
goods without price discrimination. The taxpayer-consumer adjusts his
consumption according to his adjusted (net) demand curve. The "value
of service" concept, using a vertical summation of demand curves, re-
sults in different per-unit tax-prices being paid by different individuals,
but with all individuals consuming the same units of production. The
total cost to each individual and total production is shown by Kafoglis

25. The function of pressure groups in the modern democratic state may be
somewhat similar to the process of polling a segment of the economy, if certain
assumptions are made about the nature of the pressure groups and the extent of
influence which the pressure groups have in the political process. More will be
said about pressure groups in Chapter 4.
26. Welfare Economics and Subsidy Programs. Other models of recent years
are in Buchanan, "Pure Theory of Government Finance," p. 496; Samuelson,
"Diagrammatic Exposition of a Theory of Public Expenditures," p. 350; Tiebout,
"Pure Theory of Local Expenditures," p. 416. The Samuelson model was used as
a criticism of the voluntary exchange approach to public finance, and is reviewed
in Chapter 3 (herein) to the extent that Musgrave used it as a means of pre-
senting a comprehensive review and criticism of the theory.
27. Related to the Lindahl model if the latter is interpreted as a model of
individual equilibrium rather than one of political equilibrium.
28. Kafoglis puts the Bowen model in terms of ordinary demand curves rather
than marginal substitution curves.
29. E. Seligman, Studies in Public Finance, pp. 182-90, set forth the distinc-
tion between "cost of service pricing" and "value of service pricing," relating
the former to the protection, and the latter to the benefit, theory of taxation.

19

THE PRICE THEORY OF VALUE IN PUBLIC FINANCE

to be the same in either case.30 Therefore, it follows that the net de-
mand curve analysis can be applied where the social good involves
joint satisfaction but individual consumption, while the vertical sum-
mation of demand curve analysis must be applied where the social good
has joint consumption (joint supply).
The derivation of the net demand curve makes use of indifference
curve analysis and income consumption lines which are a familiar part
of accepted price theory analysis. Figure 7 presents the indifference

All Other Goods
KK All Other Goods

KK, Individual A Individual B

II
e rf
Z S Rt _r
d R11occ

0 0QfQ 0, Qtq 0 qf q2 q q qtQ02
Social Good Social Good
Figure 7.
maps of two individuals, A and B. The process of adjustment can be
made by starting with either individual seeking equilibrium without
the knowledge that the consumption of the other individual will affect
the satisfaction derived from any given quantity of the social good con-
sumed by the first individual, or by starting with both in an equilibrium
position before the recognition of "windfall" satisfaction.
Assuming Eo is the original equilibrium combination for A with
income level LL, and e o for B with income level 11, the first step of
adjustment takes place when A realizes that he has derived satisfaction
from the quantity q purchased by B as well as the satisfaction derived
from his own purchase of Q quantity of the social good. This additional
30. Kafoglis' proof of this point is based on the constant marginal cost model
of Bowen and a simplified version of the net demand curve derived in detail
later on.

20

GRAPHICAL MODELS
satisfaction experienced by A results in a lowering of A's marginal
rate of substitution for the social good. Graphically this can be pre-
sented by indicating the level of satisfaction received by A (S = Q
+- q). At this marginal rate of substitution A would want R combina-
tion of goods if he had Ii income. Since he does not have this level of
income, A will adjust his purchases to combination T and take Q2
quantity of the social good instead of quantity Q. Individual B then
recognizes that he received satisfaction from A's purchase of quantity
Q2 of the social good. Therefore, B's marginal rate of substitution for

All Other Goods $
Individual A Collective Demand: Net
Indifference Map
G p .--.- ----- H_
IC

0 Phio / ,f Qhf iE
if i

Social Good Social Good
Figure 8.
the social good is reduced as shown by position s. Given B's income level
11, he will reduce his purchases of the social good to q2 from q. This
change, however, affects the satisfaction of A since A's purchases were
based on B's consumption of quantity q of the social good. A's marginal
rate of substitution for social goods has been increased by B's action.
Therefore, A must increase his consumption of the social good to U in
order to reach an equilibrium consistent with B's purchase of q2 quan-
tity ofthe social good is. This action, however, as shown by posilters the satisfaction ob-
tained by B. B must, therefore, make another adjustment.
The result of the adjustment process is the establishment of an equi-
librium at E, for A and ef for B. The level of satisfaction for B is re
which is the satisfaction from Q andtity q consistent with B's original
income consumption curve.
The starting income level can be changed and the process repeated.

21

THE PRICE THEORY OF VALUE IN PUBLIC FINANCE
Figure 7 for individual A indicates points H and G which are equilib-
rium combinations starting with a lower and a higher income than I.
These equilibrium positions are carried over to Figure 8 where a "Net
Income Consumption" curve is indicated. The net curve reflects a
change in the indifference map resulting from the recognition of joint
satisfaction on the part of individual A. Based on the net income con-
sumption curve, a demand schedule can be established which also takes
into consideration the joint satisfaction derived from the social good.
Again assuming I level of income for A, the price of the social good
can be varied (Pa, P1, and P2). The quantities Qh, Qf, and Qj are
determined. These price and quantity relationships are a part of A's net
demand schedule (DNA ); ef is an equilibrium combination for indi-
vidual B. The balance of B's net demand curve (DNB) can be derived
in the same manner as A's. The two curves can then be horizontally
summed to determine the "Net Collective Demand" (CDN). Assuming
a constant cost social good, with AC and MC equal to Pi, the total
output would be Q and both A and B would pay Pi. A would take Qf
and B would take qf.
Kafoglis' formulation is of particular importance because it points
out the distinction and importance of the two types of external econ-
omies of consumption; joint satisfaction and joint consumption (joint
supply). The Lindahl and Bowen models involve goods which have
the characteristic of joint consumption (joint supply). The Kafoglis
model involves a good which has the characteristic of joint satisfaction.
The methodology used in analysis must be consistent with the partic-
ular characteristic of the public good which gives rise to the situation
where external economies of consumption do exist. This also implies
that when a particular methodology is used, the good in the analysis
could be discussed in terms of the characteristic with which the meth-
odology is consistent.

22

3. REVEALED PREFERENCES

T here are two basic criticisms of the voluntary exchange theory of
public finance involving revealed preferences. The first states that
the individual will not reveal his true preferences for public goods. The
second is that even if the individual did reveal his true preferences for
a public good, there is no single solution to the problem of allocating
resources analogous to that found in the allocation of resources to pri-
vate goods. Both criticisms have been raised by Richard A. Musgrave
and have apparently been accepted by many economists. In fact, al-
though Musgrave was one of the first to bring the voluntary exchange
or price theory of public finance to the attention of American econo-
mists, he was also one of its strongest critics and has led the way to
the rejection of the theory.1
The first criticism was raised by Musgrave in relation to Lindahl's
model. As it relates specifically to the Lindahl model, the criticism was
treated in Chapter 2. However, it may be taken as a more general crit-
icism about the applicability of the price theory of public finance to the
problem of allocating resources to any good which has the character-
istic of joint consumption. Therefore, the first section of this chapter
analyzes the criticism as it applies to the allocation of resources, with-
out reference to any particular formulation of the price theory of pub-
lic finance.
The second criticism is raised by Musgrave in relation to the appli-
cability of the theory in a general equilibrium framework. Therefore,
the general equilibrium model which was adopted by Musgrave to
state the criticism is presented in the second section. The model is also
applied to two private goods in order to determine whether it is the
allocation of resources to a public good with joint consumption which
is not analogous to the allocation of resources to private goods, or
whether it is the model used in the Musgrave analysis which is not
analogous to the theory of the allocation of resources to private goods.
CRITIQUE OF THE FIRST CRITICISM
The question of whether or not preferences will be revealed by indi-
viduals for a public good through the political process is both a practi-
cal and a theoretical consideration. The theoretical issue is whether or
1. See Theory of Public Finance; and "Voluntary Exchange Theory."
23

THE PRICE THEORY OF VALUE IN PUBLIC FINANCE
not there is something inherent in the nature of public goods or in
the supply of and demand for public goods which makes it neces-
sary or likely that the individual acting rationally would not re-
veal his preferences for the public goods. One situation that might
lead to such a conclusion is one in which an individual can derive sat-
isfaction from the supply of a public good without having to express a

Price, Cost
D

P MC
b

0 q, q q2 Public Good,X

Figure 9.
desire for the good and without having to pay for the good according
to his actual individual satisfaction. Musgrave's attempt to illustrate
such a situation is based on two propositions: (1) an equal quantity
of public goods and services is consumed by all taxpayer-buyers; (2)
an individual taxpayer's demand exerts no influence over the quantity
of public goods supplied.2
The first proposition involves a problem of defining a public good
in terms of its characteristics. The public good is said to be a good
which has the characteristic that each individual receives benefits from
the entire supply as if he were the only individual consuming it (i.e.,
joint consumption). The equal-consumption definition of a public good
2. Theory of Public Finance.

24

REVEALED PREFERENCES
is accepted as a polar case which is possible even if it may not exist
for many goods.3 The issue here is whether or not a good which does
fit this definition is likely to be the cause of individuals not revealing
their preferences for the good.
Figure 9 presents one possible formulation of the process through
which preferences might be revealed even when the equal-consumption
definition is accepted and when each individual pays according to his
revealed preferences.4 There are two taxpayers A and B. If taxpayers
A and B reveal their true preferences, a vertical summation of their
individual demands (aa and bb) would be designated by DD. The
optimum amount of public good X, then, is Oq, and the optimum
distribution of the costs of producing good X is OPa" Oq for taxpayer
A and OPb* Oq for taxpayer B. Assume that taxpayer A reveals his
true preferences and that taxpayer B does not reveal his preferences.
The collective demand is only A's demand (aa) and only Oq, of good
X will be made available for equal consumption. Taxpayer A is in
equilibrium but taxpayer B is not. If B's tax share is zero, as it would
be if B does not reveal any preference for X, B really desires Oq2 of
X at the existing zero price instead of the quantity Oqi which will be
made available. Therefore, taxpayer B may have an inclination to re-
veal at least some of his preferences. If B reveals part of his prefer-
ences, his tax share of the Oqi of X rises above zero and A's tax share
declines. At the lower price to A (OP B's price), A demands a
greater quantity of X. The process, followed to its logical conclusions,
results in a situation where both A and B do reveal their true
preferences.
Musgrave's second proposition involves the question of the effect that
having a large number of individuals participate in the determina-
tion of what quantity should be produced will have upon a single in-
dividual's revealing his preferences. In Chapter 2, Musgrave's analysis
was rejected. The rejection of the duopoly type of analysis was not
based on the use of small numbers in the analysis, but on the assump-
tion that the individual bargained with other individuals as if he were
a producer attempting to maximize his profits. The individual who has
preferences for goods is a consumer, not a producer. Therefore, the

3. A great deal of discussion was created, as to whether or not the equal-
consumption definition had any application in the real world, after Samuelson
used it in his model as a polar case ("Diagrammatic Exposition").
4. Sharp and Escarraz, "Reconsideration of the Price or Exchange Theory of
Public Finance."

25

THE PRICE THEORY OF VALUE IN PUBLIC FINANCE
analysis must be based upon the individual's attempting to maximize
his satisfaction. Thus, it is necessary to assume that the individual does
have preferences in regard to public goods, or that he does receive
satisfaction from public goods in relation to the quantities he con-
sumes. The latter will be assumed in the analysis which follows, so
that simple mathematical expression of the assumption of maximiza-
tion of satisfaction in terms of marginal utilities may be used.5
If the individual derives satisfaction from each public good as he
does from each private good, the maximization of satisfaction would
be expressed exactly the same for both private and public goods
MUa MUb MUy MUz
(-Ta Tb = Py Pz ). The goods represented by a and b can be

taken as public goods, such as national defense and education, and the
goods represented by y and z can be taken as private goods, such as
automobiles and fountain pens.
Given this type of maximization of satisfaction criterion, it would
be impossible for the individual to maximize his satisfaction if one of
the goods has equal consumption and if at the same time everybody
must pay the same price. The tax-price and the quantity supplied can-
not both be the same for all individuals unless it is assumed that each
individual has the same utility function for the good. Therefore, the
individual under these conditions would have no reason to reveal his
preferences for the public good.
However, if the tax-price is permitted to vary between individuals
and if it is determined by the tastes and preferences of the individual
(i.e., in accordance with the benefit theory of taxation), he can maxi-
mize his satisfaction. The fact that one of the goods has equal consump-
tion does not interfere with the individual's ability to maximize his sat-
isfaction. In fact, the quantity of the public good which is supplied
does not have to be based upon the tastes and preferences of individuals
just so long as the individual's tax-price is determined by the individ-
ual's preference for the given quantity.6 Therefore, the individual un-

5. The acceptance of indifference-curve analysis and relative diminishing mar-
ginal utility between two goods instead of marginal-utility analysis and absolute
diminishing marginal utility for all goods does not affect the conclusions about
revealed preferences which follow.
6. The fact that the quantity of the public good is not based upon the tastes
and preferences of individuals does affect the allocation of resources, but it does
not affect the individual's ability to maximize his satisfaction or his motivation
to reveal his preferences. More is said about the effect of this type of situation
on the allocation of resources in Chapter 5.

26

REVEALED PREFERENCES

der these conditions would have a motivation to reveal his preferences
for the public good.
The fact that a large number of individuals might be involved is sig-
nificant under the foregoing analysis only as a practical consideration.
The individual maximizing his satisfaction is not affected by the number
of other individuals attempting to maximize theirs except as the num-
ber of individuals affects the government's ability to base the tax-
price on the individual's tastes and preferences.7
Another practical consideration, however, should be made at this
point. The analysis assumed that the individual knows his tax-price
will be based upon his tastes and preferences for each public good. If
it is assumed that the individual accepts the total of government activ-
ity as one public good, it would not be necessary to assume that the
tax-price is based upon the individual's tastes and preferences for each
good supplied by the government.8 The maximization of satisfaction
criterion becomes = MU MU In this case g represents
criterionbecomes .. p=g Py--P
all government activity and Tg represents the individual's average tax
bill per unit of government goods and services. The allocation of re-
sources to particular public goods, such as national defense, highways,
education, etc., would have to be based upon the least-cost combination
of these goods in providing various quantities of the good total
government activity.
Given this type of maximization criterion, it would be possible for
the individual to maximize his satisfaction. This follows even if the
good, total government activity, is assumed to have the characteristic
of equal consumption and if the tax-price is not based upon the indi-
vidual's tastes and preferences. In this case, the individual's m is
determined independent of his tastes and preferences. The individual
maximizes his satisfaction by adjusting his private consumption.9 Pref-

7. The effect of various types of organizations upon the applicability of the
voluntary exchange or price theory of public finance is treated in Chapter 4.
8. DeViti DeMarco states a belief that as the practice of special assessment
decreases, "the taxpayer, in making up his own budget no longer compares every
special assessment with the consumption of the corresponding service but com-
pares the whole of his taxes with the whole of the services he consumes" (First
Principles of Public Finance, p. 110).
9. In accepted price theory of private goods the adjustment takes place solely
as a result of the decreased income available for private consumption. In the
above formulation of the price theory of public goods, income available for pri-
vate consumption is reduced by the same process, but the individual's private
consumption is restricted still further by the necessity of making his marginal

27

THE PRICE THEORY OF VALUE IN PUBLIC FINANCE

erences for public goods are revealed but the revealing process must
be done through the adjustment of private consumption.10
However, if the government does attempt to base the tax-price upon
individual tastes and preferences (the benefit principle of taxation),
the individual will be able to maximize his satisfaction by adjusting
his tax-price as an alternative to adjusting his private consumption.
Therefore the individual may have a motivation to reveal his preferences
for total government activity through the political process.
In either case, preferences are revealed. In the one case, the assump-
tion about the nature of the political process makes it necessary for
the individual to reveal his preferences through his behavior in the
market process. If the political process is capable of basing taxes upon
individual tastes and preferences, the individual has a motivation to
reveal his preferences for the public good in the political process.

CRITIQUE OF THE SECOND CRITICISM
Assuming true preferences are revealed, Musgrave contends that
there is still another flaw in the voluntary exchange theory model. "Even
if all preferences are revealed, there is no single best solution analogous
to the Pareto optimum in the satisfaction of purely private wants. In-
stead we are confronted with large number of solutions, all of which
are optimal in the Pareto sense.""11
The equilibrium model used by Musgrave to derive these conclusions
is based upon a model developed by Samuelson.12 Figure 10 is a re-
production of the Musgrave version of this model. The bottom diagram
is the familiar transformation curve, and the other two are indifference
maps of individuals A and B. OC and OD are said to represent the
distribution of income between A and B, since OC and OD are the
quantities of private goods they could hold if they held only private
goods with their income. Individual A is arbitrarily moved along his
indifference curve il, which contains combination OC of private goods.
Given the transformation curve's production limits, this process limits
individual B to a specific combination of social and private goods for

utility per dollar's worth of spending for each private good equal to the arbi-
trarily determined marginal utility per dollar's worth of spending for public goods.
10. Tiebout presents still another means of revealing preferences when he con-
cludes from his analysis that preferences for local government services are
expressed by individuals through their choice of suburban community around the
large cities in our modern society ("Pure Theory of Local Expenditures").
11. Theory of Public Finance, p. 84.
12. Ibid., p. 81n.

28

REVEALED PREFERENCES

each point on individual A's indifference curve. Curve MD, therefore,
represents the various combinations of public and private goods avail-
able to individual B as individual A is arbitrarily moved along his in-
difference curve ii. Point W is the point of tangency with the highest
possible indifference curve and determines the quantities OG of public

Public Good
Individual A

Public Good
Individual B

SC D L U E Private Good

Figure 10.
goods and OK of private goods which individual B would desire with-
out individual A being worse off than if he held all of his income as
private goods. The same process is then followed for individual A by
moving individual B along his indifference curve il. Curve NC is then
developed and quantities OJ of public goods and OQ of private goods
are found to be the combination individual A would desire without mak-

29

THE PRICE THEORY OF VALUE IN PUBLIC FINANCE

ing individual B worse off than if he held all his income in private
goods.13
The optima developed in the foregoing analysis are presented on a
utility frontier (Figure 11). Point X represents the ordinal measure-
ment of satisfaction for individuals A and B when individual A has the

Ordinal Index of Welfare, A

i2P ----- -

I 2

ZI

iT i2W
Ordinal Index of Welfare,B

Figure 11.
13. Musgrave assumes that the distribution of income is given and does not
change but this is incompatible with the methodology used. If we consider it a
general equilibrium view with only two goods and two individuals, the dis-
tribution of the physical units represents the income distribution. Figure B
shows that the one solution resulted in individual A holding OQ of the private
good and individual B holding OR of the private good and the two holding OJ
of the public good. The other solution gave individual A, OS of the private good
and individual B, OK of the private good and both individuals had OG of the
public good. It, therefore, does not appear to be correct to say that the distribu-
tion of income remains OC/OE for individual A and OD/OE for individual B.
30

REVEALED PREFERENCES
combination P and individual B has the combination T of public and
private goods. Point Y represents the ordinal measurement of satisfac-
tion when individual A has the combination V and individual B has the
combination W of public and private goods. The other points on the
utility frontier could be developed by varying the original distribution
of income so that either or both individuals are on a different indif-
ference curve at the start of the analysis. The conclusion drawn from
the analysis is that "the area ZYX [in Figure 11] shows the infinite
number of possible solutions that leave A, B or both, better off than at
Z, where no public services are supplied."14
The above review of the methodology used by Musgrave raises the
question of whether the arbitrary movement of one individual along
an indifference curve, to determine what combination of goods a second
individual would like to hold, is compatible with price theory analysis.
The "Edgeworth box analysis" of exchange makes use of this method
to establish a contract curve which contains an infinite number of op-
tima. In other words, it establishes those changes in social variables
which can take place through "trading."15
Trading, however, is not the object of the voluntary payments model.
The voluntary exchange approach must be based upon a money econ-
omy and not a barter economy. The Musgrave analysis tells us nothing
more than what the "Edgeworth box analysis" tells. In other words, it
is the barter nature of the analysis (i.e., the arbitrary holding of one
individual on a given indifference curve while permitting the other
to choose the combination of goods which maximizes his satisfaction)
which causes the existence of an infinite number of Pareto optima
points.
Figure 12 presents the Musgrave analysis using the private good defi-
nition for both goods. The change in definition does cause a basic
change in the procedure. This change is that the placing of individual
A at a point on his indifference curve leaves a line of attainable com-
binations (based upon the price ratios set by the transformation curve)
available to individual B instead of a specific combination of the two
goods. Assuming the individuals maximize their satisfaction, we can still
determine the one combination which individual B will hold when
individual A is at each point on his given indifference curve. Therefore,
we can still determine a curve MD1, which is analogous to the MD
14. Musgrave, Theory of Public Finance, pp. 83-84.
15. Kenneth E. Boulding, "Welfare Economics," in American Economic Asso-
ciation Committee, Survey of Contemporary Economics, pp. 18-19.
31

THE PRICE THEORY OF VALUE IN PUBLIC FINANCE
curve found with one good defined as a public good. Using arbitrary
movements along individual B's indifference curve, we can determine
individual A's NC1 curve which is analogous to the NC curve found with
the public good definition. The combination of private goods 1 and 2
which individual A could hold without making individual B worse off

Private Good 2

Individual A

Private Good 2

Individual B

0U D ULC E Private Good I

Figure 12.
is OQ and OJ, respectively. Individual B could hold OG of private good
2 and OK of private good 1 without making individual A worse off.
The optima developed in the analysis with two private goods can be
presented on a utility frontier (Figure 13). Points X and Y have the
same meaning as points X and Y in Figure 11, except that now we are
considering the quantity of two private goods to be supplied. The area
ZYX shows the infinite number of possible solutions that leave A, B, or

32

REVEALED PREFERENCES
both better off than at Z, where no quantity of private good 2 would
be supplied.
It has been shown that the model used by Musgrave results in an
infinite number of optima when a public good and a private good are
used or when two private goods are used. Any conclusion derived from

Ordinal Index of Welfare, A

iP__P....____ x

Ipx

SIL

i iT i W
Ordinal Index of Welfare,B

Figure 13.
Musgrave's model is applicable to price theory in general. Musgrave is
correct when he concludes from his public goods model that a single
optimum cannot be reached. However, it appears that the absence of
a single optimum solution is not due to the inclusion of a public good
in the model. The rejection of the criticism is based on the fact that
the model used by Musgrave to prove the validity of the criticism is not
consistent with the price theory of private goods, and therefore could
not be expected to yield a single optimum when applied to public goods.
33

THE PRICE THEORY OF VALUE IN PUBLIC FINANCE
Samuelson did originate the model and did criticize the voluntary
exchange approach to public finance in the same article.16 The criti-
cisms, however, were in terms of whether or not preferences would be
revealed and the model was in terms of a solution to the problem. Al-
though Musgrave and other economists appeared to believe that the
cause of the large number of solutions in the model was the existence
of a public good with the characteristic of joint consumption, Samuel-
son never made such a statement. In fact, Samuelson in developing his
model refers to his original work on an exchange model in Foundations.
In this original exchange model the goods are not assumed to have the
characteristic of joint consumption, and yet his conclusion is that "Be-
cause the original specification of the second man's utility was arbitrary,
the final equilibrium is also arbitrary and not unique." 17The statement
was made with respect to the "Edgeworth box analysis," but in fact the
Samuelson model is nothing more than a presentation of Edgeworthian
analysis where the quantity of goods is not fixed but is limited to the
various quantities that could be produced under the conditions of effi-
ciency. The existence of the public good in the model modifies the an-
alysis but does not affect the nature of the conclusions. The arbitrary
statement of the second man's utility is the cause of the large number
of solutions in the model, and not the nature of the goods used in the
model.
Samuelson solved the problem of a large number of solutions by using
a welfare function for society. The traditional solution to an Edgeworth-
ian analysis, however, is usually stated in terms of the relative bargain-
ing powers of the individuals involved in the exchange. Price theory
follows this traditional frame of reference in that income derived from
the productivity of resources used in production determines the bargain-
ing power of the individuals involved in the exchange. In the next
chapter an attempt is made to convert the Musgrave-Samuelson model
from a pure exchange model which requires a welfare function or an
arbitrary statement of bargaining power of individuals to a model which
rests on the principles of price theory.
16. "Pure Theory of Public Expenditure."
17. Foundations of Economic Analysis, p. 238.

34

4. A SUGGESTED APPROACH

Musgrave's criticism that there is no single optimum with respect
to the voluntary exchange theory of public finance was rejected
because the methodology used was not consistent with price theory
analysis. It does not provide a single optimum when only private goods
are used in the model. However, the Samuelson general equilibrium
framework used by Musgrave has some merit. The problem is to modify
the Musgrave-Samuelson model so that it is consistent with price theory
general equilibrium anaylsis. The modified model then can be used
with the restriction of a public good that has the characteristic of joint
consumption in order to further evaluate the criticism of the voluntary
exchange theory of public finance. The modified model may also be
considered as a new approach to the presentation of the theory, which
makes explicit some of its seldom stated conditions.

THE TRANSFORMATION CURVE
The Musgrave-Samuelson model starts with a given transformation
curve. This curve is based upon the production possibilities of firms
producing the two classes of goods in the limited society of the model.
By assuming that one firm, or that one group of firms with identical
production functions, produces each of the two goods, derivation of the
transformation curve can be shown graphically.' It is assumed that all
of the existing (given)2 resources will be used in the production process,
and the determination of which firms will use the resources is to be de-
termined on the basis of efficiency. It is also assumed, as in the case of
Walrasian general equilibrium analysis, that the original distribution
of ownership of resources is known (given).3
The combinations of X and Y (private good products) indicated by
the transformation curve in Figure 15 are derived from the points of
tangency of isoquants in Figure 14. These points of tangency indicate
1. Bator, "Simple Analytics of Welfare Maximization," pp. 3-24.
2. If the quantity of resources is not given, the transformation curve cannot
be determined.
3. If the original ownership of resources is not given, there is no single best
solution because the distribution of income in a market society depends upon the
ownership of resources at the beginning of the productive process. This does not
mean that the distribution of income is given. It is determinable with a market
society and a given original distribution of ownership of resources.

35

THE PRICE THEORY OF VALUE IN PUBLIC FINANCE

the combinations of A and B (resources) that would be used by the
firms producing products X and Y under the efficiency condition that
MPP? MPPX
In a market society even more can be said from the simple deriva-
tion of the transformation curve. Under the conditions of pure compe-
tition in resource markets and in product markets, the ratio of the
marginal productivities of the resources will also be equal to the ratio of

QB
Q TE
QA PA \ PA

3Qy

Qy
643

Slope= 6 QMP

x Mpp
MPPM P

PA

Figure 14.

the prices paid to the resources; "P =p.- Since the quantity of
A and B is given (Figure 14) and the ownership of A and B is assumed
to be known, the ratio of prices paid to the resources determines the
distribution of income. The level of money income is still indetermi-
nate, but the distribution of any money income level among the owners
of the resources is determined.
The transformation curve, under the conditions of pure competition
in the product markets, determines another important condition for equi-
librium in the market-price theory model. The slope of the transforma-
tion curve is the ratio of the marginal costs of producing the two goods
4. Bator (pp. 31-32) recognizes this point but does not assume that the orig-
inal distribution of the ownership of resources is known and thus does not carry
the analysis further.

36

A SUGGESTED APPROACH

(MC ). Since, under pure competition market conditions, the price
of the product is equal to the marginal cost of producing the product,
the transformation curve also determines the ratio of the prices of the
products ( t ) .5 This fixes the relationship of the value of X to Y but
not the level of the money value of production. The combination of X
and Y indicated by point 1 in Figure 15 cannot be an equilibrium
solution under the conditions of pure competition. Given the production

For Point I
Px) Py
Y x y
Qx> )0y
Slope= MC YPy MC 5 Slope= Px but YPY TEy
6g Y Xs.f TEx
from Figure 14
5 4
3

I

0 x

Figure 15.

of X and Y and the relationship of price between X and Y, the rela-
tionship of the expenditures by firms X and Y is determined. This de-
termined relationship of expenditures for point 1 is, however, incon-
sistent with the relationship of expenditures indicated in Figure 14.
The inconsistency can be seen more clearly if the analysis is carried
further to consider the demand side of the picture.6

DEMAND ANALYSIS
The distribution of income but not the level of money income was
determined in Figure 14 for each combination of X and Y that might

5. Bator, pp. 32-33.
6. Bator works backwards from this point to show how exchange would take
place with the determined relationship of value between X and Y. His solution,
however, would require that revenue from one firm be redistributed to the other
firm or that one firm operate at a loss.

37

THE PRICE THEORY OF VALUE IN PUBLIC FINANCE
be produced under the conditions of efficient production (i.e., for each
point on the transformation curve). Under the simple assumption that
all of resource A is owned by individual A and that all of resource B
is owned by individual B, and the determined price ratio of the prod-
ucts from Figure 15, the lines of attainable combinations can be shown
for the two individuals. There are a large number of such lines of at-
tainable combinations for each efficiency output, depending upon the
absolute prices paid for resources A and B, as is shown in Figure 16 for

Figure 16.

point 1 and the transformation curve. Given the tastes and preferences
for X and Y by individuals A and B, the points of tangency between
the various lines of attainable combinations and the indifference curves
determine the individuals' demand for products X and Y at the different
money income levels. Demands aA and aB can be summed to obtain the
total demand. The summing of the various demands for X and Y at
different money incomes can be shown as a summation of individual
income consumption lines and can be superimposed on the transfor-
mation curve diagram (Figure 17). The fact that the line of the sum
of the income consumption lines does not intersect the transformation

38

A SUGGESTED APPROACH

curve at the point 1 combination of X and Y indicates that there is
no level of money income with the distribution of income determined
by producing point 1 combination of X and Y under conditions
of pure competition which will equate the demand and supply for
products X and Y. Therefore, the combination of X and Y indicated
by point 1 under the conditions of pure competition can only be an
equilibrium solution if one of the firms is subsidized and the distri-
bution of income is different from that which is provided by the market.
With the traditional assumptions of price theory analysis there will

y L. of A.C.

1ICL, ICL! associated with income distribution
X L.ofA. cA c and product price ratio for output Y,,X.-
Lof A. Z ICs associated with income distri-
Y4 bution and product price ratio
GIGA,ao A 4S for output Y4, x4.
I L. of A.C.

0 4 X

Figure 17.

be only one combination of X and Y which can be produced efficiently
and which will be demanded when the distribution of income is deter-
mined by the productivity of the resources used to produce X and Y.
(Again it should be noted that pure competition is assumed in both the
product and the resource markets and the original ownership of the
resources is known.) Figure 17 also shows this unique solution as well
as the inconsistency between demand and supply which exists for one
of the other combinations of X and Y.
Another approach to the problem can be presented in terms of the
demand for product X and for product Y. In the above analysis the
price ratio was given by the slope of the transformation curve. This
price ratio is the only one which is consistent with the assumptions

39

THE PRICE THEORY OF VALUE IN PUBLIC FINANCE
made about the markets involved. However, the price ratio is just the
price of each good at equilibrium and a demand curve for both goods
still exists. Thus instead of using income consumption lines the anal-
ysis could be based upon price consumption lines. Figure 18 shows

Figure 18.
the usual development of price consumption lines for the two indi-
viduals A and B. These individual price consumption lines are summed
(i.e., the combination of X and Y desired by A with the same given
price of X and Y is added to the combination of X and Y desired by
B with the same given price of X and Y). The point where the summed
price consumption line intersects the transformation curve gives a

40

A SUGGESTED APPROACH

possible equilibrium. Whether or not it is an equilibrium solution
under conditions of pure competition can be checked by summing the
indifference curves of the two individuals. If the summed indifference
curve is tangent to the transformation curve at the point where the
summed price consumption line intersects the transformation curve, it
is an equilibrium solution. The distribution of income must be given
in order to use price demand analysis, but this is no problem since the
income distribution was determined. In fact, as developed earlier, the
equilibrium solution is known before the analysis is started. The
price demand analysis merely adds one more consideration. It is an

Y

2 PCL's
A

B IPCL A,PCL

C 2 PCL'S
2 i's

0-

Figure 19.

important consideration later when the model is used with one private
and one public good.
The single "best" solution derived in Figure 18 does assume that
pure competition exists in both resource and in both product markets.
If pure competition does not exist in the markets of both products, the
Pareto optimum will not be achieved because there is no market force to
cause the ratio of prices to be equal to the ratio of marginal costs (i.e.,
the slope of the line of attainable combinations would not have to equal
the slope of the transformation curve at equilibrium). Figure 19
shows the three possible situations. Point A indicates a situation where
the price of X is greater than the marginal cost of producing X. Point

41

THE PRICE THEORY OF VALUE IN PUBLIC FINANCE
C indicates a situation where the price of Y is greater than the mar-
ginal cost of producing Y.7 Point B indicates the Pareto optimum
presented in Figure 18. It is apparent that there are an infinite number
of solutions, depending upon the specific market situations which might
exist.8 However, it is only when pure competition exists that the line
of the sum of the individual price consumption lines intersects the
transformation curve at a point where the curve of the sum of the
individual indifference curves is tangent to the transformation curve.
When any other type of market situation exists in the product market
of either good, the price of the good is greater than the marginal cost.
Therefore, the ratio of prices (i.e., the slope of the attainable com-
binations and the slope of the individual indifference curves when the
individual maximizes satisfaction) cannot equal the ratio of marginal
costs. It should also be noted that the income distribution has not been
altered even though the slope of the line of attainable combination is
different from the slope of the transformation curve. In other words,
if the ratio of prices does not have to equal the ratio of marginal costs,
the income distribution does not determine a unique equilibrium. It
would also be difficult to show graphically that the "correct" distribution
of income has been maintained. The relative value of the two goods is
different if pure competition does not exist. The supply of the good
sold under conditions other than pure competition is restricted, and
its price is higher than it would have been if pure competition had
existed. Also excess profits will exist and would have to be distributed
in some manner. Therefore, the absence of pure competition may create
an income feedback problem and there may be no equilibrium solu-
tion. An equilibrium solution may exist but it need not exist because
of the distribution of the excess profits in the system.
DEMAND ANALYSIS WITH A PUBLIC GOOD
The changes necessary in the model to consider a public good with
the characteristic of joint consumption are minor. The existence of an
equilibrium is not changed, even though the equilibrium level is
changed.9 The distribution is still determined by the original owner-
7. In both situations it is assumed that the price of the other good in the situ-
ation is equal to the marginal costs of producing the good.
8. The infinite number of solutions here are not the same as those which
exist in the Musgrave-Samuelson model. There, a specific solution depends upon
the bargaining power of the individuals because it involves a barter exchange
of goods. In this modified model a specific solution depends upon the market
situations which are assumed to exist in the market economy.
9. The difference in the two equilibriums is the topic of the next section.
42

A SUGGESTED APPROACH

ship of the resources and the prices paid to the owners of resources
based upon their use in the production of the two goods. The govern-
ment can be assumed to purchase the resources they use under the
conditions of pure competition in the resource market. The other assump-

Y Y

Individual A Individual B
3

PCLA
5 PCL8

D

\A B C B
0 Public Good Public Good

Y

:PCLA PCL
iA .B

0 Public Good

Figure 20.

tions which are necessary for a demand analysis are that individuals
do in some way express their demand for the public good as well as
the private good and that the government collects the taxes based
upon the expressed demand.
Figure 20 is the diagrammatic presentation of the determination of
the Pareto optimum allocation of resources with one good defined as a

43

THE PRICE THEORY OF VALUE IN PUBLIC FINANCE
public good. The methodology used is basically the same as in Figure
18 when both goods were private goods sold in the market. The pro-
cedure for the development of the individual price consumption lines
is not changed by the fact that one of the goods is a public good. How-
ever, because of the change in the definition of one of the goods, the
procedure for summing the price consumption curves must be changed.
The combination of the two goods desired by individual A, when he
must take a given quantity of the public good, is added to the combina-
tion of the two goods desired by individual B, when he must take the
same given quantity of the public good. This change in procedure is
just the change to a vertical summation of demand curves from the hori-
zontal summation normally used in the private goods model.10 The
quantity of the public good is held constant and the demand for the
two goods is summed, whereas before, the price of X was held con-
stant and the demand for the two goods was summed.
The intersection of the line of the sum of the price consumption
lines with the transformation curve provides the Pareto equilibrium
so long as the curve of the summation of indifference curves is tangent
to the transformation curve.'1 The same basic conditions for general
equilibrium and for the Pareto optimum allocation of resources have
been met with a public good in the model as with just private goods.
The market conditions cannot be assumed to force the allocation of
resources toward the optimum since one good is a public good, but
this does not mean that such a single optimum does not exist. The
government would have to indulge in price discrimination in the sense
that the two individuals would not pay the same price for the public
good. Individual A will pay for the public good in accordance with
the price ratio given by the 3C line of attainable combinations, and in-
dividual B will pay for the public good in accordance with the price
ratio given by the 5D line of attainable combinations. This, of course, is
simply taxation based upon the benefit theory of taxation, where the
individual determines the benefit provided by the public good.
10. The vertical summation of demand curves when a public good has
the characteristic of joint consumption was developed by Bowen, "Interpretation
of Voting in the Allocation of Economic Resources."
11. The method of summing indifference curves is the same as that used by
Samuelson. The difference between the methodology used here and Samuelson's
is that the modified model employs the price consumption lines of individuals to
determine the indifference curves which are to be summed rather than using the
arbitrary placement of a combination of the two goods on one individual and per-
mitting the other individual to maximize his satisfaction. The modified model fol-
lows market analysis, the Samuelson follows barter exchange analysis.

44

A SUGGESTED APPROACH
COMPARISON OF THE EQUILIBRIUMS
Despite the similarity of the analyses and the fact that a single
optimum exists in each analysis, the optimum allocation of Figure 18
is different from the optimum allocation of Figure 20. The difference

Individual A

Individual B

PCiK

Z PCL

0

Figure 21.

is shown in Figure 21. It is caused by the fact that the summation of
income consumption lines must also be modified when a public good
exists in the model. The price demand for the two goods is based upon
the vertical summation of demand curves. Therefore, the income de-
mand for the two goods must also be based upon a vertical summation
of the individual income consumption lines. The difference in produc-

45

II

THE PRICE THEORY OF VALUE IN PUBLIC FINANCE
tion does also cause a difference in income distribution, but there is
still only one distribution of income which is consistent with the as-
sumptions of the model. The difference in production and distribution of
income is the logical result of the one good in the second model having
the characteristic of joint consumption.
If the private good X in Figure 18 was private protection, the logic
of the difference in production may be put in words. For protection
to have the characteristics of a private good, it must be assumed that
the resources used to protect individual A cannot be used to protect
individual B. Thus, individual A hires protection but will not permit
the protection to be used to protect individual B. Individual B does
the same thing with the protection he purchases. The result is that both
individuals (A and B) can purchase their protection at the same price
and each will only purchase the quantity he wants at that price. The
public good in Figure 20 can also be considered as protection. The
difference in the analysis results from the fact that individual A is
willing to permit the use of the same resources for the protection of
individual B. Likewise, individual B is willing to permit the use of
the same resources for the protection of individual A. The result is
that the good protection takes on the characteristics of a public good
with joint consumption.
Less units of protection can be produced in the second case because
the same units are provided to both individuals. If less units are
produced, less resources will be used in the good's production. If less
resources are used, less total expenditures will be made to whoever is
producing the good. Thus more income is available for the purchase
of the private good, and more total expenditures will be made to the
firms that produce the private good. Both individuals may pay less
for the public good protection than they would for the same quantity
of the private good protection. The individual who owns the resource
which is relatively more productive in the production of protection will
lose income relative to the individual who owns the resource which is
relatively more productive in the production of the other good. In
either case the distribution of income is determined by the original
ownership of the resources and by the productivity of the resources
used to produce the goods which are demanded. It is simply that less
units of protection will be demanded if it is publicly supplied because
the same units can be consumed by both individuals.12 The individuals
12. The individual's demand is not affected by the way in which the good
is supplied but the total demand or market demand is affected.

46

A SUGGESTED APPROACH
are motivated to express their demand for the public good because,
even though they may be discriminated against by having to pay a
higher price for the same protection provided to some other individual,
the price they pay may be less than they would have to pay if they
purchased the same good as a private good. However, the problem
still exists that once it is determined that protection is to be supplied
publicly, each individual may benefit by not expressing his true de-
mand for protection. The danger is that if everybody tries to conceal
his demand, the good will not be supplied publicly, and then all in-
dividuals end up paying more for the good than they would have if
they had revealed their true demand for the good as a public good.
This explanation of the difference between protection as a public
good and as a private good also gives a basis to the paradox that,
when asked, people want the government to provide more and more
services but want to pay less and less taxes. Such a position is en-
couraged by the separation of the decision-making process into two
parts. This consideration, however, borders on the topic of the next
chapter: the criticisms of the application of the theory to the political
process.

47

5. TAXES AND THE POLITICAL
PROCESS

There are two broad categories of practical criticism involving
taxes and the political process. They are practical criticisms be-
cause they do not question the logic of the theory itself, but rather
question its application to the real world. The first criticism is that
taxes are compulsory payments and cannot be considered analogous
to prices in the market. The second criticism is that the political
organization of society acts in a unique way and cannot be considered
analogous to the market mechanism. Both of these criticisms are im-
plicit in E. R. A. Seligman's history of taxation.1 He presents the history
of taxation as an evolutionary process, moving from the voluntary con-
tributions to tribal chiefs to compulsory payments (such as direct
taxation by a central government).2
It cannot be denied that the history of taxation does indicate that
there have been elements of coercion in taxation in the real world. This
is as true about the payments to tribal chiefs as about direct taxation
by a central government. To approach the two criticisms logically,
it is necessary to separate them. Taxation only exists when a political
organization exists, but the first criticism implies that taxes are com-
pulsory per se, no matter what form of political organization exists.
Thus, this chapter will take up this criticism by itself and then include
it in the analysis of political organizations. It is also necessary to con-
sider the coerciveness relative to some specifically stated criterion.3
Therefore, the discussion places taxes in a specified political mechanism,
1. Essays in Taxation, pp. 1-6.
2. DeViti DeMarco on the other hand has presented the history of taxation
as an evolution in forms of voluntary payments, moving from voluntary contri-
butions of goods and services to tribal chiefs to voluntary contributions of
money, such as direct taxation by a central government. The existence of con-
stitutional provisions of all representative governments that no tax be determined
or collected unless it is approved by the representatives of the people is cited
as evidence that taxes are still voluntary in nature (First Principles of Public
Finance, p. 120).
3. Patinkin gives a good discussion of voluntary and involuntary employment,
pointing out the necessity of having an established criterion upon which to
evaluate the degree of voluntariness that exists in a particular situation (Money,
Interest and Prices, pp. 211-14).
48

TAXES AND THE POLITICAL PROCESS
and the conclusions are in terms of the degree of coercion relative to
prices determined in a specified market situation.4
The second criticism is difficult to evaluate in the form in which it
is often stated, because to give a complete evaluation, it would require
data from real world situations. However, as it is stated here some
evaluation is possible. The approach is to define political organizations
in the terminology which is common to the analysis of market struc-
tures.5 The conclusions about coercion are in terms of the degree of
coercion in one political situation relative to alternative political situa-
tions and relative to stated market situations. The very fact that the
political organization can be defined in terms similar to those used for
market structures suggests that the criticism is not entirely valid. The
analysis would also suggest that in the real world taxes are likely to
be coercive but that this is because the political organization is not
any more likely to be the ideal than is the market structure.

PRICES AND TAXES
Location of the point at which there is compulsion to act in a
specified way in the case of both prices and taxes is one approach to
considering the degree of coercion which exists for taxes relative to
prices. It is assumed in the discussion that prices are impersonally
determined in a purely competitive market situation, and that taxes
are impersonally determined by a vote of all the individuals in the
society.
The market determines the individual's per-unit price of a good by
the equality of the total demand for the good to the total supply of the
good. The total demand for the good is the sum of the individual
demands. The individual demands are expressed by the individuals'
purchasing the good in the quantity desired at the price at which it
is offered for sale. The market supply schedule of the good is the sum
of the quantities which will be produced by individual firms at various
marginal costs. Each firm must offer the good for sale at the per-unit
price determined by the entire market for the good, because if a firm
offered it at a higher price, the firm would have no sales, and if a
4. Coercion must be discussed in terms of the degree of coercion because
compulsion exists in every form of organization. DeViti DeMarco, p. 50n, states:
"Compulsion exists in every legal association of individuals; in business organiza-
tions, in partnerships, in the church, and especially in labor unions."
5. Haavelmo's discussion of the need for a comparison between alternative
economic models or frameworks under which a society may operate is the basis
for the approach used here ("Notion of Involuntary Economic Decisions").

49

THE PRICE THEORY OF VALUE IN PUBLIC FINANCE
firm offered it at a lower price, the firm would in the long run not be
able to cover the costs of production.
The vote determines the individual's tax per unit of the good by the
equality of the total demand for the good and the marginal cost of the
government's production of the good. The total demand for the good
is the sum of the individual demands. The individual demands are
expressed by the individuals' voting on the quantity that they would
desire at each of the various prices possible. The government is under
a policy rule to deliver the quantity of the good to every individual
in accordance with their expressed demand at the tax-price determined
by the equality of the total demand and the marginal costs of production.
In both of the above frameworks of analysis, the good can be assumed
to be the same good in order to eliminate problems which are related
only to the differences in types of goods generally supplied through
the use of prices and those generally supplied through the use of taxes.
Basic to the analysis is the issue of what constitutes a sale in the
market. The legal and accounting concept of a sale is accepted in this
analysis.6 A sale takes place at the time at which some legally binding
evidence of sale has changed hands between the buyer and seller. This
means that the point (time) of sale is dependent upon policy rules
of the government as to what is considered as legally binding evidence
of a sale. It logically follows that a sale in the market is a compulsory
act once it is considered to have taken place and that the price is a
compulsory payment once the sale has taken place. The legally binding
evidence of sale may be the exchange of money or goods for goods.
It may also be the joint signing of a contract which legally binds the
buyer to pay a certain sum (the sale price) at a specified time and
the seller to physically deliver certain goods at a specified time.7
Neither money nor goods have to physically change hands for a sale
to take place. The sale price stated in the contract reflects the per-unit
price to the individual as determined in the market.
The point of sale in the case of a tax comes when the individuals of
society cast their votes for the quantity of the good desired at the

6. The concept of the point of sale in accounting has been one of the never-
ending problems of the accountant. See Paton and Paton, Corporation Accounts
and Statements, Chap. 10.
7. The laws and customs of nations regarding when and what constitutes a
sale vary as to the degree of compulsion exerted by the government to enforce
contracts of sale, but most nations whose economic systems can be classified as
a market system make the contract for sale a legally binding transaction.

50

TAXES AND THE POLITICAL PROCESS
various possible prices. The government is legally bound by a policy
rule to establish the price in accordance with the vote of the individuals
and the marginal cost of production. The individual is legally bound
to accept the quantity of the good that he voted for at the tax-price
set in accordance with the established policy rule. The casting of a
vote is fully analogous to the signing of a contract. No money or goods
change hands between buyer and seller or between taxpayer and gov-
ernment at the point of sale, but once the point of sale is reached, the
price or tax and the quantity to be supplied are determined. Once the
sale is consummated, the price and tax are both compulsory under
the given policy rules. Before the point of sale is reached, there is- no
market price and likewise no tax-price.
The conclusion that taxes are no more coercive than prices is de-
pendent upon the type of political mechanism which is assumed to
exist. The conclusion clearly may not be valid if the political mecha-
nism does not provide a means by which individuals vote for both
quantities and prices of each good. The conclusion also may not be
valid if the government is not subject to a policy rule which makes
taxes and quantity of the good supplied dependent upon the expressed
desires of individuals. However, the conclusion makes it clear that
there is nothing inherent in the collection of taxes which is more
coercive than the collection of a price. Taxes and prices are merely
a means of expressing the payment side of a transaction. If coercion
exists in taxation, it is not because a tax was used as a means of pay-
ment instead of a price. Coercion in taxation must result from some
factor which affects the level of taxes to be collected for a good or the
quantity of the good to be supplied at a particular level of taxes.

THE MARKET MECHANISM AND THE POLITICAL MECHANISM
The degree of coercion which exists in the political mechanism
relative to that which exists in the market mechanism may be analyzed
by defining different political situations (i.e., constitutional rules) in
terms of accepted definitions of market situations.8 The political situa-
tions like the market situations are merely hypothetical. Specific real-
world political situations come closer to being described by one of

8. For purposes of analysis, Machlup's terminology is adopted because it is
based on the psychological aspects of the market which are more easily com-
pared with the psychological aspects of the political situations and because it
considers the market situations separately from the concept of the entry of new
firms, pliopoly. See Economics of Sellers' Competition.

51

THE PRICE THEORY OF VALUE IN PUBLIC FINANCE
the hypothetical situations than by any of the others. However, no
specific real-world political situation is completely described by any of
the hypothetical situations. Therefore, the conclusions only refer to
hypothetical situations. However, the conclusions are likely to apply
for the real-world situation as long as it can be said that a particular
real-world political situation is described most closely by one particular
hypothetical situation.
Market polypoly is "a state of mind of sellers who know that they
have competition, but, in making up their minds about changing their
selling or productive policies do not ponder over what their com-
petitors' reactions might be."9
Political polypoly is a state of mind of voters who know that they
have competitors in the form of other voters with different desires for
the same public good, but in making up their minds about voting for
particular selling or productive policies do not ponder over what their
voter-competitors' reactions might be.
In market polypoly it is usually considered that many buyers and
many sellers of a homogeneous product exist. In political polypoly
this condition is not of importance. The buyers and sellers are the
same individuals in a very direct sense, and the existence of many
is assured. All of the individuals which constitute a governmental
unit of society are both the buyers and the sellers. A homogeneous
product is also not an issue since all voters vote on the production of
each good separately. Even where the economic good is considered to
be all governmental services, the homogeneous-product condition is
met by the political mechanism. The necessary condition is for the
government to act in accordance with the vote of the individuals in
regard to the quantity and price of the good to be supplied and in
accordance with known policy rules of government. The government
is thus considered to be nothing more than an organization for the
production of the goods and services desired by the individuals of
society.
It would be necessary for the voting to be for various quantities of
the good at various possible prices in order to meet the conditions of
the voluntary exchange theory. A vote on one quantity of the good at
one price is not sufficient for a governmental organization which is to
be neutral in its own productive activities. The government must know
the various combinations of quantities and prices that individuals de-
sire so that they can be compared with the cost of producing the various
9. Machiup, p. 136.
52

TAXES AND THE POLITICAL PROCESS
quantities of the good. The essence of such a political situation is that
the voter reveals his true preferences without concern for the prefer-
ences which others are revealing. The voter knows that the governmental
organization is restricted by constitutional rules that require the pro-
duction policy of the government to be based on the total revealed
preferences and costs of production. He also knows the constitutional
rules require the taxation policy of the government to be based on the
individual preferences for the quantity of the good to be supplied to
the individual.
The situations in the market and political mechanism are basically
the same as those used in the analysis of taxes and prices. The con-
clusion, as would be expected, is the same. Only now it can be said
that in the market situation and political situation as defined there
is no difference in the degree of coercion which would exist.
Market oligopoly is a state of mind of sellers who know that they
have competitors, and in making up their minds about changing their
selling or production policies do take into consideration what their
competitors' reactions might be.10
Political oligopoly is a state of mind of governmental officials who
know that they have competitors (other governmental officials), and
in making up their minds about changing their selling or production
policies do take into consideration what the competitors' reactions
might be.
The usual cause of market oligopoly is fewness of sellers, which
gives the individual seller an awareness of the fact that his actions
affect the total market situation and that others notice his actions and
react to them. Political oligopoly is similar in that its cause is fewness
of voters directly affecting the total market situation. Based on the
considerations made in Chapter 3, it is assumed that true preferences
would be revealed by individuals if they had the opportunity to vote.
Therefore, the difference between political polypoly and political
oligopoly is not considered to lie in the desire of the individual to
reveal his true preferences. The difference is that in political polypoly
the government as an organization is neutral in the determination of
quantity of goods to be produced, whereas in political oligopoly the
government as an organization is not neutral. The situation is one
where the government's selling and production policies are directly
determined by a vote of representatives of individuals in the society
rather than by a vote of all individuals in the society. Each representa-
10. Machiup, pp. 349-53.
53

THE PRICE THEORY OF VALUE IN PUBLIC FINANCE
tive is aware of the fact that his actions affect the total market situation
and that his competitors notice his actions and react to them. His
competitors are the representatives of other individuals in the society.
Each representative will temper his actions because of the reactions
which might be forthcoming from his competitors. The consequences
of the constitutional rules are that the representative is aware of his
position in the determination of what and how much at what price is
to be produced by the government, and each representative takes into
consideration the reactions of other representatives when deciding the
preferences he will reveal.
It is still possible, but not necessary, to assume that each representa-
tive is attempting to obtain for those whom he represents the quantity
and price relationship for each public good which they would desire.
If the representative is not attempting to obtain the quantity and price
relationship desired by the individuals he represents, it can be con-
sidered that coercion is greater than in political polypoly. The higher
degree of coercion is a result of a situation where the constitutional
rules for the political organization do not permit the type of voting
necessary for the government to be neutral in the determination of
selling and production policy.
Market monopoly is a state of mind "of a seller who knows neither
any individuals nor any particular groups of sellers with whom he
is in competition."11
Political monopoly is a state of mind of a government official who
knows neither any governmental officials nor any particular groups
of society (political party) with whom he is in competition.
In market monopoly the individual seller is unaware of a need for
considering the reactions of any other sellers in the market. Therefore,
his selling and production policies can vary greatly depending upon
the motivation which is assumed to be the basis of his actions. He does
not believe that the market process will require him to choose any
particular policy. The pessimistic monopolist will attempt to make the
most of the situation for himself in the short run. The optimistic
monopolist may attempt to maintain his position by operating to make
the most of the situation in the long run, or he may attempt to main-
tain his position by advertising and research.12
Political monopoly is very similar to market monopoly. The single
government official determines the selling and production policies for
11. Machiup, p. 544.
12. Machiup, pp. 555-57.
54

TAXES AND THE POLITICAL PROCESS
all public goods without having to compete (vote) with any other
governmental officials or political parties. He does not feel a need for
considering the reactions of any other representatives of individuals
of society because he believes he is the sole representative of the people.
However, he may be pessimistic about his position because other repre-
sentatives of the people may gain popular or military support. There-
fore, he will attempt to make the most of the situation for himself in
the short run. The political monopolist may also be optimistic about
his position because he feels that he can act to prevent any other
representative of the people from interfering with his position. As a
result, he may operate to make the most of his situation in the long
run by relying upon his influence over all possible competitors (all
other political officials or all other political parties), or he may at-
tempt to maintain his position by propaganda and by public demon-
strations of being the "true" representative of the people.
In political monopoly the taxpayer is reduced to a buyer and serves
little, if any, role in the determination of what is to be produced. The
potential buyer of a good in the market may be faced, because of the
existence of a monopoly seller, with a higher price and therefore must
modify the quantity which he purchases. The taxpayer-buyer of a
public good has no such opportunity in the case of political monopoly.
Public goods which have the characteristics of jointness of supply
would have both price and quantity determined independent of the
desires of the individual. Even without the characteristic of jointness
of supply, in the case of political monopoly, the price and quantity
might both be determined arbitrarily. The only opportunities for the
individual to obtain his desires in regard to public goods are to escape
from the political control of the governmental unit under which he
lives or to find some governmental official or group which can take
over as the accepted representative of the people.
Coercion in political monopoly is considerably greater than under
market monopoly. Market monopoly may cause higher prices than under
alternative market situations, but the individual can still adjust the
quantity of the good he purchases in accordance with the higher price.
Therefore, economic freedom, in one sense at least, is not restricted by
the existence of market monopoly. This, however, is not true for political
monopoly, where both quantity and price are arbitrarily set by the
government. Economic freedom is restricted and coercion does exist.
However, the individual can still maximize his satisfaction for all
goods, if he considers all governmental services as a single good. In

55

THE PRICE THEORY OF VALUE IN PUBLIC FINANCE

this case, he must alter his consumption of private goods in accordance
with the marginal utility per dollar's worth of public goods arbitrarily
established by the actions of the political monopolist.
Coercion does not depend upon whether or not the individual can
maximize his satisfaction, because the individual can always maximize
his satisfaction by altering what he considers as an economic good.
The degree of coercion does depend upon the constitutional rules that
have been established in the society. A change in the type of the
market situation may not affect the degree of coercion that exists.
Therefore, the political mechanism is more coercive in nature than
the market mechanism unless it is assumed that the political mecha-
nism can be classified as political polypoly.
Pliopoly is the term applied by Machlup to the concept of the
entry of new firms in an industry, and it is the existence of pliopoly
which tends to eliminate profits in the supply of goods in the market
mechanism.13 Pliopoly, however, does not have to be restricted to the
actual entry of new firms. It depends upon an objective evaluation of
an outsider as to whether or not it is probable that new firms will
enter any given industry.
A similar concept could be developed for the political mechanism.14
Political pliopoly would refer to the probability that the officials in
the government will act in accordance with the desires of the individual
in the society. The existence of political pliopoly would, therefore, tend
to eliminate coercion in the political mechanism. The objective factors
which should be considered in evaluating whether or not governmental
officials are likely to so act are complex, but at least a few could be
briefly pointed out. The most obvious is whether or not there is a

13. Machlup, p. 211.
14. The political mechanism has no automatic factors which tend to eliminate
profits. Whether or not the government should make profits could be established
in the form of a constitutional rule, or, as is more likely, in the form of a
policy rule of government. The absence or presence of profits in the supply of
public goods is of extreme importance, since it determines whether the total
budget of the government will be a surplus budget, balanced budget, or deficit
budget. Therefore, four possible policy rules are listed with their effects upon
the total budget, assuming that they are consistently applied to the pricing of
every public good: (1) Average Cost Pricing Rule-balanced budget; (2)
Marginal Cost Pricing Rule-budget determined by the value of goods supplied
having increasing or decreasing costs; (3) Maximum Production of Public
Goods Pricing Rule (i.e., increasing-cost goods at average cost and decreasing-
cost goods at marginal cost)--deficit budget; and (4) Minimum Production
of Public Goods Pricing Rule (i.e., increasing-cost goods at marginal cost and
decreasing-cost goods at average cost)-surplus budget.

56

TAXES AND THE POLITICAL PROCESS
regular process by which the individual can express his desires. Another
would be whether or not desires are expressed for just a quantity at a
given price, or a price at a given quantity, or for various quantities
at various possible prices. Still another would be whether or not the
governmental policy rules encourage the governmental officials to act
in accordance with the desires of the individuals in the society.
It can be considered, from these few factors affecting the existence
or nonexistence of political pliopoly, that it would be most likely to
occur under the constitutional rules (political situation) classified as
political polypoly. The individual voter does have the opportunity to
express his desires for the various quantities at the various prices
through the voting process, and the policy rules of government require
the governmental official to act in accordance with the vote-expressed
desires of the individuals in society. However, political pliopoly is not
necessary, because governmental officials once in office may be able
to circumvent the policy rules or even the constitutional rules. There-
fore, political pliopoly is not assured as a component part of political
polypoly, but it is most likely to exist under the constitutional rules
of that political situation.
In the case of political oligopoly the three objective factors leading
to political pliopoly, listed above, are not an inherent part of the
political situation. However, this does not rule out the possibility of
political pliopoly existing. Under political oligopoly the extent to
which the representative can reveal desires different from the "true"
desires of the individuals whom he represents depends upon the con-
stitutional rules as to the voting for representatives and upon the con-
stitutional rules15 as to the voting (balloting) process for specific goods
and services. In other words, the likelihood of coercion (the absence
of political pliopoly) depends upon whether or not the representative
is aware of possible reactions on the part of the voters who choose the
representative, and this may in turn depend, at least in part, on the
knowledge that the voter is likely to have concerning whether or not

15. DeViti DeMarco states the necessary conditions as follows: "Only if the
taxpayers participate in the initial calculation of wants, in which each person
judges the economic advisability of paying a given tax in order to obtain in
exchange a given public service, and only if this calculation is subjected to
annual revision and is open to criticism and continuous public discussion by the
Press, the political parties, the parliament, is it possible to have a guarantee
that what is involved is a productive public expenditure-that is, one which
is regarded as such by those who bear the cost" (First Principles in Public
Finance, p. 118).

57

THE PRICE THEORY OF VALUE IN PUBLIC FINANCE
the representative actually does attempt to express the desires of those
whom he represents. If the representatives had to cast ballots for various
quantities at various prices for each public good because of a con-
stitutional rule, the voters could be aware of the fact that the repre-
sentative is modifying the individual voters' true preferences. If the
representative merely casts a vote for or against a specific quantity
and price of each public good, as is usually the case, the voter has
less opportunity to be aware of the modification of the individual
voters' true preferences. The latter constitutional rule makes it possible
for the representative to bargain in the political process, before the
decision to produce any public good comes to a ballot, and to assure
himself that his vote can be cast without causing reactions on the
part of those who vote the representative into office.
Political pliopoly is least likely to occur under the constitutional
rules of political monopoly. The only apparent reason that political
pliopoly might exist would be the altruistic motives of the governmental
official. The existence of policy rules of government, which correspond
to the objective factors considered above, would constitute an objective
factor indicating the existence of political pliopoly even in the case of
political monopoly. The policy rules of the government replace the
constitutional rules as objective factors, but policy rules are not con-
trolled or limited by other constitutional rules in the case of political
monopoly and therefore depend upon the public spirit of the govern-
mental officials.
The conclusion to be drawn from the analysis of the market mechan-
ism and political mechanism in regard to coercion is that the political
mechanism is likely to be more coercive than the market mechanism,
but that the degree of coercion in the political mechanism is dependent
upon the constitutional rules that establish the particular mechanism.
Also it can be concluded that certain constitutional rules and/or policy
rules of the government can be considered as objective evidence that the
degree of coercion present in any specific political situation is less than
it otherwise would have been.

58

6. APPLICATIONS OF THE
SUGGESTED APPROACHES

The approach adopted in Chapter 5 to analyze the criticisms of
the operation of the political organization with respect to the
price theory of public finance represents a suggested approach to the
general area of the effects of political organization on the supply of
public goods. This chapter will carry the approach one step further
to indicate how it may be applied to the existing area of intergovern-
mental relations. The second part of this chapter will carry the theo-
retical framework suggested in Chapter 4 one step further to indicate
how it may be applied to the existing area of national goals.
INTERGOVERNMENTAL RELATIONS
Intergovernmental relations has been an area of study within the
fields of political science and public finance. In many cases the political
scientist does his research in terms of the administrative relations and
the economist does his research in terms of the financial relations. The
study of administrative relations being independent of the study of
financial relations, and vice versa, may lead to conflict between the
conclusions derived. Interdisciplinary studies are sometimes used as
a method of eliminating the conflict in conclusions, but the results
have not been too encouraging. The problem to a large extent lies in
the difference of terminology in the two fields, and in the fact that
neither the political scientist nor the economist can visualize the im-
portance of small distinctions being made with the special terminology
of one field on analysis being employed by the specialist of the other
field. There is simply a growing need for specialists trained in more
than one field. The economist in the area of intergovernmental rela-
tions must understand the terminology and concepts of the political
scientist. Furthermore, the economist must recognize how the concepts
of political science may modify the economic analysis which is appro-
priate in a given situation, and how to express the concepts of political
science in terms which are consistent with economic terms and frame-
works of analysis used in specific situations.
Defining political organizations in terms of economic market struc-
tures represents a possible approach to part of the problem. The broad
categories of political structures used in Chapter 5 are not adequate.
59

THE PRICE THEORY OF VALUE IN PUBLIC FINANCE
Market oligopoly is the general case in the real world, just as political
oligopoly is the general case for all levels of government in the United
States. Oligopoly theory, however, suggests that market oligopoly tends
to be unstable and leads to forms of collusion. Therefore, market oli-
gopoly is defined in terms of various forms of collusion. The envisioned
area within intergovernmental relations may be termed comparative
governmental institutions and would logically follow the same form of
definitions as has been adopted in market oligopoly analysis. Each
real-world situation would have to be defined in terms of the type
of collusion existing in the political organization and the likelihood of
pliopoly factors affecting the actions of the political organization.
Examples of the application of this approach are beyond the in-
tended purpose of this monograph. However, the next chapter will
in general terms consider the probability of the future use of this and
other frameworks derived from the price theory of public finance in
empirical or applied areas of studies within the field of economics and
political science. It is sufficient here to note the possible application.

NATIONAL GOALS
Contemporary public finance has emphasized the role of government
in achieving the goals of the nation. In the United States these goals
have been stated by Congress to be related to full employment, price
stability, and economic growth. A fourth goal which is important to
many nations is related to economic development. The Western nations
have not stressed economic development, in part because they consider
that they have already achieved a relatively high level of it.
The existing terminology in the literature causes some difficulties
because it is often difficult to ascertain the difference, if any, between
economic growth and economic development. Changes in Gross Na-
tional Product or per-capita Gross National Product from one period
of time to the next period of time are often thought to measure changes
in economic development and economic growth. However, there also
exists literature which cites various factors that determine a nation's
development and another set of factors that determine a nation's
growth. The set of factors cited for each, development and growth,
is not entirely consistent between authors, but generally the factors
cited as determining economic development have to do with the allo-
cation of given resources with a given level of technology in a period
of time, while those determining economic growth have to do with
changes in resources and technology over time.

60

APPLICATIONS OF THE SUGGESTED APPROACHES
If the above general differences between development and growth
are accepted, the suggested approach to the price theory of public
finance provides a means of more explicitly stating the differences.
Economic development could be expressed in terms of the degree to
which the nation has achieved its optimum allocation of resources dur-
ing a given period of time. Figure 22 illustrates this concept of de-
velopment. Point A represents the actual allocation between public
and private goods, while point B represents the allocation which would
result from an optimum allocation of resources. The level of economic
development achieved would be expressed in terms of the percentage

Private Goods

PCL's

90% Development
80% Development
A

0 Public Goods

Figure 22.
of full development. The factors determining the level of development
achieved would be the structure of the market sector of the economy,
the structure of the political sector of the economy, the extent of
knowledge about both public and private goods, the measurability of
public good demand, the mobility of resources, etc.
Economic growth can be differentiated from economic development
with the suggested approach because economic growth takes place
over time. Two different concepts of growth are clearly possible with
the suggested approach. One concept illustrated in Figure 23 would
be that economic growth can be expressed in terms of the change in
the optimum allocation of resources (i.e., the change from point B
for time period 1 to point C for time period 2). In this context the
factors determining economic growth would be changes in the quantity
or quality of existing resources, changes in technology, changes in
the tastes and preferences of the individuals of the nation, changes in

61

THE PRICE THEORY OF VALUE IN PUBLIC FINANCE

the ownership of economic resources, etc. A second concept of economic
growth illustrated in Figure 23 would be that economic growth can
be expressed in terms of the change in the transformation curve. In
this context the factors determining economic growth would be limited
to changes in the quantity and quality of resources and changes in
technology. The former concept of economic growth has the advantage
of tying growth to the welfare economics concept of the optimum
allocation of resources. The latter concept has the advantage of being
closer to the literature on the factors determining economic growth.

Private Goods

t 1: PCL t IPCLt2

122
At A

0it2

Public Goods

Figure 23.

With either concept of economic growth it is apparent that growth
may affect the nation's economic development in subsequent periods
of time. This would be particularly true for the first concept, but to
some extent true for the second. Economic development in a given
period is also likely to affect growth over time. The analysis of these
effects is beyond the scope of this monograph. However, it should
be noted that Gross National Product, or even per-capita Gross National
Product, is not an adequate measure of either economic development
or economic growth as they are stated here. Development compares
the actual output with a potential output, while growth compares the
potential of one period to the potential of another period of time. A
change in the actual output from one period to another period of

62

APPLICATIONS OF THE SUGGESTED APPROACHES
time may be caused by changes in the determinants of development
or by growth, with the determinants of development given.
The suggested approach to the price theory of public finance also
provides a means of linking the goal of full employment to economic
development, economic growth, and the optimum allocation of re-
sources. Full employment exists with any combination of private and
public goods which lies on the transformation curve. Thus the goal
of full employment is achieved when the actual output for a period
is any one of the potential outputs expressed by the transformation
curve. Full employment in both of two periods where economic growth
has taken place would indicate that the growth has been accompanied

Private Goods

I PCL's

0%
A 0/
70%

0 Public Goods

Figure 24.

by an increase in output. However, the achievement of full employ-
ment may be in conflict with the achievement of economic develop-
ment. The possible conflict is expressed by Figure 24.
Point A represents the combination of private and public goods
which would actually be produced if the government did not take
fiscal policy measures designed to achieve full employment. Point B
represents the combination of private and public goods associated with
the optimum allocation of resources. Point C represents the actual
output that would occur if the government takes certain actions in
order to achieve full employment. In the particular case cited the
combination given by point A with less than full employment repre-
sents a higher level of development than the combination at point

63

THE PRICE THEORY OF VALUE IN PUBLIC FINANCE
C with full employment. In this case full employment would be achiev-
ed by producing more of public goods than the society desired and
therefore is in conflict with the goal of economic development. The
relative effects of combinations A and C on economic growth, how-
ever, may be a different matter. Combination C with full employment
may result in more or less economic growth than combination A.
Again this is a question which is beyond the bounds of this mono-
graph. The potential of further work within this framework appears
to be very great. The interrelationships that exist between full em-
ployment, development, and growth cannot be completely specified
by the graphs, but the separation of concepts that can be set forth
should facilitate further study. One aspect of special note is the effect
of changing ownership of resources. The "best" distribution of income
is put into the context of happening over time rather than happening in
a period of time. The discussion of the "best" distribution of income
without specifying the ownership of resources has been one of the
principal problems in welfare economics. In the framework of the
suggested approach the problem is put into a more dynamic context
which recognizes that the distribution of income (best or otherwise)
is the result of organizational structures as well as.of the ownership
of resources at any given period of time, and that even the ownership
of resources over time is the result of the actual distribution of income
in past periods of time.
Although the suggested approach to public finance does not pro-
vide a diagrammatic framework which simplifies the considerations
necessary for the problem of price stability, it may put that problem
into a new context which has special merits. In the framework the
prices of products may vary as long as the variation does not affect
the distribution of expenditures on products and as long as the price
paid to the owners of resources varies in accordance with the prices
of products without affecting the distribution of income. The level of
money income and price levels are related but do not affect the real
income and the real level of prices. The problem of price stability
may be an important factor in the determination of development and
growth but only because price stability may affect market and political
structures, market knowledge, technology, tastes and preferences, etc.
The problem of price stability as it is usually stated also involves
the redistribution of income from those who are on fixed incomes to
those whose income varies with economic conditions. The model of
the suggested approach eliminates this aspect of the problem of price

64

APPLICATIONS OF THE SUGGESTED APPROACHES
stability by the assumptions that all income is spent and that all in-
come is derived from the use of productive resources in the production
process. In the real world, money and the process of the creation of
money are a source of money income to individuals. The result is
that money income is redistributed from what it would be if money
were neutral, as it is in the model. Thus, the existence of financial
assets in a society is another reason why the optimum allocation of
resources (100 per cent development) will not be achieved. As in-
dividuals save by making financial investments (purchase financial
assets), the money income earned by the owners of the factors of
production is transferred into the hands of those who previously owned
or created the financial assets. The new owners of the money income
are the individuals who then demand products and determine the
combination of private and public goods which should be produced.
This distribution of income, like a distribution of income resulting
from monopsony resource markets, would also affect the achievement
of economic development and may have implications for economic
growth.
One approach which would bring money as a non-neutral factor
into the model would be to accept money as a productive resource. In
the real world, money is a necessary factor for the production process
to operate efficiently, and the creation of money makes possible changes
in market structures. However, the development of a transformation
curve from isoquant analysis is very questionable if money is con-
sidered one of the resources used in the production process. There
appears to be no a priori basis for stating the shape of an isoquant
with money as one of the resources.
The answer to this problem is not within the scope of this mono-
graph. However, it is apparent that leaving money neutral in the
model may not be an adequate simulation of the real world because
money, financial assets, and the process of creating money do affect
the distribution of income which determines the demand for products.
The inadequacies of the model are the same as most price theory
models. Monetary effects are difficult to deal with in most resource
allocation models.

65

7. OTHER APPLICATIONS
OF THE THEORY

In Chapter 6 an attempt was made to indicate areas of economics
wherein we might make valid applications of the specific framework
developed earlier in this monograph. The present chapter is also con-
cerned with the application of the theory, but not within the specific
framework developed here. First, two applications of the past will
be commented upon, and then the prospects for future applications
in general will be considered. The first of the past applications, as
in the previous chapter, will deal with an area that may be more
appropriately considered as political science. This application applies
the price theory of public finance only in that it is an analysis of
political behavior in terms of the traditional price theory assumption
that individuals attempt to maximize their satisfaction. The second ap-
plication does not involve an application to specific economic prob-
lems, but rather represents one of the broadest applications of the
terminology of price theory to public finance in general.
EXISTING APPLICATIONS
Buchanan and Tullock in The Calculus of Consent begin with the
premise that political behavior, just as economic behavior, can be
analyzed by making the assumption that individuals attempt to maxi-
mize their satisfaction. Under this assumption it might follow that
political polypoly would be considered the ideal form of governmental
organization. This follows from the fact that with such a political
structure the political mechanism works as efficiently as the purely
competitive market structure, and the individual maximizes his satis-
faction by equating the marginal utility per dollar's worth of all
goods, including public goods.
Buchanan and Tullock point out that a representative form of
government (political oligopoly) is not inconsistent with rational be-
havior of individuals, because there may be some costs associated with
the act of collective decision-making.' There may be costs associated
with obtaining any specified number of individuals to vote in favor
of any particular proposal, and costs associated with the taking of a
vote of all individuals on various quantities and various prices for
1. Page 44.
66

OTHER APPLICATIONS OF THE THEORY
each public good. The costs can be expected to increase more than
proportionately as the number of individuals increases. In obtaining
a specified number of individuals to vote in favor of a particular
proposal, the costs can be expected to increase more than propor-
tionately as the number of individuals necessary to vote in favor of
the proposal increases. The unanimity rule would, therefore, have the
greatest cost of decision-making associated with it. Buchanan and
Tullock concluded that it can be considered rational for an individual,
attempting to maximize his satisfaction, to prefer the representative
form of government over one which requires many individuals to
vote on the supply of each good produced by the government.2
This conclusion is even more likely to hold true if there are addi-
tional constitutional rules establishing a system of checks and balances
which limit the functions of the various branches of government, so
that the branches of government are somewhat analogous to the market
organization.3 The function of the legislative branch can be limited
to the interpretation of the quantity and price of particular goods
desired by individuals of the society. The function of the executive
branch can be limited to the determination of how to combine re-
sources in the production of the goods determined as desirable by the
legislative branch. The function of the judicial branch can be limited
to the evaluation of whether or not the other two branches of govern-
ment have acted within all of the constitutional rules established by
the society.
However, once established, with the legislative branch interpret-
ing the desires of all individuals of the society, the representatives
that make up the legislative branch may come under the pressures of
minority groups of individuals organized to obtain exclusive benefits
for the group which are to be paid for by all of the individuals of
the society.4 These pressure groups are a natural outgrowth of the
system, if the assumptions about rational economic behavior are ac-
cepted, because small groups of individuals find that they can gain
2. Pages 115-16.
3. These rules may be considered as additional factors to be considered as
evidence that political pliopoly can exist.
4. DeViti DeMarco's conclusions about pressure groups are similar but are
stated in terms of his own framework of analysis. The pressure groups are con-
sidered to be evidence of a monopolistic element in government. He concluded
that if capital-owning pressure groups win, higher prices must be paid to
private firms, and if labor pressure groups win, higher prices will have to be
paid in the form of higher costs of production (First Principles of Public
Finance, p. 50).

67

THE PRICE THEORY OF VALUE IN PUBLIC FINANCE
more in benefits than it costs them to organize and obtain the benefits.5
The result is that the constitutional rules establishing the representative
form of government do not operate as they were intended to operate.
The benefits from the goods supplied by the government become sepa-
rated from the costs (taxes). The majority of the society, rather than
the minority of the society, must adjust their private consumption to
maximize their satisfaction as a result of the government supply of
goods.
Buchanan and Tullock suggest the adoption of a policy rule which
would require all goods that benefit a particular minority group be
paid for by special taxation of another equal in size minority group.
The logic of this rule is that in this -manner countervailing powers
would be established without causing a further growth of either power.6
Buchanan and Tullock also consider the possibility that no matter
which of the possible constitutional and policy rules exist, coercion
may not exist as long as unanimity exists concerning the rules.7 In other
words, as long as each individual in the society agrees that the rules
should exist, it can be assumed that they believe that the gains to be
derived from changing to any alternative set of rules do not equal the
costs of making the change.8 However, a point not considered is that
some of the costs of changing to an alternative set of constitutional
rules may be the direct result of the existing constitutional rules regard-
ing the process necessary in order to obtain a change. This last point
may be a basis for the changes in the interpretation of the Constitution
in the United States during recent years. The process of changing the
Constitution is difficult and involves costs which can be avoided by sim-
ply having the Supreme Court reinterpret the existing Constitution in
such a way as to accomplish the changes that the individuals of society
would write into the Constitution if the costs of doing so were not so
great.
In any case the work of Buchanan and Tullock is an interesting
application of one of the basic assumptions of price theory to the area
of political behavior. It puts political behavior into a frame of reference
that the economist should be able to understand more clearly and
should be more willing to accept. It also provides a mixing of terminol-
ogy from the two fields which should lead to a better understanding of
concepts in both fields of study.

5. Buchanan and Tullock, pp. 286-87.
6. Pages 291-94.
7. Pages 250-53. 8. Pages 260-62.

68

OTHER APPLICATIONS OF THE THEORY
Antonio DeViti DeMarco in First Principles of Public Finance pro-
vides an example of the application of the terminology of price theory
to the field of public economics. He does not develop a specific model
but merely applies the models and concepts of price theory to his ex-
planation of public finance concepts and to the history of public finance.
Therefore, his application primarily deals with the tax side, but he
does carefully state that public finance is not just the study of tax-
ation, politics, or law. "The discipline which gives the really necessary
and fundamental explanation of the phenomena of public finance is,
however, economics."9 DeViti DeMarco's definition of public finance or
public economics gives a still better indication of the extent to which
he would apply price or value theory to the public sector of the econ-
omy. Public economics "investigates the conditions to which the pro-
ductive activity of the State must be subjected in order that the choice
of the public services which are produced, the determination of their
respective amounts, the distribution of the costs among the consumers,
etc., may take place according to the principles of theory of value-
that is, with the least possible waste of private wealth, in order to at-
tain the greatest satisfaction of collective needs."10
This definition contains all of the elements of the voluntary exchange
or price theory of public finance. All three of the economic problems
related to public finance are specifically stated in relation to the prin-
ciples of the theory of value (price theory). The function and goal of
public economics is to investigate the means of attaining the greatest
satisfaction of collective needs with the least possible waste of private
wealth. The relationship of this function and goal to price theory is
obvious. Also, the definition considers the state as a producer of goods
and services and the taxpayer as a consumer. The state is a producer
of goods and services not just when the goods resemble goods which
can be supplied through the market mechanism but whenever the state
satisfies collective needs.
Public goods and services are classified as either "Special Public
Services" or "General Public Services." A public good is in the for-
mer classification if it meets both of the following criteria: (1) the
supply of the service must be technically divisible into salable units;
(2) the service must be constantly demanded by individuals.11 Public

9. Page 34.
10. Page 36.
11. DeViti DeMarco believes that some services such as public safety are an
example of a service which is not constantly demanded by individuals. The de-

69

THE PRICE THEORY OF VALUE IN PUBLIC FINANCE
goods and services fall into the second classification if they do not meet
both of the foregoing criteria.
Special public services require fee type pricing which makes their
supply somewhat analogous to private goods and services. However,
since the government can act monopolistically in the supply of public
goods and services, a rule of average cost pricing must be adopted by
the government. General public services, on the other hand, are more
unique in that they are generally supplied by the government and
require a tax type of pricing. With general public services, individual
consumption is an unknown quantity. However, this does not rule out
the use of value theory in answering the economic questions about their
supply. Consumption can be assumed to be proportionate to income.
It is an assumption, but DeViti DeMarco contends that it has both an
empirical and a logical foundation.
Basing it on this assumption, DeViti DeMarco develops a concept of
individual net income. The concept is analogous to the value added
concept of gross national product in that individual net incomes can be
summed to arrive at a measure of national income. No income is to be
counted twice, and no income is to be deducted which is not counted as
income of some other individual. Developed in this manner, individual
net income is considered an indication of consumption and, therefore, the
measure of individual taxable income. If the sum of the individual tax-
able incomes is greater than national income, double taxation exists. If
the sum of the individual taxable income is less than national income,
price discrimination exists in the supply of public goods and services.
Price discrimination can exist because of the monopolistic nature of
the government in the supply of goods and services. However, DeViti
DeMarco also recognizes that the single tax-price is based upon the con-
cepts of pure competition and that care must be used in its application
to public goods and services. Multiple pricing does not necessarily mean
price discrimination exists, according to DeViti DeMarco. Price dis-
crimination only occurs with general public services when an individ-
ual net income is not taxed on a proportionate basis with all other
individual net incomes. Multiple pricing, therefore, exists for general
public services in that different individuals pay different prices, but
price discrimination only occurs when an individual taxable income re-

mand only recurs when public safety is actually impaired. Danger is always pres-
ent but the individual demand for protection is dormant until the danger is
recognized by the fact that the service has not been supplied and someone's
safety has not been protected.
70

OTHER APPLICATIONS OF THE THEORY
ceives special treatment.12 Multiple pricing proportionate to individual
taxable income is based on consumption and thereby follows the con-
cepts of value theory. Multiple pricing based on special treatment of
particular individual taxable incomes is the result of the monopolistic
nature of the government in the supply of goods and services, and is a
case of price discrimination. Likewise, in the supply of special public
services, multiple pricing may or may not be evidence of price discrim-
ination, depending upon whether or not it is a result of the monopo-
listic nature of the government in the supply of these goods. When mul-
tiple pricing exists because of differential costs, price discrimination
does not exist. In fact, in this case a single price would result in price
discrimination. However, if multiple pricing exists in the supply of spe-
cial public services only as a result of the monopolistic nature of the
government supply, the multiple pricing does result in price discrim-
ination.
The concept of grouping similar special public services together and
using a multiple pricing technique so that the total cost equals total
revenue is based upon the monopolistic nature of the supply of public
goods, and therefore constitutes a form of price discrimination.13 Using
tax pricing for special public services or attempting to supply general
public services by using a fee type pricing system also is based on the
monopolistic nature of government, and is a form of price discrimina-
tion. Also, the concept of using the total budget of the government, which
includes both special and general public services, as a basis for the
supply of public goods would result in price discrimination. However,
the total budget of just general public services is to be used as a basis
for the determination of what to produce, how much to produce, and
how much to charge. Here individual consumption is assumed to be
proportionate to individual net income, and the sum of all individual
net incomes should equal national income.
DeViti DeMarco's work represents an era of Italian economics which
saw a fairly wide application of price theory concepts to the field of
public finance and to some extent crossing over to the area of political
science. The work of Maffeo Pantaleoni is an example of the latter. The
era, however, died out, and this type of broad application of price the-
ory concepts and terminology to public finance and the political organ-
ization has to some extent died with it. The works of Wicksell, Lindahl,
Bowen, Kafoglis, Buchanan, and Tullock are modern examples of appli-
12. Pages 114-15.
13. Pages 81-88.
71

THE PRICE THEORY OF VALUE IN PUBLIC FINANCE
cation, but none of these carry the application of price theory terminol-
ogy as far as did DeViti DeMarco.

FUTURE APPLICATION
The applicability and limitations of the price theory of public finance
to three broad areas of study are considered in the remainder of this
chapter. The three areas of application are (1) as an explanation of
the real world, (2) as a framework for policy proposals, and (3) as
a framework for discussing concepts of public finance.
The political mechanism which is necessary for the government to be
able to provide an optimum allocation of resources is not likely to exist
in the real world. Therefore, political polypoly is not an explanation of
the operation of the political process in the real world. Neither is the
optimum allocation of resources model an explanation of the actual
allocation of resources by the government in the real world. These lim-
itations are obvious to even the casual observer of the actual political
process who understands the necessary conditions of political polypoly
and of the optimum allocation of resources model. However, this con-
sideration does not have to affect the acceptance of the price theory of
public finance as an explanation of real-world events. The same type
of observations can be made in relation to the pure competition model
and the real-world market situations. Market oligopoly is the most likely
market situation in the real world, just as political oligopoly is the most
likely political situation. The difference which affects the relative ac-
ceptability of the two frameworks of analysis lies in the fact that the
economic implications of market oligopoly have been developed and
studied by leading economists of England and the United States, while
the economic implications of political oligopoly have never been system-
atically set forth. The development of precise definitions for, and of
analysis of the economic implications of, political situations is essential
to the future application of the price theory of public finance to real-
world situations.
The political polypoly model which does provide an optimum allo-
cation of resources is important to economic analysis, even if it does
not provide an explanation of the operation of the real-world political
process or of the operation of the real-world allocation of resources to
public goods. In a democratic representative society it is likely that the
general principles of the optimum allocation of resources model can be
applied to specific real-world allocation problems.
In any case, there is no apparent reason why the tools of price theory

72

OTHER APPLICATIONS OF THE THEORY
analysis would not provide insights into the allocation of resources to
public goods in the real world. The political situation which exists will
have to be taken into consideration, but this limitation is not sufficient
reason for rejecting price theory tools of analysis.
The hypothetical political situation defined as political polypoly and
the optimum allocation of resources model do provide objective criteria
for making policy proposals. However, there are many problems of
applying the conditions of the hypothetical situation and of the model
to real-world allocation problems. Whether or not these problems of
application can be overcome cannot be known until attempts are made
to interpret the concepts and arrive at specific proposals. In any case,
it is likely that any proposals for sweeping changes in the operation of
government would not be accepted in our society. Policy proposals by
economists are called for by our society and by the governmental or-
ganizations which represent society. Therefore, as particular situations
arise, the economist can make proposals which will tend to make the
operation of government come closer to political polypoly and the pro-
duction of public goods come closer to the optimum allocation of re-
sources if the theoretical concepts can be translated into reasonable pol-
icy proposals.
Political polypoly as a hypothetical set of constitutional rules is pri-
marily the concern of the political scientist. However, the economist
may very well be concerned with proposed changes in constitutional
rules which affect the government's ability to interpret the demands
of individuals for public goods. One example of such a change can here
be considered for illustrative purposes. The state of Oklahoma has con-
sidered several proposed changes in its constitution relating to repre-
sentation in its legislative branch. A non-population basis for repre-
sentation is likely to result in the favored group having a greater vote
in the allocation of resources by the state. The economist has a respon-
sibility to point out what effects the various proposals might have upon
the allocation of resources.
The optimum allocation of resources model and policy rules which
determine the role of government in the production of public goods are
more directly the concern of the economist. This fact does not imply
that the economist should propose a policy rule that will make the opti-
mum allocation of resources the role of government in the production
of public goods. Such a policy rule would probably not be accepted by
our society. Other considerations must be taken into account. These
other considerations, however, do not prevent the economist from evalu-

73

THE PRICE THEORY OF VALUE IN PUBLIC FINANCE
ating specific proposals in particular situations and stating whether or
not the proposal will cause the allocation of resources to correspond
more closely to the optimum allocation than the present allocation of
resources. In other words, the optimum allocation of resources can
serve as a standard of reference for policy proposals by economists. In
many specific allocation problems it may be that the proposal based
upon the optimum allocation of resources would be acceptable to our
society. The problems of measurement and interpretation of the situa-
tion in this case would be the primary stumbling blocks to the accept-
ance of the proposals. In any case, the price theory of public finance
provides the theoretical framework for objectively analyzing policy pro-
posals. Whether or not the proposals would be accepted by our society
with our existing political situation can only be answered when specific
proposals are actually made.
The area of most importance to the present application of the price
theory of public finance is the discussion of concepts of public finance.
Future applications of the theory to specific allocation problems ulti-
mately depend upon whether or not economists think of public finance
in terms of applying price theory concepts to public goods. If econo-
mists discuss public finance concepts in terms of price theory concepts,
the application of the theory to specific problems will more or less nat-
urally follow.
DeViti DeMarco's work is a classic example of what can be done in
this area. The general principles of price theory analysis can be applied
to existing concepts in public finance. The basic problem lies in the
economists' existing views that the government acts in an arbitrary man-
ner not related to the demands of society for public goods and that
taxes are coercive payments. Taxes can be discussed as prices paid
for the goods and services produced by the government. The govern-
ment can be discussed as a producer of economic goods. It may be nec-
essary to recognize the fact that the political process is likely to be more
coercive than the market process in the allocation of resources. This
limitation need not interfere with discussing the production of public
goods in terms of the process being a transaction which has a payment
side and a production side that are determined by supply and demand.
Kafoglis' work in defining public goods in terms of the existence of
external economies and diseconomies is another example of what can
be done to apply price theory concepts to the discussion of concepts of
public finance. It is conceivable to define public finance as the study
of goods which have the characteristics of external economies or exter-

74

OTHER APPLICATIONS OF THE THEORY
nal diseconomies. Any good with these characteristics is of public con-
cern. It therefore may be considered as a public good even if it is not
presently produced by the government. In any case, it appears that a
great deal more work can be done in the area of defining public goods
as to the characteristics of the goods. National defense can be discussed
as a good with the characteristic of jointness of consumption. The allo-
cation of resources to national defense can be discussed in terms of the
supply and demand for national defense. That the existing political
mechanism cannot perfectly measure the demand must enter the dis-
cussion, but this need not preclude the discussion of national defense
as a public good.
The main point to be made is that the future development and ap-
plication of the voluntary exchange or price theory of public finance
depend to a large extent upon the application of the general principles
of price theory analysis to existing concepts of public finance. If and
when economists discuss taxes as prices, the government as a producer,
the activities of government as public goods, and the allocation of re-
sources by government based upon supply and demand, the price theory
of public finance will be applied to specific problems of government.

75

SELECTED BIBLIOGRAPHY

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77

THE PRICE THEORY OF VALUE IN PUBLIC FINANCE

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78

	Front Cover
	Title Page
	Table of Contents
	Front Matter
	Preface
	Introduction
	Graphical models
	Revealed preferences
	A suggested approach
	Taxes and the political proces...
	Applications of the suggested...
	Other applications of the...
	Bibliography

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