PUBLIC GOODS AN PUBLICLY PROVIDE PRIVATE GOODS
PUBLIC GOODS
AN PUBLICLY PROVIDE PRIVATE GOODS
INTODUCTION
This Lecture deals with the public
provision of goods and services. We are concerned with four basic questions:
1. How
do we characterize those goods that are, or ought to be provided publicly?
2. If
the government knew the preference of all members of society, how ought the
supply of each of the public goods to be determined?
3. How
are the supplies of public goods in fact determined, and how does this contrast
with the optimal provision?
4. How
can the government ascertain the preferences of the members of society
regarding the provision of public goods?
The questions
are considerable importance and have generated a great deal of controversy. There
are those who claim that the government is engaged in supplying goods that
ought to be privately marketed, for instance, that education ought to be
privately rather than publicly provided. There are others who claim that public
programmes receive insufficient funds and that there are activities at present
privately supplied that ought to be provided by government. What we shall have
to say here does not resolve these controversies, but we believe that a careful
consideration the kinds of issue treated in this Lecture will have focus the debate.
At the outset we
need to make an important distinction, between public production and public provision. The two are often confused, though
both logically and in practice they are distinct. The government provides for
the national Defence, yet much of the production of the goods purchased for
national defence is within the private sector. The government has, in many
countries, amonopoly of the mail service, yet in charges for the use of mail a
manner little different from that of private enterprise. In the previeus
Lecture we dealt with the pricing of publicly produced commodities; here are
concerned with goods and services that are provided freely, perhaps a rationed
amounts, to all members of society. (we are also at this stage concerned with
public goods are discussed in the next Lecture) .
Characteristics
of Publicly Provided Goods
The free provision of goods may be seen
as the limiting case of subsidization. i.e., the delivery to consumers of
commodities at price below the cost of production. In this sense, the analysis
of this Lecture, and that of public sector pricing, are aspect of the same
subject. There is however a distinct feature of public provision which approach
does not capture and which is focus of much of our discussion: with public
provision there is not necessary any monitoring of usage, whereas with any
price, positive or negative, usage must be recorded.
The
issue of monitoring usage introduces the first aspect that is relevant to
characterizing those goods that are or ought to be publicly provided: it may be
impossible, or extremely costly, to charge for the use of specified commodity.
In other words, it may not be possible to exclude
non-contributors. This is essentially a technical question, and depends on the
available technology. In the case of television, calculation of the extent of
use depends on it being possible to determine from outside whether the receiver
is in operation or no the employment of scrambling devices. It has been suggested
that automatic metering devices could be installed to record the passage of
vehicle through the highways system and that with large scale computer networks
it would be feasible to charge for actual usage. For some goods, such as
national defence, it is hard to imagine that even future developments in
information processing will allow individual benefit to be determined; so that
for these exclusion is indeed impossible.[1]
Where
exclusion is not technically impossible it may still be decided to supply the
good publicly, for reasons parallel to those discussed earlier in other
contexts. The first is that it may not be desirable on efficiency grounds to use prices to govern the usage of commodity.
The effects of charging depend on (1) the conditions of demand and (2) the
conditions on which the good can be supplied to additional individual. If the demand is high inelastic, there is
no efficiency loss from not charging for the commodity (although there may be
other arguments, such as raising revenue, as we have seen). Many place do not
charge for the quantity water used, because it is judged that the benefits for
metering would be relatively small, demands not being very elastic, and
insufficient to warrar the installation of metering devices. (there may also be
external economic in consumption-at least, that was an important historical
reason for public provision).
Standard
discussions tend in effect to focus on the second aspect- that usage by one
person does not reduce the amount that other can consumer. In the words, the
cost of supplying a fixed quantity to another individual is zero. Examples typically given include television
programmes (my listening to a TV programme transmited over the airwaves does no
deract from other listening); information (my knowing something does no deract
from others knowing the same thing); and national defence. These are extreme
cases, and are referred to as pure
public goods, where “each individual’s consumption” (Samuelson, 1954, p. 387).
More generally, there is arrange of commodities that have the property that an
increase in the person’s consumption (keeping aggregate expenditure on the
commodity constant) may not decrease the consumption of the other people by the
same amount. If one person travels on a little-used highway, the benefits of
the road to others are reduced only slightly.
On
this view, private goods are at one extreme of a spectrum, where an increase of
one unit in the consumption by Mr X reduces the consumption available to the
others by one unit; and pure public goods at the other extreme, where an
increase in Mr X’s consumption leads to no reduction for others. These polar
cases are sometimes characterized in the following way. Let
be the consumption by household h of the ith commodity. Then for private goods,
be the consumption by household h of the ith commodity. Then for private goods,
(16-1)
Where Xi
is the aggregate supply. In contrast, for a pure public good,
all h (16-2)
It may be noted that his assumes no free disposal. For many public goods,
such as defence, this may not be an unreasonable assumption; on the other hand,
for goods such as television, free disposal is possible, and (16-2) should be
replaced by
all h (16-2’)
The intermediated case are somewhat
harder to characterize, and various approaches have been suggested in the
literature. One is to write the consumption possibility frontier for economy as
being for good i:
(16-2)
with
Private good
|
Pure Public good
|
450
|
Consumption of good i by household k
Figure Public
and private goods.
These are illustrated in fig, 16-1 and
the reader is invited to consider how intermediate cases can be handled. An
alternative approach is in term of consumption externalities (as discussed in
Lecture 14), and this has been developed by Samuelson (1969). In this case the
purchase of good i by household h may enter the utility function of the
other individuals.
In
both cases, we have a problem of defining what it is that is being consumed,
and how it is to be measured. For instance, for television and radio
broadcasts, the obvious unit to measure consumption is “programmes listened
to”. In this case, the first approach seems more natural. On the other hand, if
individuals privately purchase protective services (e.g., police guards),
utility may be a function of the level of “safety” in the community which may
be function of the aggregate expenditure on protective services, as well as on
the private level of protection. Individuals, in providing protection for
themselves (and thus lowering the return to crime), are providing a public good
(safety), and the consumption externalities representation seem natural. This
problem can however be reformulated in terms of our first approach, although
one must be careful how this is done. For instance, if P represents the total number of policemen available, and Ph household h, then
= P, and police appear to be a private
good, yielding consumption externalities. If however what is consumed
(negatively) is the expected number of crimes suffered by household h, denoted by Ch, then we have a consumption possibilities curve
all h (16-4)
Where an increase in the number of
policemen reduces the crimes committed.
The
third set of reasons for public provision relates to distributional objectives.
This may stem either from a general distributional goal, for example embodied
in a social welfare function, or from principles of specific egalitarianism as
discussed in Lecture 11. Thus, distributional reasons are probably the primary
rationale for the public provision of education-either because it reduces
inequality of endowments, or because access to at least a minimum level of
education is an objective in itself this commodity an optimal non linear price
function. For certain goods, that function may have the characteristic that no
price is charged for consumption below a specified minimum.
We
have tried to bring out some of the features that characterize goods that may
be publicly provided. In determining whether or not they are supplied in this
way, the various factors are likely to be of differing importance. In table
16-1 we have listed some of the goods that are commonly, but not necessary
universally, publicly provided. In each case, one can ask whether exclusion is
feasible (at reasonable cost), what are the properties of demand, what are the
cost of supplying to the individual, and whether there are likely to be
distributional arguments. For the first six, we have suggested our own
judgement; the reader may like to consider how far he agrees, and to complete
the remainder.
In what follows, we concentrate
particularly on the cases that are at the extreme ends of the spectrum for the
cost of indivisual spply. In sections 16-2 and 16-3, we consider the provision
of the pure public goods; in 16-4 we take the opposite extreme of publicly
provided private goods. These sections are concerned with the arguments
regarding the optimum level of provision, and-in the case of publicy provided
private goods-its allocation among individuals, on the assumption that the
government has full information about individual preferences and endowments.
The actual procedures by which public spending decision may be effected, and
preferences revealed, are the subject of Section 16-5 and 16-6.
Table Characteristic of publicy
supplied goods
Table Experimental
evidence on willingness to pay
Costly
exclusion
|
Demand
irresponsive
|
Low cost of
individual supply
|
Distributional
arguments
|
|
?
|
?
|
?
|
?
|
|
National
defence
Roads and
bridges
TV and radio
Education
Water
police
|
Yes
Yes
Yes ?
Yes
|
Yes
Yes
|
Yes
Yes ?
Yes
Yes
|
Yes
Yes ?
Yes
|
Medical care
Fire
protection
Legal system – criminal case
– civil cases
Leverage and rubbish
National park
|
16-2 OPTIMUM PROVISION OF PURE PUBLIC
GOODS-EFFICIENCY
In
this section we consider the optimum level of provision of a single, pure
public good, consumed in quantity G by everyone. There is an aggregate
production relationship :
F (X,G) = 0 (16-5)
Where
X denotes the vector of total
private good production.
Firs-Best Allocation
The
goverment of fully controlled economy is assumed to choose the level of G, and
the allocation of private Xh to household h (where h = 1…….H) to maximize an individualistic social
welfare function.[2]
If the individual utility function is Uh(Xh.G).
then the social welfare function ma be written as
[U 1,…, U h,…, U H] (16-6)
where
is assumed to be a twice differentiable,
concave function an to be increasing in all arguments. If we form the
Langrangean
=
– λF (X, G) (16-7)
the
first-order conditions are
(X,G) = 0 (16-8a)
F (X,G) = 0 (16-8b)
The
condition (16-8a) yields the standard first-best welfare conditions (equality
of marginal rates of substitution and transformation). The new condition is
(16-8b).
From
(16-8a) we can see that (i.e., the left-hand side is the same for all h). we can then divide the hth term in the sum on the left-hand
side of (16-8b) by giving
This
is the basic condition for the optimum supply of public goods : the sum of the marginal rates of substitution between the public
good (and some private good) must equal the marginal rate of transformation
(∑MRS = MRT). There is a clear intuitive interpretation of these conditions for
a full optimum. The marginal benefit of an extra unit of a public goods is the
benefit that person 1 gets, plus the benefit that person to gets, etc. in contrast,
an extra unit of a private good is either given to person 1 or given to person
2.
The
solution may be illustrated diagrammatically foe the case where there are two
individuals and two goods (X = private good, G = pure public good). Figure 16-2
shows in the upper part in the indifference curves for citizen I and the
production constraint AB. Suppose we
fix citizen I on the indifference curve UI.
the possibilities the citizen II are shown in the lower part of Fig. 16-2 by CD (the different between AB and UI). Clearly, pareto efficiency requires the marginal
rate of substitution of the second individual be equal to the slope of the
curve CD (i.e., at point E). but this is just the difference
between the marginal rate of transformation (the slope of the production
possibilities schedule) and the marginal rate of substitution of the first
individual (the slope of his indifference curve). Thus, we have
MRS11
= MRT-MRS1
A
|
B
|
Public good
|
D
|
C
|
Public good
|
XII
|
UI
|
G
|
XI
|
Figure
16-2 optimum provision of public goods-two-person example.
MRS1
+ MRS11 = MRT
The
sum of the marginal rates of substitution must equal the marginal rate of
transformation.[3]
The
analysis so far has been conducted in terms of a fully controlled economy. It
is however equivalent to the situation
in a competitive economy where the government is able to levy first-best
lump-sum taxes, both to finance the expenditure and to redistribute income. As
in earlier Lectures, we need to ask aht happens when first-base taxation is not
possible. In the remainder of this section, we consider the efficiency aspect,
taking for this purpose the case where individuals are all identical ; in the next
section, we take up the issue of redistribution.
Financing
of Public Goods by Distortinary Taxation
When
the public expenditure is financed by taxes that generate an excess burden, it
appears likely on intuitive groundsthat the rule of equating ∑MRS with MRT
will lead to too high a level of spending. As it was put by Pigou,
The raising of an additional £ of
revenue... inflicts indirect damage on the taxpayers as a body over and above
the loss they suffer in actual money payment. Where there is indirect damage,
it ought to be added to the direct loss of satisfaction involved in the
withdrawal of the marginal unit of resources by taxation, before this is
balanced againts the satisfaction yielded by the marginal expenditure. [Piqou,
1947, pp. 33-4]
Piqou’s
intuitive argument is not, however, necessaril correct. In order to explore
this, let us take the case of two private goods-consumption (X) and
labour (L)- and one public good. We take leisure (= minus labour) as the
numeraire, and dotonate the producers price of the consumption good by p,
that of the public good by pG. For convenience, we assume a
linear production constraint :
If
all individuals are identical, and are treated identically, this can be written
(where
X , L now detonate the individual level of consumption).
In
order the examine the effect of different methods of financing, we assume that
the public good is financed partly by uniform lump-sum tax T on all
individuals and partly by a spesific tax at rate t on the consumption good. The
individual budget constraint is therefore (there is no profit income)
And
the first-order conditions for individual utility maximization,
Where
detonates the private marginal utility of income. From these we can have the
individual demand and labour supply functions of, p, t, T, and G.
The goverment aims to maximaize welfare measured by HU, subject to production
constraint. The Langrangean can therefore be written :
The
necessary conditions for optimalty involve
From
this it follows that goverment expenditure should be carried to the fint where
:[4]
The
left-hand side represent the sum of the marginal rates of subtitution between G
and the numeraire good (leisure), while on the right-hand side p G
correspond to the marginal rate of transformation.
From
this expression we can see that the existance of indirect taxes modifies the
conventional ∑MRS = MRS formula in two ways :
1. To the extent that an a increase in G leads to an
increase in the consumption of taxed goods (), this reduces the revenue to be
raised (throught the term ). The right-hand side is therefore lower than with
the conventional formula, or vice-versa . If, for the example, the provision of
a further television channel increases the demand for television sets, and
these are subject to an indirect tax, it may be socially optimal to carry
provision to a point where the sum of the marginal rates of substitution is
less then the marginal rate of transformation, even though the expenditure has
to be financed by distorionary taxation.
2. The conventional formula is based on the
assumption that raising $1 extra revenue would have a social cost equal to the
marginal utility of income. However, where there are non-lump-sum taxes this is
no longer true. The social cost of raising $1 () may in fact be greater or less
than the private marginal utility of income ()
The
intuition behind these result is that the goverment whises to the marginal
rates of subtitution equal to the marginal economic rate of transformation (as
in earlier Lectures). With taxes that are not lump-sum, the marginal economic
rate of transformation is in general different from the marginal physical rate
of transformation. The different arises from the fact that, when there is
distortionary taxation, the changes taxes required to raise he extra revenue to
finance the addition to public expenditure affect the deadweight loss (Stiglitz
and Dasgupta, 1971). The relationship between and may be seen from the
condition for the choice of t :
Using
the fact that , we obtain
X, L
|
Exercise
16-1 Carry out the same analysis where there
ia a tax on wage income and no indirect tax. What differences are there in the
result and how can they be explained? (See Atkinson and Stern, 1974)
Comparison
with Lump-sum Taxation
The
analysis so far has considered the effect of non-lump-sum taxation on the ∑MRS
= MRT rule ; it is important to emphasize that he result do not tell us
anything about the optimum level of provision for public goods-whether the
optimim provision in the case of distortinary taxation is larger or samller
than where lump-sum taxation can be employed. One cannot in general make
deductons from the first-order conditions about the behaviour of the optimum
quantities-a point that is often confused. (For example, the form of the
first-order conditions depends on the choice of the untaxed god, but this has
no implications for the optimum level of G.)
In
order to investigate how the optimal quantity of the public good may be
affected by the method of financing, we assume that the utility function is
additively separable between “private utility” u (X,L), and the public
good :
U = u (X,L) + g (G) (16-20)
Where
g’ > 0, g” < 0 and u is strictly concave. The
goverment constraint is
U+ g (G) = constant
|
G
|
Lump-sum
(t = 0)
|
Distortionary
(T = 0)
|
Q
|
Figure
16-3 Provision of pblic goods with distortionary
Wen
by : [5]
H (tX + T) = p G G (16-21)
In
the case t = 0 (lump-sum financing), we can tarce out the transformation curve
between u (X,L) and G, with slope given by (see Fig. 16-3).[6]
The optimum level of provision is found by maximizing the welfare of a
representative individual, which with contours as shown in Fig. 16-3 gives the
point . the concativity of u implies that is a declining function of
lump-sum income, and hence that the frontier is concave to the origin.
Let
us now consider the case ot the indirect tax, with T = 0. The level of private
utility is given by
And
the goverment budget constraint
HtX = pGG (16-23)
The
slope of the transformation frontier is therefore
This
frontier is illustrated by the curve nearer the origin in Fig. 16-3, althought
it should be noted that there is no necessary reason why it should be concave.
Optimality
again requires a tangency between the social welfare function and the
transformation curve. The slope of the social welfare function is –g’ and is a
function simply of G. If the distortionary tax tarnsformation curve is
steeper than the no-distortionary tax transformation curve, then this implies
that at the level of G that was optimal with lump-sum taxation, the
distortionary tarnsformation curve cuts the indifference curve from below ;
i.e., optimality requires a smaller level of production of public goods. This
situation is illustrated in Fig. 16-3. However, while “on average” the distortionary
curve is steeper, and hence there may be a presumption that expenditure wil be
reduced, it is not necessarily so and global result cannot be deduced. At the
same time, sufficient conditions can be given for the level of G with
indirect taxation to be lower than that with lump-sum taxation, for example,
for small levels of t and G. (N.B.: the tranformation fontiers have
identical slope at G = 0.) it is also possible to establish that a small
reduction in the possibilities for lump-sum taxation from the first-best
optimum (t = 0) leads to a fall in the optimim quantity of the public
good (Atkinson and Stern, 1974, p. 124).
Exercise
16-2 for the Cobb-Douglas utility function
Describe
the transformation frontiers with t = 0 and T = 0. What conclusions
can be drawn about the optimum quantity of G in the two situations?
16-3
OPTIMUM PROVISION OF PURE PUBLIC GOODS-DISTRIBUTION
In
this section we examine how the conditions for the optimum supply of public
goods are influenced by distributional considerations, paying particular
attention to situations in which there are restriction on the set of feasible
taxes.
Redistribution
and Non-Distortionary Taxation
In
the previous section we derived the firs-best allocation rule ∑MRS = MRT,
where the optimum could be attained b the use of lump-sum from taxes and
transfers. Typically, the government does not enjoy complete freedom in its
choice of lump-sum taxes, and indeed we have earlier argued that these may be
restricted to a uniform poll tax or subsidy.
Where this is, the ∑MRS = MRT condition ia no longer necessarily
applicable. To see is, let us suppose that the government can levy tax Th on household h, where Mh is the (fixed) income. There is oneprivate good
(quantity h = Mh- Th)
and one public good (G). the
government chooses G and X to maximize
Subject
to
And
a set of restriction on feasible tax rates.
The
solution depends on the nature of the restrictions. If Th can be varied freely, the first-order
condition imply
Which
imply ∑MRS = MRT, the result used earlier. If government is constrained to set Th = T all h, it follows that T = pGG/H,
and the first-order condition may be seen to be
Or
the social marginal utility of income, we obtain
Where
is the mean value, in other words, the appropriate measure of benefits is
wighted sum of marginal rates of substitution, the wheigts being proportional
to the social marginal utility of income and summing to unity.
This
corresponds to the distributional wheight sometimes used in cost-benefit
analysis (see, for example, Weisbrod, 1968). An alternative way of writing the
rule is
Where
cov [A,B] detones the covariance
between A and B. the ∑MRS = MRT, rule is therefore modified by
taking account of the covariance between the social marginal utility of income
and the marginal rate of substitution. As in the earlier optimal tas
discussion, this may be written in thrms of the “distributional
characteristic”, (see Arnott, 1978) :
Where
If falls with Mh, this means that for public
goods that are valued more highly by the poor than by others the level of
provision will be taken to a point where ∑MRS
is less than MRT, (as before, one
cannot draw conclusion about quantities from the first-order conditions.)
Distortionary Taxation
and Redistribution
The
taxes considered above are not distortionary ; we now consider the conbined
implications of dead loss and distributional objective. For this purpose, we
take the case where there are two private goods (consumption, X, and labour, L) and one public good. Individuals have identical utility
function, but differ in their wage rate, detonated by wh.
The
government is assumed to determine the level of indirect taxation, t, and public goods, G, to maximize [V(t,T,G,w)], where V denotes the vector of indirect utility
functions, and T denotes a uniform lump-sum tax (for the present assumed to be
zero). We form the Langrangean
Where
the backet gives the revenue constraint.
The
firs-order conditions are : [7]
Where
denotes the mean consumption. Rearranging, this gives :
Is
the ditributional characteristic for the private good. The ∑MRS = MRT
rule has therefore to be modified for the distributional effect of public goods
(on left-hand side) and for the indirect tax (distibutional characteristic on
right-hand side), in addition to the corrections for distortionary taxation
(compare Eq. (16-19)). If provision of the public good is more progressive than
consumption of the private good, in the sense tahat , this raises the relative
weighting of the benefit side.
Suppose
now that the goverment can levy a uniform poll tax-as with the linear income
tax. There is the further first-order condition :
Using
this to subtitute for , the right-hand side of (16-34) becomes
The
marginal economic rate of transformation exceeds pG where and
consumption is a normal good.
16-4
PUBLICLY PROVIDED PRIVATE GOODS
In
this section we consider goods tahat, as far as cost of supply to an individual
are concerned, are exactly like private goods, but are publicy provided. The
examples most commonly given, such as education and medical care (in some
countries), may not strictly have these properties (e,g., because of
externalities). However, just as we considered an idealized version of public
goods in the preceding sections, so here we tahe the pure case of a private
good supplied at zero charge in a specified quantity. We begin with the
situation where all individuals are identical and there is uniform provision of
the good ; we then exted the analysis to that where pepole differ, but the
goverment is again required to provide an identical allocation t each
individual. Finally, we consider the case where the goverment can provide for
different individuals a different quantity of the good in question. We assume
troughout that the good cannot be traded ; the reader should consider the
impliction of this assumption.
Uniform
Public Provision
With
identical individuals, and financing via a poll tax (T), the optimum public provision of the private
good, detoned by E, must satisfy a first-order condition identical
to that implied by individual choice if we had used a price system.[8]
Suppose that there is private consumption, X, and labour, L, in
addition to the publicy provided good. The price of private consumption is p,
that of E is pE, and labour is the numeraire.
The goverment maximizes :
HU
(X,L,E)
Subject
to T = pE E. The first-order condition is that
HU
E = HpE (-UL) (16-35)
Or,
where MRSh = UE/(-UL)
MRSh
= pE (16-36)
This
is identical to the first-order condition for invidual utility maximization
when faced with a price pE. As one would expect, there is in
this case no summation of individual marginal rates of subsitution.
Where
the public provision is financed by distortionary taxation, the first-order
conditions have to be modified in the sme way as before. The marginal physicak
rate of transformation, represented in (16-36) by pE, has to
be replaced by the marginal economic rate of transformation. This is left as an
exercise.
Exercise
16-3 suppose that the method of financing is
an indirect tax on X at rate t. Show that the first-order
condition for public provision is
What
conclusions can be drawn abaout the optimum public spply compared with that in
a parivate market?
If
people differ, then uniform public provision is closer to a public good in the
sense taht we have to determine a single level for all individuals. Suppose
first taht the goverment has complete freedom in the use of lump-sum taxes, Th,
on individual h. The goverment’s problem may be formulated in terms of
the Langrangean :
The
first-order condition may be written :
Since
Be
average MRS should be equated to the MRT. Clearly, the success of
public provision depends on he extent of divergence of tastes for consumption
about this average. Where there is not full freedom to vary Th,
when there is a distributional adjusment ; for example, with = T all h,
where is an additional covarience term, cov , as in the discussion public
goods.
Optimum
Allocation of Publicly Provided Private Goods
The
model just discussed, the good is provide uniformly ; we need however to ask
whether this is social optimal. This is a question taht is frequently debated.
Should educational resources be concentrated more heavily on gifted children,
should the goverment provide aqual inputs, or should it aim to ensure
equal outputs (e.g, as measured by earning ability)?
There
were free use of lump-sum redistributive taxes and transfers, when-in an
otherwise firs-best world-the criterion would be straight-forward : we allocate
the good according to private demand. In other words, we would not have a
uniform level, absed on an average MRS, but would allocate so that
individual MRS equal the cost of provision. However, in the absence of
such freely flexible lump-sum taxes, the conditions for optimum public
provision will, in general, be different from hose arising from private
alocation.
The
illustrate the way in which public provision may differ, suppose that the
social welfare function is the sum of identical individual utility functions
which are additive in he publicly provided god. Then the optimal provision is
uniform, and unless the tax policy equates the marginal utility of income, this
involves differing marginal rates of subtitution across individuals.
To
set this out formally, and to see what happes when we relax the assumption of
additivity of the utility and welfare functions, supose that individuals differ
only in health needs, where . the firs-order conditions for an optimim
allocation, Eh, is (for an interior solution)
Where
is the the multiplier associated with the total expenditure caonstraint. This
model is that examined by Arrow (1971a), who is concerned with the utilitarian
objective . he defines a policy as “input-progressive” where > 0 ; i.e.,
people with greater health needs context-a natural conclusion ; however, from
(16041) we can see that, differentiating totally with resoect to (where =1)
If
UhEE < 0, the optimum policy is
input-progressive if and only if . in other words, resources are allocated
according to their effect at the margin. If a worsening of a person’s medical
condition makes health care less productive, then the optimal input may
decline.
We
can also ask wheter the allocation is less than or more than fully
compensatory. Since
It
follows that an equal input policy is stiil not fully compensatory. In the
light of our earlier discussions, it should not come as a surprise to see that
a utilitarian policy does not ensure a fully compensatory policy. The role
played by the form of thr social welfare function may be seen by alowing for.
Differentiating (16-41) and re-arranging then gives
The
terms in are both positive, and tend to make it more likely that the optimum
policy is input-progressive. (The reader may like to consider the implications
of a Rawlsian objective function)
Different
Abilities and the Allocation of Education
We
noe examine the case where individuals difer in ability, as in earlier
Lectures, but where this “raw” ability () is supplemented by education (E) so
that the wage of an individual is given by w = E). As in Lectures
12-14, we assume that ability is distributed continuously with density function
and this is the only chracteristic in which people differ.
The
goverment s assumed to determine the optimum allocation E () and the
optimum method of financing. If lump-sum tax, T (), related to quality
is not feasible,[9]
then the alocation departs from that which would be made on grounds of
allocative efficincy. To see this, let us compare the use of the lump-sum tax
with a linear income tax, at rate t and such an income gurantee G*.
The goverment’s problem may be formuated as maximizing
Subject
to
The
first-order condition for the choice of E () and T () are
(introducing the multiplier for the constraint)
Where
V denotes the derivative with respect to the after-tax wage. Since the
use of lump-sum taxation, with t = 0, implies
An
other words, the first-order conditions imply that education should be
allocated so that its amrginal contribution to wages (weighted by L) is
equalized. (A full treatment should consider the form of the function (E)
and possible non-convexities.)
Where,
however, there are restriction on lump-sum taxation, this “efficiency”
condition for the allocation of education ceases to aplly. This can be seen
from (16-47a). Where we can no longer simplify by using (16-47b) and . In this
situation one cannot in general treat the allocation of publicly provided goods
separatelly from the redistibutive tax policy, even when the latter parameters
(t and G*) are optimally chosen. (The reader may like to
check that this is also true with a nonlinear income tax-see (Ulph, 1977). In
determining in allocation, one has to balance te fact that-with the assumption
made here-the more able can use education more efectively, againts the redistributive
factors embodied in , taking account of the contribution to goverment revenue.
Choice
Between Public and Private Provision.
Many
goods can be alocated either publicly or privately ( i.e., they can be supplied
without charge, or they can be allocated on the private market); moreover,
there are cases where there are private goods (e.g., security agencies) that
are a close substitute for public goods (plice). Thus, the required services
can be supplied in either a public or a private mode, and we have to consider
which gods are to be provided publicly.
The
problem may be seen in general terms as that of designing the optimal price
schedule, and the way in which it is likely to work may be describe
heuristically. Where public provision of a uniform quantity, E*, is vertically
(i.e., there is an infinite price of further units). Where public provision of
unlimited quanities is desirable, then the optimal price is zero troughout.
Where private provision is preferable, then the optimal price of the first unit
of public provision is infinite. In this way, we can see the relation to the
earlier analysis of the optimal indirect tax and public sector price schedule.
There
are two features of this general problem that should be noted. First, the
solution may depend sensitively on the range of instrument at the goverment’s
disposal-as we have stressed earlier. Thus, consider the finding that a uniform
allocation of he publicly provided goods is socially optimal where the welfare
function is utilitarian and the individual utility function additive (page
499). This appears to be in conflict with the earlier result (Lecture 14) that,
where individuals differ in wages, and the utility function is locally
separable in labour and commodities, the optimal price schedule is linear for
commodities. However, we did not allow for the choice between public and
private provision-it was assumed that the good was supplied by the
goverment.
The
second feature of the problem is that non-convexities are likely to be most
important. We have seen in the discussion of optimum taxaxion that there is no
reason to expect the maximization problem to be well behaved, and in the
present case there are further reasons to expect serious non-convexities. A
clear example is provided by administrative costs. There are good reasons to
suppose that these are likely to be less in certain fields with public
provision, for example, because of economies
of scale or because monitoring of individual usage is not required. It
may well be necessary therefore to make global comparisons, reliance on local
optimally conditions not being sufficient.
In
the comparison of public and private provisin, several factors are likely to be
influential. In addition to the administrative costs just mentioned, diversity
of tastes and distributional objectives play a major role. To illustrate the
effect of tastes, suppose that individual differ in their preferences
(detonated by ) concerning the good, but not otherwise, and that utility
functions have the spesial form (as in Weitzman, 1977)
Where
Xh is the (composite) consumption of other goods, taken as
the numeraire. With private suply of the good at its production price, p,
the demand by household h is
And
the resultant level of utility is (up to a constant) :
The
good is supplied publicly in uniform quantity E, financed by a pool tax, the level of utility is (again
dropping the constant)
As
we have seen earlier, E is optimally chosen according to the average of the
marginal rates of subtituton (in this case ccording to (16-50) with . The
provision of a uniform quantity involves a loss of total utility, Which may be
calculated (16-52) and (16-52), with . the loss
Which
can be shown to reduce to H times the variance of . the loss in efficiency of
allocation from public provision is therefore governed by the variance of the
taste parameter.
In
making the comparison between private suply and uniform public supply, the
efficiency loss has to be balanced againts any advantage in administrative
costs on the side of public supply (and distributional actors). Suppose, for
example, that the costs of administration are less in the public sector to the
extent of units of the good per person ; then the condition for private supply
to be superior to public (with uniform provision) is that :[10]
Where
denotes . a sufficient conditions for this to hold is that the coeficient of
variation in the taste parameter is greater than. On the other hand, if we
consider quantities at zero price (e.g., with water supply) can consume
unlimited poll tax, then the condition for private supply to be
Superior
is that :[11]
In
this case, differences in tastes are provided for, and the efficincy loss
arises on account of consumption in excess of that demanded at price equal to
marginal costs. Where this excess consumption is relatively small ( is small)
it requires only a small advantage in terms of administrative costs for public
provision to be justified.
Teh
full-scale analysis of the choice between private and pblic provision in a
general model is beyond the scope of these Lectures. The example of education
may however serve to illustrate how the problem may be formulated in more
general terms. People are supplied with a uniform level of public education
(which may be zero), and may purchase private education in addition (they are
not alternatives as assumed in Lecture 10). The goverment can impose a tx on
the private purchase of education in, addition to an optimal linear income tax.
They key question for policy are whether the uniform level of public provision
is strictly positive and wheter or not the tax on private education should be
ser at a prohibitive level. The working out of the details of this analysis are
left as an exercise, but it can be shown that, even with an optimally chosen
income tax, free public provision of education may be desirable on
distributional grounds. (this result can be demonstrated from local properties,
but for a fuller characterization of the optimum, care needs to be taken to
allow for possible non, convexities.)
Exercise
16-4 Consider the model set out on pages
500-501 and show how it can be extended to include individual purchase of
additional education, so that a person’s outlay on education is where is the public provision, te is the rate
education, and . the level of public provision is assumed niform fao all. The
goverment can vary the tax rates te, t (on income) and the poll subsidy, G*.
Formulate the maximazation problem and write down the first-order conditions
under which a stricly positive level of state provision is desirable. Show tht
under certain conditions it is optimal to levy a tax on education. In wht
circumstances should this tax be prohibitive?
The
argument discussed above are not intended to capture all important features of
the case for public provision of education. It has for example been assumed
implicitly that an individual has no constraints on the access to resources to
finance education, whereas in practice capital markets are less than perfect,
and parental wealth may be a major determinant of access to eduaction. The
scope for the expression of individual preferences and the extent of response
of the school authoritiee may be important. These , and other broader
considerations, need to be borne in mind in assesing the case for the public
provision of educatation; and similar issues arise with other publicly provided
private goods such as medical care.
16-5
EQUILIBRIUM LEVELS OF PUBLIC EXPENDITURE
The
preceding sections have been concerned with the optimum provision of pure
public, or publicly provide private, goods; we now ask how this compares with
the levels of provision likely to emerge from actual procedures for determining
public spending. We consider three classes of models. In the firts, we ask,
what would be the equilibrium supply if there were no government? This is
sometimes reffered to as a ‘’subscription equilibrium’’ , where each individual
voluntarily contributies the amount he wishes to pay. In the second set of
‘’political’’ models, we discuss the level of public expenditures that arises
in a voting equilibrium. Is the public budget likely to be too small in a
democracy?cthe third model is known as the ‘’Lindahl’’ equilibrium. This
represents an attempt to devise a mechanism that attains a Pareto –Efficient
allocation of public goods and has certain formal similarities to the
competitive equilibrium model. We confine our attention to the case of pure
public goods.
No- Government Equilibrium
Even
in the absence of government, individuals may contribute to public goods; and
indeed, in actual economies, with substantial public provisions, there is still
extensive private support for such items as medicine, education and research.
The motives for this support are varied, and are perhaps not adequately
captured by the kind of individualistic utility functions we have positied for
most of the analysis. But it is worthwhile analysing what the economy might
look like with such individualistic functions in the absence of government
provision of the public good.
We take the conventional approach of
analysing the Cournot-Nash equilibrium of the economy: each individual takes
the others’ supply of the public good as given, independent of his own
purchase. For convenience, we assume that there is a single public good, which
can be produced at constant marginal cost, PG . There is a single
private good, X, taken as the numeraire
of which iindividual h has endowment Mh. The individual purchases Gh of the public good, chosen to
maximize
Each
individual treats the sum (over i ≠h as fixed; we then obtain the first-order
condition :
In
other words, he determines his expenditure such that his own MRS is equal to
the marginal rate of transformation. The aggreagate MRS is therefore H times PG,
and hence greater than PG at this level of public goods.
The
solution is illustrated in Fig. 16-4. The upper part shows the choice of Gh
given ∑i≠h Gi;i.e.,
the person chooses S on QR. By varying the sum, we can generate tthe reaction
curve indicated. If we now assume that all individuals are identical, then it
is a condition of overall equilibrium that X=M-PG G/H. The
interactions P with the reaction curve in the lower part of the diagram gives
the Nash equilibrium. It is clear that the individual indifference curve cuts the line X=M-PG/H at P, and
that the maximization of social welfare (with lump-sum taxation) indicates aa
higher level of G. The condition ∑MRS= MRT is in fact satisfied at P*.
The
comparison of the optimum with the no-government solution is less
straightforward where individuas differ and where the government cannot levy
freely variable lump-sum taxes. In fact case, the level of public expenditure
in the optimum depends on the social weights associated with different groups.
It is clearly possible that the Nash
equilibrium leads to greater spending if thr welfare-maximizing solution
attaches particular weight to people who do not like the public good iin
question. On the other hand, it is possible to make some statements. Suppose
that the government provides a equqntity G of the public good, financed by a
uniform poll tax. The level of social welfare is given by
Differenting
with respect to G, and evaluating at G=0, it may be seen that social welfare is
locally increasing in the level of public provision, where (after some
rearrangement)
(we
have used the fact that MRSh = PG at the Nash equilibrium, and have divided by
pG).
The left –hand side is positive, where an increase in G increases the total
rpovision. Where this is the case, a sufficient condition for social welfare to
be locally increasing in government spending is that the more’’deserving’’
(according to
h) individuals reduce
the private provision by more.
Nash
Reaction
curve
|
G
|
Xh
|
Mh
|
Gh
|
Q
|
A
|
S
|
R
|
Nash
Reaction curve
|
G
|
R
|
X
|
M
|
X = M- pG G/H
|
P*
|
P
|
Figure 16-4 Nash
equilibrium for public goods
Voting over Public Goods
The
determination of public spending by means of voting was disccused in lecture
10, where we drew attention to a number of the problems that arise. When there
is a single decision variable then resctrictions on preferences of individuals
such as
how resonable such assumptions are(the example
was given there a public and private education, where theses are alternatives),
and once move to two or more dimensions the conditions on preferences necessary
to ensure a voting equilibrium are extremely restrictive. On the other hand
determine outcome may be ensured if there are exogenously determined rules
governing the agenda.
Here we simply make the comparison
between the level of expanditure determined by majority voting under conditions
in which and equilibrium exist. In particular, we assume that there is a single
decision—that the concerning the level of a public good financed by a uniform
poll tax. It is assumed that individuals votev ‘’sincerely’’(see Lecture 10).
The utility of the h-individuals is
Uʰ (Mh
And,
as we saw in Lecture 10, the individual valuation of different levels of G is a
single-peaked function. The votinf equilibrium is therefore characterized by
the preferred level of a median voter (denoted by m) :
Does
the voting outcome lead to a higher or lower level of G than is socially
optimal? Suppose that we consider a small increase in G above the level
determined by the median voter. The effect on social welfare is given by (this
tells us whether or not social or not social welfare is locally increased by an increased by an increase in spending above
the amount in the voting equilibrium)
It
is clear that there is no presumption that this it either positive or negative.
If the government has no distributional preferences, the ∑MRS may be greater or
less than PG at the median voter
equiibrium, as is illustrated by Exercise 16-5. If ¥h. UhX differs across individuals, then whether
(16-62) is positive or negative depends on the weights attached to different
individuals and their position relative to the median. If, for example, the
preferred level of government spending is a strictly declining function of
income, and the government is concerned solely with the welfare of the lowes
income group, then the social optimum involves a higher level of public spending
than in voting equilibrium.
Exercise 16-5 for the special case of the utility function
Show that the social optimum may involved more or less government speending
than voting equilibrium where the government has no distribuional preferences does it make if
the public good is financed by a proportional tax oon imcome? (See Stiglitz, 1974a.)
The analysis just
given should be treated simply as a counter-example to the proposition that
majority voting leads to a level of government spending that is below(
conversly baove) the social optimum. The example shows that there is no
persumption either way. In order to reach more positive conclusions,it is
ncessary to specify more fully the political machinery and procedures lyiing
behind public spending dicisions. This mould need to make account of the
conditions that ensure a determinate outcoome, and role played by legislators
ad bereaucrats in addition to that of voters.
Lindah Equilibrium
The
inefficiency of the Nash equilibrium aries because each consumers i s faced
with a price equal to that of the public good, whereas some of the benefit
accrues to others. By anology with the case of comsumption externalities, we
can seek therefore a set of corrective subsidies, whic will in general have to
vary across individuals-we need ‘’personalized’price. This procedure was
discussed by Samuelson (1969) as a ‘’pseudo-demand algorithm’’ to calculate the
optimal level of public goods supply, but was proposed as an actual allocation
process by Lindahl (1919)
The essence of the Lindahl procedure
is that individuals ‘’demand’’ a total quantity of public goods on the basic of
a specified distributions of the tax burden (see Johansen, 1965,Ch.6). thus
each individual faces a tax share
h of the expenditure , where ∑h
h=
1, and these tax share erform the function of personalized prices. Reffered to
as ‘’Lindahl prices everyone demands the same level of each public good. In the
case of a single public and a single private good, individual h maximizes.
The
Lindahl equilibrium satisfies the necessary condition for a Pareto- officient
of public goods in full conditions.
D1
|
G
|
D2
|
Lindahl equilibrium
|
Figure 16-5 Lindahl
equilibrium : two person example.
The Lindahl equilibrium is illustrated in Fig.
16-5 for the case where there are two (types of) individuals. The share of the
first is denoted by and the demand is
shown by D 1the share of the second is given by 1-15 and the demand
is shown by D2 The intersection is the Lindahl equilibrium.
The general properties of the
Lindahl equilibrium have been extensive discussed in the literature. These
include the Pareto efficiency reffered above, and converse of this result that,
under certain conditions, every Pareto-efficient allocation can be generated by a Lindahl equilibrium with
suitable lump-sum taxes and transfers.[12] A particular questions that have recieved
considerable attention is the relationship between Lindahl equlibria and the
core. An allocation (of goods among individuals) is to be in the core if no
coalition of iindividuals can together propose an alternative allocation of its
own resources that make at least one member better off and no member worse off-
they cnnot in this sense improve upon the allocation.[13]
For a two –good, two person economy, the core is simply the set of
Pareto-efficient points that represent and improvement for both individuals
over their no trade position. It is shown. In the standard. Edgeworth box diagram, by the points on the contract
curve between the indifference curves through the inditial endowment.
In an example economy with no public
goods,complete maekets and full information, there are two basic theorems
concerning the relationship between the core and the competitive economy :
1.
The competitive economy is contained in
the core;
2.
The core ‘’shrinks’’ to the competitive
economy as the number of traders increase.
The first proposition is trivial. Since the
competitive economy represents an improvement for all individuals(or at least
no dcrease in welfare) relative to the no trade point, and since the
competitive economy is Pareto-efficient, it is clearly contained in the score.
The second proposition may be illustrated as follows. Suppose that there are
two types of individual, but a large number of each type. The first step is to
show that any allocation in the core must be symmetric;cie,. Everyone of the
same type gets the same comsumption bundle.[14]
The second step is to show that, if we can repliciate the economy by any
arbitrary factor, then the only possible
core allocations are the competitive equilibria. For this, we need only to
consider points on the contact curve. Suppose that we consider a point such as
Q in Fig. 16-6, which is not a competitive equilibrium. A line from the initial
endowment point to Q, inteesects at least one of the indifference curves
through Q, and there exist points such as P where advantageous trades can be
made. A group consisting of individuals of type I and II in approciate ratio
can improve on the allocation at Q, and replication ensures that this is
feasible(with integral numbers of individuals).
When we introduce public goods, the natural
parallel result would be for the lindahl equilibrium to belong to the core, and
the core to shrink to the save of Lindahl equilibria ask the number of traders
increases. The latter would particularly significant, since.
One could them ague that, no matter by
what sytem (public) goods actually are allocated, if..... we assume that trade
and production will take place among agents as long as it is advantageous, then
any allocation that actually arose could have been achieved by the Lindahl
price mechanism. (Roberts.1974b,p 38)
However , although the first result- that any
Lindahl equilibrium is in the core-can be demostrated under certain conditions
(Milleron.1972), the second result does not hold. For instance, muench (1972)
gives an example where the Lindahl equilibrium is unique but the core is very
large (see also Milleron, 1972). The reason for this can be seen to lie in the
requirement.
Initial
endowment
|
Indifference
Curves of individual
II
|
Indifference
Curves of individual
I
|
Contract
curve
|
Q
|
P
|
A
|
Figure
Competitive equilibrium and the core
that
the coalition must be able to make its members better off irrespective of the
actions of the remaining group. In the context of public goods, this means that
they must be better off even if the remaining individuals decide to produce no
public goods. It thus becomes difficult
for small groups to improve upon the proposed allocation: the core of the
economy is likly to be bigger.[15]
Since
much of the appeal of the concept of a Lindahl equilibrium, the results just
describe reduce the strenght of the claims that can be made. We must therefore
reconsider either either the cincept of the core as applied to a public good
economy, or the status of the Lindahl equilibrium. In any event the Lindahl
equilibrium is probably best regarded as an analytical benchma
RELEVATION PREFERENCES
Throughout
the previous sections, we have assumed that the governmnet knows the
preferences of individuals (in the voting model) that individuals vote for
their ‘’true’’ preferences. This raises two closely related questions: how can
we the government learn the preferences of consumers, and how can we be sure
that in any actual procedure for determining the provision of public
goods,individuals will be have ‘’honestl’’?if we start from a presumption that
individuals reveal the truth,unless it is their interest not so to do, then
this means examining the icentivies for lying of for providing the government
with false information.
That the demand for public goods may
provide people with such incentivies has been recognized for a long time. If
the amount an individual has to pay for the public good is related in some way
to his demand. As Samuelson expressed it in his classic paper, ;;it is in the
selfish iterest of each person to give false signals, to pretend to have less
interest in a given collective consumption activity than he really has’’ (1954,
pp. 888-9). This is sometimes referred to as the ‘’ free-rider problem’’ ;and
it arises in a variety of contexts apart from public goods. Unions claim tthat
the reason that all individuals should
be required to contribute dues is that there exsist a free-rider problem. They
provide a collective good (negotiating better terms with the management); and
any individual disclaiming interest in the good has the advantage of enjoying
the benefit without paying the cost. The
general problem is the same as that of incentive compatibility in a
(finite) competitive private economy, which we referred in Lecture 11. In that
case, the incentive for individuals to misrepresent their preferences disappears
as the economy becomes ‘’Large’’. For public goods however , the incentives do
not improve as the number of people increases (see Roberts,1976) and in this respect there is indeed a contrast between the
allocation of public and private goods.[16]
Mechanisems for the Revelation of Preferences
A
general class of mechanisms can be describe as follows. The hth individual is asked to report a
valuation of public goods, zh (G). The government announces that the
tax shares of the hth individual and
the supply of public goods will be a function of all statements according to
some rule :
In
designing the mechanism, the government may seek to scure properties such as
the following :
1.
Thee Nash equilibrium (where everyone
takes the announcements of others as given) is Pareto-efficient where each
person chooses his announcement maximize his own welfare.
2.
In the Nash equilibrium, everyone
reports truthfully their valuation of public goods(for Pareto efficiency thi is
not necessary; all that is required is that the government can’’translate’’ the
announced valuations).
3.
Trurhful reporting is a dominant
strategy ( thatit, it pays each individual to report zh (G)
accurately regardless of the announcement of others).
There have been a number of attemps to devise
mechanisms that have some or all of these propoties. The earliest of these
mechanism was that of Vickrey (1961), who developed a procedure for a public
marketing agency faced by monopolistic buyers and sellers. He showed that it
would be possible to motivate individuals to give correct iinformation by
paying themt the net increase in the sum of producer and consumer surpluses of the other persond in the market that
resulted from the supply or demand curve revealed. This procedure was then
independtly discovered and developed by Clarka(1971,1972) and Groves (1970.1973; Groves and Loeb, 1975).
(See also the discussion of elititation functions in Kurz, 1974)
The
procedure may be described in a partial equilibrium model where utility
functions are of the form
Uh =gh(G)+Mh
It
is assumed that lump-sum transfer of income Mh can be made freely.
The stated valuation function of individual h
(note that it is a function and not
simply a single value) is zh (G). The level of public provision, G*,
is chosen to maximize ∑hzh(G). And individuals are
taxed in a lump-sump way according to the schedule
Where
the last term is an arbritary function of the vector z, excluding zh. The level of individual utility is
With
the procedure, the dominant strategy is for each person to reveal the true
marginal valuation. To see this, suppose that is function of G and some
variable (so that we can think of his answer as being represented by the
choioce of ). A variation in has no direct effect via dG* / d . By
the conditions determining the choice of G*, this has no effect on
the underlined term in (16-69), and the
variation is therefore proportional to ghG-z
hG. With the optimal choice of , this is zero, so zh (G)
must equal gh (G) up to the addition of a constant.[17]
This
preference revalation mechanism has
therefore certain attractive properties, and Green and Laffont (1977a) have
shown that this is the only class of mechanisms such that stating one’s true
preferences is a dominant stretegy and that outcome is Pareto-efficient. It is
however limited, both by the assumptions made and by the fact that the
mechanism does not guarantee a balanced
budget for the government (on this, see Groves and Ledyard, 1977). It
does not allow for collusion between individuals, and coalition incentive compatibility
further issues(see Green and Laffont, 1979). Finally, no equity considerations
are allowed for.
Empirical Significance of Free-Riding
Preference
revalation and incentive compatibility is an active area of research. This is
undoubtedly a valuable antidote to much of the earlier literature, which, with
axceptions such as Samuelson (1954) and Buchanan(1968), has tended to ignore
the problem-as in previous sections of this lecture. On the other hand, there
are those who argue that there is little
evidence to suggest that the problem of correct revalation of preference has
been of empirical significance:
We have a lot of public goods around
probably more than we would expect on the basis of the thory of the free-rider
tedency...and there are also many groups and individuals around who by no means
appear to conceal their preferences for public goods. (Johansen, 1977,p.148)
There are two principal reasons for questioning the
importance of the free-rider problem . the first is that honesty may itself be
a social norm, rather than simply the outcome of maximizing utility :
Economic theory, in this as well as in
some others fields, tends to suggest that people are honest only to the extent
that they have economic incentivies for being so....the assumption can hardly
be true in its most extreme form.(Johansen, 1977,p.148)
In
societies where honesty is a social norm, one would not expect
misrepresentation of preferences unless the pay-off to dishonesty reaches a
threshold level. Where there is too complicated consuming and resort to telling
the truth:’’since i cannot find a way to beat
the system, I had just as well tell the truth’’ (Bohm, 1971,p.56). The
secomd reason why the revalation of
preferences may be less important is that the decision os not made directly by
individuals but typically through elected representatives. Johansen argues that
in this case misrepesentation is unlikely to pay, either in terms of eloctoral
success or in terms of decisions made by legislative assemblies. This brings us
back to some of the issues discussed in Lecture 10.
There have in fact been experimental
studies of individual preference revalation under different incentive schemes.
For example, Bohm (1972) carried out an experiment at the Swedish Radio –TV
Company, where 211 people were asked to express their willingness to pay to see
a new programme, nnot yet shown to the public. They were paid on arrival 50 Kr (approximately) $10) for
taking part, and then asked to specify how much they would contribute to see
the programme under a specified payments
sructure. They were told that the programme would be shown if the total sum stated exceeded the costs
(500 Kr). The main results are set out in Table 16-2. Although there are some
differences in the means and medians between the different incentive schemes,
none of the differences are significant at the 5 per cent level. This
experiment is clearly on a small scale, and intended more to assess the
feasibility og the method, but ia is none the less interesting that so little
diffrence emerges.
Table
Experimental evidence on willingness to pay
Number of
cases
|
Payment
scheme
|
Amount mean
willing to pay (Kr)
|
|
Mean
|
Median
|
||
23
29
29
37
39
|
(I) The amount stated by respondent
(II) A percentage
of the amount stated (so that collected = total cost)
(III) One of four possibilities
determined by a lottery (with equal probabilities)-designed to represent the
case of “uncertainty
(IV) Five Kr
(V) Nothing
|
7.61
8.84
7.29
7.73
8.78
|
5
7
5
6.50
7
|
Decentralization and Information
The models employed in earlier sections
asssume that the government knows not
only the preferences of the individuals, but also the production possibilities
of all firms. In, fact the government does not have at its disposal all the
requisite information and allocation, nor does it have the ability to solve all
the problems of production and allocation simultaneously.
This is one of the main motivations
for organizing governments in a decentralized manner, i.e., having branches
responsible for different activities os functions. Thus, Musgrave’s (1959)
division of the branches of government into the stabilization, allocative and
distribution branches may be thought of
as more than just an analytical device. On the other hand, the sense in which
the different branches can carry on their business seperarately from one
another is not made clear in Musgrave (or in most of the subsequent literature)
, and the conditions under which various schemes of decrentralization lead
to a full optimum are not spelled out.
This may be illustrated by
reference to the provision of public goods. Suppose that lump-sum taxes
may be frelly used, and that public instructed to maximize social welfare
subject to the bugget (public goods being charged for at the producer prices).
The agency will then equate the ∑MRS to MRT where is the multiplayer associated
with the budget constraint, and if us chosen correctly the social optimum is
reached. (we are ignoring here the problem of revelation of preferences.)
where, however, there are non-lump-sum taxes, we have to allow both for the
fact that varying G may affect government revenues and for the
distributional effects of public
goods. There is than fundamental
interdependence between decision about the relative quantities supplied of
various public goods and the stucture of for the finance of these goods. As a
consequence,the marginal rate of
subtitution between two public goods is not in general equal at the optimum to
their marginal rate of transformation (the ratio of the producer prices).[18] Moreover,
the benefits for public goods need to be weighted according to the social marginal utility of income,and
these weights depend on other aspect of distributional policy.
There is therefore a persumption
that decentralization will entail
certain costs, which have to be balanced against the administrative and
informational advantages. The rigorous analysis of this problem, taking account
of such factors as the motives of those who administer government programmes
and political power, is clearly a major task. In the next Lecture, we consider
one particular form of decentralization- where individuals form local
communities for the supply of local public goods
READING
Key
references on the optimal provosion of pulic goods are the papers by Samuelson
(1954,1955,1958b,1969) . a valuable survey of the area is provided by Milleron
(1972). On tthe public provision of private goods,see Arrow (1972a)and the subsequent literature.
The discussion of voting on public goods draws on Stiglitz (1974b). A useful
review of dynamicc procesess for the provision of public goods iin provided by Tulkens (1978).
The revalation of preferences is dealt with in depth by Green and Laffont
(1979), and the references contained therein.
[1] It should be noted
that term “exclusion” is being used in a slightly different sense from for
example, that employed by Musgrave. He refers to the exclusion principle as
indicating that a person “is the included from the enjoyment of any particular
commodity or service unless he is willing to pay the stipulated price” (1959,
p. 9). This however reflects a choice about the method by which the good is to
be allocated. Our definition relates solely to the technical possibilities.
[2] The
modern general equilibrium treatment of the optimum provision of
public good lates from Samuelson (1954), he has returned to the subject in
Samuelson (1955, 1958b, 1969)
[3] As recognized by
Samuelson (1954), his treatment was a general equilibrium version of the
earlier partial equilibrium analysis of Lindahl (1919) and Bowen (1943). In
that case, the “total demand” is found by adding up the dermand curves ; but
unlike private goods, where we add horizontally the total dermand at a given
price), for public goods we add vertically (the total amount that all
individuals are wailing to pay for the given amount of the public good)
[4] Using the fact that (p + t)
obtained from differentiating the individual budget constraint (16-12)
[5] This can be
obtained by summing the individual budget constraints (p+t) HX = HL
- HT and subtracting the agregate production constrain (16-11)
then
[8] Note that we are
assuming uniform provision. The reader should consider wheter there can be
situation where the goverment would want to allocate different amounts to
identical
[9] As in earlier
Lectures, this assumes that information may be used by the goverment for
certain purpose but not others. It is assumed that a is observed by he
education authorities with sufficient accuracy to allocate E, but that
this information either is not available to the tax officials or else is not
acceptable as a basis for determining tax liabilities. Although a more complete
treatment of information would be desirable, we feel that this captures an important
feature of the problem.
[12] On this, see, forexample. Foley (1970)
discussion of the existence of Lindahl equilibria. See Milleron (1972) and
Roberts (1974b) Reference should also be made tobe planning procedures for
public goods, such as those proposed by Malinvaad (1971a. 1971b) and Dreve and
de la Vallee Poussin (1971). A useful survey of
work in this area contained in Tulkens (1978)
[13] The reader should
note that we have read Shapley (1973) and have resolved not to use the
term ‘’blocking’’
[14] if not , the
‘’uderdogs’’ can form a coalition. For an exposition, see Hildenbrand and
Kirman (1976.Ch.1) or Varian (1978,p.181-2).
[15] The assumption
that the best cost of the public good is totally independent of the size of the
economy may be questioned or discussio of the question of ‘’returns to group
size’’ an ‘’semi-public goods’’ see Roberts 1974b).
[16] The problem of
incentive compatibility may arise quite widely where there is government
intervention in the economy. For example, we have seen in Lecture 13 that the
first-best redistributive tax many involve utility being a declining function
of ability, and that this would give people
an incentive to misrepresent their
ability.
[17] the Clarke
procedure has a rather simpler form with the arbitary function being replaced
by the valuation of public goods to the remaining H-1 people, at level G chosen
to maximize ∑. hzh (G)-pG G. See Tideman and
Tullock (1976).
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