7.The Publicness of Political Decisions
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| Individuals demand certain goods and services that they supply publicly
through political rather than market organization. These goods enter as arguments in
individual utility functions, and a theory of demand can be derived. The modern theory of
public goods has been largely devoted to such derivation. If interpreted properly, this
theory provides predictive hypotheses concerning the outcomes of collective decision
processes under certain highly restrictive assumptions. At the same time and in a more
familiar context, the theory provides allocative or efficiency norms for the provision of
these goods and services. In either usage, the theory applies to any goods and
services that are, for any reason, organized publicly. The technical characteristics of
goods may and should influence the decisions on the appropriate organization of supply.
This will be discussed more fully in Chapter 9. But the theory, as such, is appropriate to
public organization for any good or service. |
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| This "publicness" in the organization of supply requires
further discussion. To the extent that decisions are made politically, regardless of their
specific content, there are "public-goods" elements present. It is in this
context that the theoretical exercises of Chapter 6 provide a useful bridge between the
analysis of private demand and that of "public supply." In a world without a
private-good numeraire, all decisions are necessarily public, whether these be concerned
with the supply of particular goods or with rules that govern behavior. For this reason,
in Chapter 6, quantities of public goods, issues and even candidates for elective office
were often used interchangeably as the objects of collective choice; deliberate ambiguity
was employed as a means of stressing the identity of the analysis in each case. |
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| Public goods and private goods are indistinguishable as they enter
individual utility functions. Individuals want different things. With privately supplied
goods, market exchange facilitates individual adjustments to preferred quantities, within
limits imposed by resource constraints, in total and in individually divisible shares. The
outcome of a private-goods trade is a changed allocation or distribution of commodities
among individual traders. The situation is quite different with public goods. The outcome
of "exchange," through some collective decision rule, is "agreement"
on the same quantity of good, to be shared by all traders and commonly consumed.
There is no individual quantity adjustment. Individual adjustments must be made in
"prices," not in quantities, if the outcomes are to be classified as efficient
in the standard sense. |
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| Earlier chapters have shown that the required differentiation in the
structure of prices for public goods may emerge as a result of "trades" among
individuals when the number in the trading process remains small. Adjustments in the
cost-shares measured in money, a perfectly divisible numeraire, will take place until
agreement is reached on a quantity of the common good. When the number of persons is
large, the autonomous emergence of such a "pricing" pattern cannot be predicted.
In the real world where public goods are shared by large numbers of persons, the
"pricing structure" must be agreed on in much the same manner as the quantity of
good to be provided. This aspect of public-goods theory has been relatively neglected,
perhaps largely because the emphasis has been placed on the derivation of efficiency norms
rather than on the processes of collective agreement. In the strictly formal sense, the
satisfaction of the necessary conditions for efficiency or optimality implies the presence
of a structure of marginal prices. When this level of formalism is dropped and the process
of reaching agreement among persons is analyzed, the problem becomes two-dimensional at
best. Agreement must be reached on the quantity of the public goods to be supplied and on
the sharing of the cost, both in total and at the margin, among separate members of the
group. |
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| To an individual, these are clearly related decisions. The amount of any
public good that he will prefer will depend on the share in its cost that he individually
must bear. Most persons would prefer a larger quantity the lower their own share in the
payment. This is a simple application of the first law of demand which, when combined with
commonality in consumption, provides the basis for the free-rider problem already
discussed in Chapter 5. It is misleading, however, in the large-number model to attempt to
derive a structure of individual shares from an analysis of offers and counter-offers.
Conceptually, this sort of analysis is possible, because individuals can make such offers
differentially in the private-goods or money numeraire, which is fully divisible among
persons, but it is relevant only when very small numbers are involved. And, in these
cases, strategic elements of behavior tend to be unduly stressed. A different analytical
framework is required for large-number settings. |
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| At one level of analysis, there seems nothing public about the
individual's own tax-share. Different individuals may be subjected to different
tax-prices; there seems to be no common sharing in the ordinary sense. However, this
approach overlooks the necessary publicness of the decision over the sharing of
public-goods cost among persons. Individuals can express their preferences, through some
voting scheme, only on tax-sharing schemes or structures. They can vote on a
whole set of tax-prices or tax-shares, total and marginal, and this set necessarily
includes not only their own liability but those for all other members of the group. It is
impossible for an individual to "offer" his own desired payment, independent of
payments to be made by all others. It is in this sense that alternative sharing schemes
are "purely public." Each person must adjust his own behavior to the same
scheme of payment; the fact that this is chosen and enforced politically insures its
publicness, despite the fact that individual payments are to be made in a fully divisible
numeraire. The scheme, or schemes when alternatives are considered, may contain widely
differing shares for different persons. Descriptively, any alternative here is a vector
with characteristics of individual tax shares as components. |
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The General Nature of Tax-Sharing Schemes
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| As the small-number trading models as well as the more formal
mathematical ones suggest, "price" differentials among separate demanders of
public goods must reflect differentials in preferences, even down to the individual level,
if the necessary conditions for optimality are to be satisfied. In large-number situations
appropriate to real-world fiscal decisions, the fine discrimination dictated by such
conditions can hardly be achieved. Not only would great difficulties be encountered in
reaching agreement, but the large number of sharing possibilities cannot even be
considered. Alternatives presented for political decision must be severely limited. This
suggests that, almost necessarily, the sharing arrangements presented will reflect
objectively determinate criteria for "price differentials." At best, therefore,
alternative tax-sharing vectors among which choice is possible will subdivide individuals
into broad groups, classified not in terms of their privately expressed public-goods
preferences but in terms of general characteristics that are presumably related to such
preferences in some representative or average sense. General criteria will be
employed to establish classificatory systems, and the satisfaction of the necessary
conditions for efficiency in public-goods supply will be approached only to the extent
that actual preferences of individuals are arrayed roughly in accord with these general
criteria. |
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| One common and almost universally used general classification relies on
the relative economic positions of individuals (families) as defined by appropriate
income-wealth measures. Personal income or wealth is taken as an externally selected
criterion for imposing relative tax-shares, and the more sophisticated fiscal theorists
have supported this procedure on the ground that this criterion does correspond roughly to
relative demands for public goods. This relationship is likely to hold only for
general-benefit goods, and only to the extent that they exhibit positive income
elasticities of demand. This seems to be one general presumption underlying modern fiscal
structures. |
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| Any general classification in which tax liabilities are related to
variables that individuals can control creates difficulties. Individuals will attempt to
reduce their relative shares in the costs of public goods by shifting their position as
defined by the basis of the sharing scheme. Such shifting can take place only within
limits, however, and the underlying classification in accordance with income-wealth
criteria is also presumed to remain relevant. Given a general income-wealth criterion,
more explicit definition of the relative shares will depend on the predicted shifts in
individual behavior, and, this aside, specific allocation of shares will arouse
disagreement, but this aspect of the problem need not be discussed at this point. |
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| Within an income-wealth classification and given some specific rate
structure, an individual's tax-share will finally be determined, not by his own particular
demand for or evaluation of the public good (or public-goods bundles) but by his position
in the private economy after he has made his tax-base adjustments. He is never in a
position where he can react to the "offers" of others in any direct sense. He
cannot express his public-goods preferences explicitly. He can, however, express these
indirectly through the political process. He can, directly or through his participation
(or nonparticipation) in electing representatives, approve or disapprove various tax-share
vectors and various proposals for public-spending programs. Preferring high levels of
public-goods supply, he will vote for larger spending projects and, perhaps, for
tax-sharing arrangements that place higher shares on his own income-wealth class. As the
analysis below will indicate, however, there is much less likelihood that individuals will
positively approve increases in their own tax-shares. |
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A Simplified Two-Person Model
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| To analyze collective agreement on both public-goods quantity and
tax-sharing arrangements, it will once again be helpful to resort to the simple two-person
model because much of the analysis carries over into the relevant many-person models. We
want to examine the behavior of two persons, High and Low, as they adjust to two public
variables: first, the quantity of public goods, and, secondly, the specific tax-sharing
scheme to finance this quantity. For simplicity in presentation, we shall assume initially
that all tax-sharing alternatives to be considered embody marginal tax-prices to
individual taxpayers that are constant over quantity. |
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| The individuals are assumed to be independently classified by their
relative economic positions. High stands high by income-wealth criteria and Low stands
low. The single public good is assumed to be beneficial to both and to have a positive
income elasticity of demand for both. |
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| Figure 7.1 |
The situation can be shown in Figure 7.1, which is related to the constructions
introduced in Chapter 6. The quantity of the public good is shown along the horizontal
axis, and is measured in dollars worth of outlay. This allows us to incorporate the costs
of the good in this variable. We assume that the unit cost of the good is fixed. Tax-share
vectors are arrayed along the vertical axis. To accomplish this, some index must be
selected. Given the various simplifications imposed on this model, the index can be a
relatively simple one measuring "share progressivity" in the tax structure. At
the origin, we locate that tax-sharing scheme which assigns to Low 100 per cent of the
total cost of the public good, regardless of the amount to be financed. At Y, the
other extreme, we locate the tax-sharing plan that assigns 100 per cent of the cost of the
public good to High, regardless of the amount to be financed. All possible sharing schemes
are arrayed between these limits. |
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| The preferences of the two individuals can be mapped onto Figure 7.1 in
the standard fashion. Low's most desired combination is likely to be located at some
point, Dl, where there is a large quantity of the good supplied but
where this is almost wholly financed by taxes levied on High. The most preferred
combination for High is less predictable, but presumably at some point, Dh,
he will desire a relatively large quantity of the public good that is financed through a
tax-sharing scheme that keeps his own share relatively low. The probable presence of
certain equity considerations in High's utility function insures that his optimally
preferred position will lie somewhere above the horizontal axis. |
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| Following the construction of Chapter 6, lines of optima may be drawn in
Figure 7.1. The shapes of these under our set of assumptions seem predictable. Low's line
of public-goods optima will take the general shape shown by 0Plp.
This indicates the amount of public good which Low will optimally prefer at all possible
tax-share arrangements arrayed in accordance with the share progressivity index. Clearly,
this line will be positively sloped, indicating that Low will desire a larger quantity of
the public good as his own share in the cost is reduced and High's share increased. It
also seems reasonable to expect that this line of optima for Low will have some positive
intercept on the vertical axis. This indicates that, at some level of the tax-share index,
he will prefer to forego completely the benefits of the public good because his own
payment becomes too large, and competing demands on his resources make him unwilling to
pay for the public good at these levels of taxation. |
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| High's comparable public-goods line of optima will tend to be negatively
sloped, but the absolute value of the slope will perhaps be somewhat higher than that for
Low. The line of optima may not intersect the vertical axis below Y, suggesting
that High may be willing to finance a certain quantity of the good even if he is forced to
bear the full costs. As his cost-shares fall below this level, he will prefer larger
amounts of the good, but, as the absolute slope indicates, he will be less sensitive than
Low to his share in the payment. |
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| Lines of tax-share optima can also be derived from the indifference
contours and these are drawn in as 0Plt and 0Pht
on Figure 7.1. Low will clearly prefer a tax-sharing scheme that will at all levels of
provision impose the predominant share of the cost on High. High may accept larger shares
of public-goods costs at lower budgetary levels than at higher ones. To indicate this
possibility his line of tax-share optima is drawn with a slight downslope. |
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| If one of the two persons should be assigned the decision authority over
tax shares and the other over public-goods quantity, the resulting equilibrium would be
either at M or at N. In either case, the result would be extremely
inefficient and would allow for a relatively small total outlay. |
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| Significant differences are to be noted in the relative positions of the
two lines of optima in each case, and this is important for the theory of collective
agreement. Note that the lines of optima for the two persons, with respect to the
preferred quantities of public goods, intersect at B. There is no comparable
intersection of the tax-share lines of optima. At the tax-sharing scheme, Y0,
both parties will agree on a most desired public outlay. This defines a Pareto-optimal
solution, given the limitations imposed on this model. Note that, at B, the
public-goods lines of optima intersect and also cut the contract locus. All points on this
locus are, of course, Pareto-optimal in the larger sense. These include the extreme
limits, Dh and Dl, one of which would prevail should
all decision power be vested in one man. The position shown at B, however, seems to
embody "reasonableness" characteristics for a solution not possessed by other
positions on the locus. If the two persons commence at the origin, where none of the
public good is being provided, B seems to be a reasonable outcome of negotiations
on both variables, since it is the maximum public-goods quantity upon which the two
persons can reach agreement given a unique tax-sharing scheme. This scheme reflects the
precise structure of "price differentials" to bring public-goods preferences
into agreement. |
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| Note that at B, the lines of tax-share optima remain widely
separated. There is no comparable agreement on this variable subject to collective choice.
The reason is that this variable is almost purely distributional; an increase in one
person's tax-share reduces that of the other. At any level of outlay, either person would
prefer to secure that outlay at a lower rather than at a higher cost to himself. |
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| It is interesting to examine Wicksell's unanimity proposals within this
framework. He suggested that for each expenditure proposal advanced, an array of
tax-sharing schemes should be considered, and unless at least one such scheme could secure
unanimous approval the expenditure should not be made. Suppose that, in terms of Figure
7.1, an initial proposal is made to spend an amount X1 on the public
good. Tax-sharing schemes are presented along with this spending proposal. In this
context, any tax-sharing scheme falling between Y1 and Y may be
approved by both parties, ignoring purely strategic behavior. For an amount of spending, X1,
High would, if necessary, finance the whole cost. Similarly, Low would, if necessary, pay
a major share as indicated in the scheme at Y1. Agreement becomes
possible, on some tax-sharing arrangement and on the spending proposal, anywhere
between these limits. Having adopted this initial spending proposal, suppose that a
further proposal is made in the second round to expand the level of outlay incrementally.
Agreement remains possible, with many alternative sharing schemes on such increments, but
the multiplicity of possible arrangements diminishes rapidly as X0 is
approached. At the margin, at X0, only one sharing scheme can command
the approval of both parties, that shown by Y0. For all proposals to
expand spending beyond X0, no sharing scheme will command the approval
of both parties. |
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| The position shown at B is, therefore, the uniquely determinate
Wicksellian solution to the problem of public-goods allocation and tax-sharing, given the
restrictions of our model. These restrictions include constant marginal tax-shares over
quantity. This particular restriction can be relaxed; the construction remains useful, but
only if income-effect feedbacks on individual preferences are neglected. In this case, the
solution is determinate in terms of marginal tax-shares and public-goods outlay.
Any number of sharing schemes over inframarginal units becomes possible. If income-effects
are taken into consideration, no such determinacy can be represented diagrammatically. |
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| It may also be useful to compare, in a general way, these results with
those suggested in the familiar set of efficiency norms advanced by Samuelson. These are
stated as marginal conditions that must be satisfied for optimality and do not include
explicit reference to total conditions. A uniquely determinate result is attained only by
resort to an externally derived "social welfare function" which does, of course,
specify the final distribution of "welfare." Almost by definition, the necessary
marginal conditions are satisfied at any point on the contract locus between Dh
and Dl in Figure 7.1. Samuelson then calls upon the social welfare
function to select from among these points. He does not deal with the processes of
reaching agreement on specific outcomes. |
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Extension to Three-Person Models
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| Only within two-person limits is the analysis of collective agreement on
the two fiscal variables wholly free of complexities which would tend to obscure the
essential elements under discussion if introduced too early. These complexities arise in
three-person models and are compounded as the analysis is extended to larger groups. |
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| As shown in the exercises of Chapter 6, no problem arises in adding
utility-function mappings for other persons onto a construction similar to Figure 7.1, provided
that the variables are treated as purely collective or public goods. We have argued above
that all individuals must adjust to a common tax-sharing arrangement or tax structure and
that, despite the divisibility of individual tax-shares, these structures can best be
analyzed as if they are public goods (or public bads). This creates no problems in a
purely formal sense, but serious difficulties arise in any analysis of a group decision
process. |
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| These stem from attempts to array tax-share vectors on the vertical axis
in such a way that, as between this variable and the public-goods variable measured along
the horizontal axis, individual preference mappings exhibit the standard properties of
convexity. This task of arraying tax-share vectors is greatly simplified in the two-person
case. Here individual shares in cost must be strictly related, one to the other. Since the
total must sum to unity, an increase in the share of one person can only mean a decrease, pari
passu, in the share of the second. The utility functions of both persons defined on
the two variables, public-goods outlay and an index of tax-share vectors, can be expected
to exhibit the standard properties. |
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| With three persons, no such one-to-one correspondence among individual
shares can exist; an increase in the tax-share for one person may be accompanied by a
decrease in the share of either one or both of the other two persons. For
any one person, it is possible to array tax-share vectors in such a way that a utility
mapping will exhibit convexity. But it will not be possible, in the general case, that
this same index will allow for convexity in the mappings for all three persons. |
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| To resolve this difficulty let us first place one additional restriction
on the set of tax-sharing arrangements to be considered. Plausibly, we impose the
requirement that cost-shares shall not be related inversely to the external criterion that
is used to classify persons or groups. If income is used here, this restriction suggests
only that those persons with lower incomes shall not be required to contribute cost-shares
higher than persons standing above them on the independent income scale, regardless of
relative preferences for public goods. In any real-world context, no tax-sharing
arrangement is likely to violate this additional restriction, although, in a formal sense,
particular configurations of public-goods preferences may make adherence to this
restriction produce inefficient results per se. These latter possibilities have,
however, already been ruled out by our earlier assumption that for each person there is a
positive income elasticity of demand for the public good. The practical effect of this
restriction is that the alternative standing lowest on the tax-vector index is defined by
equal sharing among all persons in the group. |
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| (a) Symmetry with respect to median income
With this restriction, we can now examine the three-person model first under an extremely
helpful, and not implausible, simplifying assumption that further limits the set of
tax-sharing arrangements to be considered as alternatives. We assume that the share of the
median-income person in the three-person group shall remain unchanged over all possible
arrangements. In an earlier work, I have referred to this characteristic as symmetry with
respect to the median-income person. An arithmetical example will clarify the precise
meaning here. As suggested, the lowest point on the index will represent a vector
indicating equal tax-shares, or vector (1/3, 1/3, 1/3) . As we move up the index or scale,
the share of the low-income man decreases and the share of the high-income man increases,
but the share of the median man remains unchanged at one-third. The highest point on the
index is represented by the vector (0, 1/3, 2/3) . This simplification, in effect,
converts the three-person model into the two-person one. |
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| Figure 7.2 |
Geometrical representation is in Figure 7.2. The situations of two of the three
persons, Low and High, are substantially identical with those in Figure 7.1. For the third
man, Median, only one of the two dimensions is intensively relevant. Since he will, under
our assumption, pay one-third of the cost of the public good, regardless of the
distribution of the remaining two-thirds among his two colleagues, he will tend to prefer
approximately the same level of public-goods outlay at all tax-sharing schemes. If we
allow him to exhibit some concern for distributional consequences, we may locate his most
preferred single combination at Dm, somewhat nearer to the upper bound
of the tax-vector set than to the lower. At best, however, we should expect his
indifference contours to be elongated, and his public-goods line of optima to be steep, as
shown by 0Pmp. If Median is concerned exclusively with his
own share, there will be no tax-share line of optima, but, again, if we allow for some
distributional motivation, this line may lie roughly as shown by 0Pmt
in Figure 7.2. |
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| With this setting, what can be predicted to emerge as a result of
collective-choice processes? The contract surface takes the shape enclosed by the heavy
solid lines of Figure 7.2. Let us initially consider the predicted outcome when the two
variables are decided upon separately and by simple-majority voting rules. As the analysis
of Chapter 6 showed, the solution in this case is given by the intersection of middle
lines of optima, shown at Dm. In the configuration as drawn, this
process of decision effectively allows Median to dictate the community outcome for both
variables. He attains his "peak" level of preference. At this solution, there
will be widespread disagreement concerning the most preferred public-goods outlay. With a
tax-sharing scheme presented at Y2, High will prefer a much smaller
budget, while Low will prefer a much larger one. Wicksellian unanimity is far from being
achieved in the shift to this solution. |
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| Consider now a modification in the decision rules that allows for
simultaneous consideration of both variables, again under simple-majority voting rules.
Suppose that the solution at Dm has been provisionally stabilized and
that a coalition between High and Low forms and proposes a shift to G. Clearly,
both men will benefit, Low accepting a somewhat larger share in cost in exchange for
High's agreement for an expanded public-goods outlay. This position, at G, will
not, of course, be majority-stable. Cyclical shifts can take place within and upon the
bounds of the contract surface. Certain plausible restrictions can be placed on such moves
in the particular configuration of Figure 7.2. Median is primarily if not exclusively
interested in shifting horizontally; he is relatively indifferent as between vertical
alternatives, at any level. Accordingly, High is much more likely to succeed in forming a
new coalition with Median to organize shifts away from G. If he does so, some shift
to a new position, say E, will take place. This will be somewhat closer to a
Wicksellian solution in that the disagreement over public-goods quantity will be
substantially less intense at this point than at Dm or at G.
However, this position, E, is not majority-stable either, and further shifts can be
made. |
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| A similar analysis could, of course, be carried out no matter where the
lines of optima should be located for Median with respect to those for the other two
persons. |
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| The construction suggests that majority-decision rules, whether these
involve separate consideration of issues or simultaneous consideration, will not produce
solutions that will be accepted by all parties, save in some constitutional sense of
acquiescence. The result produced by majority voting may, as in the above examples,
qualify as a Pareto-optimal position once it is attained, but it cannot be attained
Pareto-optimally. Distributional elements will necessarily be present in the decision
process. These are, of course, likely to be omnipresent in real-world fiscal choices and
to this extent the model is highly realistic, but it will be useful to examine the
Wicksellian unanimity rule as an alternative in this particular submodel. |
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| As drawn, there is no Wicksellian solution in the strictly marginal sense
as discussed in connection with Figure 7.1. For public-goods outlay proposals up to X3,
there are many tax-sharing schemes that will be accepted. Beyond X3,
disagreement appears; Median objects to further outlay, and given the limits on the
tax-sharing vectors imposed by our symmetry assumption, no further moves can be made with
general consent. A proximate Wicksellian solution is, therefore, attainable at an outlay, X3,
and a tax-sharing scheme, Y3. |
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| (b) Lexicographic ordering
Symmetry in share progressivity with respect to median income is unduly restrictive. Some
attempt must be made to construct an index of tax-share vectors without this crutch. We
propose to construct an index that will reflect a lexicographic ordering of the vectors.
As before, we retain the restriction that the lowest vector on the scale will be that
which indicates equal sharing among all members of the community. Above this, we first
array all possible vectors in subsets classified Low's share, in ascending order as this
share falls. The vectors in each of these subsets will represent different means of
residual sharing between Median and High. Within each of these subsets, we then array
vectors in ascending order as Median's share falls. This type of ordering can be extended
to any number of persons and can include all possible tax-sharing schemes, given the
initial restrictions imposed on all of the models. |
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| An arithmetical illustration of this ordering will be helpful. Assume
that a possible set of tax-share vectors to be ordered is:
(.1, .3, .6) (.2, .4, .4) (.1, .2, .7) (.1, .4, .5) (.2, .3, .5) (.1, .1, .8) (.2, .2,
.6)
Arraying these along a vertical scale we get:
| g |
(.1, .1, .8) |
| f |
(.1, .2, .7) |
| e |
(.1, .3, .6) |
| d |
(.1, .4, .5) |
| c |
(.2, .2, .6) |
| b |
(.2, .3, .5) |
| a |
(.2, .4, .4) |
This procedure generates a systematic ordering of all possible vectors, but it does not
eliminate the convexity problem. Consider the limited array above. Note that Median pays a
larger tax-share in both d and e than he does in c, while High pays a
lower tax-share in d than he does in c. For both Median and High, preference
mappings will exhibit nonconvexity. |
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| Figure 7.3 |
Figure 7.3 depicts the likely pattern of indifference contours for High. His optimally
preferred combination is shown at Dh, located roughly in the same
position as before. Note, however, that local peaks will occur at D', D'',
and D‴. As abrupt shifts are made from one subset to another, High's
utility is increased, locally, despite the general decline in his utility as his position
is moved northwestward. For example, at D'', because of the shift of subset, he may
be brought suddenly back to a level of utility equal to that attained on the contour I'.
The public-goods line of optima for High will roughly follow the pattern shown by the
dotted line on Figure 7.3. This lies within an area confined by the two solid lines, and
the width of this area progressively widens as we move vertically up the figure. This is
because of the greater range of distributional splits between Median and High as Low's
share is reduced. |
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| Figure 7.4 |
Figure 7.4 depicts, in similar way, the utility mapping for Median. As shifts are made
between subsets classified by Low's share, Median will also confront "cliffs,"
and his preference surface will exhibit local peaks at D', D'', and D‴.
Because of the ordering scheme used, these local cliffs will be facing opposite to those
of High. This can be noted in the arithmetical array. As a shift is made from c to d,
Median's share increases despite the decrease in his minimal share as we shift up
the scale. By contrast, High's share decreases, despite the increase in his maximum
share as we move up the same scale. |
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| Figure 7.5 |
The whole analysis is combined in Figure 7.5. As drawn, there is a broad range of
possible intersections between the public-goods lines of optima for High and Median.
Positions in the shaded area will not insure agreement between these two persons. But a
position in this intersection does suggest that agreement may be produced by appropriately
organized, and possibly minimal, changes in the tax-sharing arrangements. These can be of
a localized sort and Low's tax-share need not be modified. If Low's line of public-goods
optima cuts through this broad intersection, general agreement among all three parties
seems possible. Some approximation to a Wicksellian solution can be realized in such
cases. |
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| Note that there is not likely to be agreement on tax-sharing schemes,
even given a possible agreement on public-goods outlay. This conclusion resembles that
reached in the earlier and simpler models. Also, if the two decisions, one on public-goods
outlay and the other on the tax-sharing arrangement, should be taken separately and if
majority rule prevails, the result may tend to be in the vicinity of Dm,
also suggested by the earlier models. |
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| This model should not be treated with great respect for its helpfulness,
but neither should its suggestiveness be wholly neglected. The complexities that arise in
the analysis of agreement should not obscure the underlying need to analyze the agreement
processes. The problem to be analyzed is surely present under some circumstances.
Agreement must be reached on both of the variables and many more besides, and these surely
contain "publicness" elements in that all members of the community must adjust
to the result. |
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| As additional persons are added to the model, the ordering becomes more
difficult, although the lexicographic method can formally be used for any number.
Geometrical representation becomes messy, but the essentials of the analysis are not
changed. As additional public goods, rules or institutions are taken into account, the
prospects for agreement tend to increase in the relative sense discussed in Chapter 6. |
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| Perhaps the test of usefulness for the models of this chapter is the
question: Are hypotheses implied that can be tested by observations? Conceptually, tests
can be made to determine to what extent the real-world solutions meet Wicksellian
criteria. If, given the budgetary level and the tax-sharing scheme in existence, there is
observed to be widespread disagreement concerning budgetary size and if this disagreement
tends to be inversely related to level of income, this would provide strong evidence that
a solution approximated by Dm is present. On the other hand, if the
disagreement over budgetary size should be unrelated to income level, and if this
disagreement should, in some relative sense, be minor, strong evidence is provided that
some approximation to the Wicksellian results is achieved. Such evidence could never be
conclusive, of course, because of the many alternative explanatory models that could be
developed. It is worth recalling at this point that J. K. Galbraith, in his famous
argument over the poverty of the public sector, implicitly assumed that the sustained
budgetary position was of the sort depicted at Dm on the figures. The
tax-sharing arrangement in being was held to prevent majority approval for the expanded
spending programs that he considered to be desirable. His remedy was fully consistent with
the analysis of this chapter. He proposed a substantial downward shift in the scale of
tax-sharing in order to achieve the required approval for larger spending programs. |
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Private Decisions and Public Goods
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| This chapter draws attention to an important element of individual
participation in collective choice that tends to be neglected in the theory of public
goods in the standard sense. This neglect is evidenced in earlier chapters of this book as
well as in the works of other scholars. Individual demand for a public good is derived
from a utility function that does not include arguments for the cost-shares or tax-shares
to be paid by other members of the community. Conceptually, an individual marginal
evaluation schedule (or demand schedule under the appropriately restricted assumptions) is
related to tax-prices or tax-price offers. This schedule allows us to talk about the
behavior of the individual in "voting for" or "voting against"
particular spending proposals. In this analysis, it is acknowledged that individuals
cannot privately select preferred outcomes and that these must be determined by some group
decision rule. But the analysis does purport to explain individual participation in this
process, and, in this elementary explanation, individual demands are related only to
tax-prices or tax-price offers in the direct and explicit sense. |
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| The neglected element is the "publicness" of the tax-share
choice. The individual chooses public-goods quantities, not only in relation to the total
and marginal tax-prices that he expects to be confronted with, but also in some relation
to the whole tax-sharing scheme or arrangement which allocates tax-shares between himself
and other members of the group. Introspective experiment can make the importance of this
element clear. Consider your own possible participation in, say, a community referendum on
a proposed public outlay for improvement in municipal park facilities. Suppose that your
own share in the tax-cost is equivalent under two separate financing alternatives.
Suppose, however, that one of these alternatives exempts all high-income persons from
taxation while the other scheme exempts all low-income persons. It seems evident that you
will have some definite preferences as between the two tax-sharing schemes, a preference
which you are required to express if these alternatives are themselves presented for group
choice. |
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| The publicness of tax-sharing arrangements requires that the individual
pay some attention to the whole structure of payments. Recognition of the possible
influence of this element on his behavior should not, however, blind us to the primary
significance of his own tax-share in determining his behavior pattern. The theory of
public goods remains incomplete when this element is wholly neglected, but such neglect is
justified in the preliminary stages of inquiry when the purpose is that of isolating the
most important influence on the demand for public goods. |
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| In choosing both a quantity of public goods and a tax-sharing scheme for
financing this quantity, the individual participates in a collective decision process that
he recognizes as such. He is choosing for others as well as for himself. This very
setting will tend to make him consider the relative positions of others. This situation
may be compared with that faced by the individual in competitive market organization. In
the latter, he does not explicitly recognize the indirect effect that his behavior will
exert on others in the community. He tends to behave as if his actions exert no such
influence. There is no explicit publicness in his choice calculus. The distinction between
individual positions in these two situations provides the basis for some of the
traditional socialist criticism of market order. The argument here, in summary, is that
individuals, if forced to choose for the group, will surely widen their range of
consideration. An acknowledgement of some difference in probable motivation for
behavior in the two cases is not the same thing, however, as an acknowledgement of categorical
difference. If, in fact, individuals could be predicted to choose among "public"
alternatives on the basis of their own versions of group rather than an individual
interest, we could discard much of the theory of public goods and of welfare economics,
and devote time exclusively to analyses of the sort contained in Chapters 7 and 8.
Conflicts would arise to the extent that personal definitions of group interest differ,
and utility functions of the standard variety simply would not exist. |
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| The geometrical constructions of Chapter 7 are derived, generally, from
the works cited previously in connection with Chapter 6, primarily those of Duncan Black.
For the particular applications to the simultaneous choice of public-goods outlay and
tax-sharing schemes, the constructions for the two-person model closely parallel those
presented by Leif Johansen ["Some Notes on the Lindahl Theory of Determination of
Public Expenditures," International Economic Review, IV (September 1963),
346-58]. Figure 7.1, in the text, is substantially equivalent to Johansen's Figure 3.
Although Johansen does not extend his formal analysis beyond the two-person (two-group)
model, some of his critical comments on the Lindahl model, generally, are also relevant to
the discussion of this chapter. In his book [Public Economics (Chicago: Rand
McNally, 1965)], notably Chapter 6, Johansen's geometrical construction is less detailed,
although other comments are expanded beyond those in his paper. |
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| Johansen's point of departure is Erik Lindahl's classic work [Die
Gerechtigkeit der Besteuerung (Lund, 1919), relevant portions of which are translated
as: "Just TaxationA Positive Solution," and published in Classics in
the Theory of Public Finance, edited by R. A. Musgrave and A. T. Peacock (London:
Macmillan, 1958), pp. 168-76]. Lindahl's later papers are also relevant ["Some
Controversial Questions in the Theory of Taxation," as translated into English from
the German and also published in Classics in the Theory of Public Finance; also
see, "Tax Principles and Tax Policy," International Economic Papers, No.
10 (London: Macmillan, 1959), pp. 7-23]. R. A. Musgrave summarizes the basic Lindahl
contribution in his treatise [The Theory of Public Finance (New York: McGraw-Hill,
1959), pp. 74-78]. In an earlier paper, Musgrave discussed the Lindahl theory in some
detail ["The Voluntary Exchange Theory of Public Economy," Quarterly Journal
of Economics, LIII (February 1938), 213-37]. A more recent and more exhaustive
discussion of Lindahl's contribution, along with consideration of possible criticisms, has
been published by J. G. Head ["Lindahl's Theory of the Budget," Finanzarchiv,
Band 23, Heft 4 (October 1964), 422-54]. |
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| As several critics have noted, Lindahl's theory suffers in its extension
to the political decision process. It is in this respect that Wicksell's seminal
contribution seems superior. Wicksell was concerned with potentially applicable rules for
making political choices on both public-goods outlay and on tax-sharing arrangements, and
he did not develop his theory in an explicit two-person bargaining context. |
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| Howard Bowen, in his early contribution to the modern theory, set the
whole problem in a political context ["Voting and the Allocation of Resources," Quarterly
Journal of Economics, LVIII (November 1943), 27-48, substantially reprinted in Toward
Social Economy (New York: Rinehart, 1948), pp. 172-98]. In his treatise, Musgrave
devotes a chapter to "Budget Determination Through Voting" [The Theory of
Public Finance, Ch. 6]. Some parts of Musgrave's discussion are directly relevant to
the material covered in Chapter 7. |
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| The most complete treatment of tax systems, considered as
"public," is contained in the work of Charles J. Goetz [Tax Preferences in a
Collective Decision-Making Context (Ph.D. dissertation, University of Virginia, 1965,
available through University Microfilms, Ann Arbor, Michigan)]. Goetz examines group
agreement on tax systems largely independent of group agreement on public-goods outlay,
except as the recognition of underlying interdependence affects individual preference
patterns. One portion of Goetz's argument was published earlier ["A Variable-Tax
Model of Intersectoral Allocation," Public Finance, XIX (No. 1, 1964), 29-41].
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| The possible differences between individual behavior in the choice of
private goods and in the choice of public "goods" was stressed by William J.
Baumol [Welfare Economics and the Theory of the State (Cambridge: Harvard
University Press, 1952; Second revised edition, 1965)]. In an early paper of my own, I
attempted to examine these differences in some detail ["Individual Choice in Voting
and the Market," Journal of Political Economy, LXII (August 1954), 334-43,
reprinted in Fiscal Theory and Political Economy (Chapel Hill: University of North
Carolina Press, 1960), pp. 90-104]. The indirectness of the effects of individual behavior
in the market process and its effect is discussed in the book by Robert A. Dahl and C. E.
Lindblom [Politics, Economics, and Welfare (New York: Harper, 1953)]. In a
relatively recent paper, I have discussed some of the consequences for modern welfare
economics arising out of the presumed categorical differences in individual behavior in
voting and market processes ["Politics, Policy, and the Pigovian Margins," Economica,
XXIX (February 1962), 17-28]. |
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| Recent works, in preliminary form, by Robert Dorfman and by Martin Shubik
examine aspects of public-goods theory in a collective-choice setting [Dorfman,
"General Equilibrium with Public Goods," Working Paper No. 95, Institute of
Business and Economic Research, University of California at Berkeley, June 1966; Shubik,
"Notes on the Taxonomy of Problems Concerning Public Goods," AD 633 546, Defense
Documentation Center, April 1966]. Albert Breton has attempted to relate the theory of
public goods to the theory of collective decision-making ["A Theory of the Demand for
Public Goods," Canadian Journal of Economics and Political Science, XXXII
(January 1966), 455-67]. |
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