Public Pector Pricing and Poduction
Public Pector Pricing and Poduction
15-1
INTRODUCTION
Countries
differ in the extent to which output is supplied by the public or nationalized
sector, but in nearly all Western countries there has been a great deal of
interest in policies and the behavior of private sector. Many managers of state
enterprises seem to act in an identical way to the managers of private firms.
In such behavior socially desirable? We focus in particular on pricing and
production decisions. Should public sector prices be equal to marginal cost,
and, if not, how should the deviate? In choosing the technique of production,
should state enterprises use market prices or should the instructed to use
shadow prices? If the latter, how should these shadow prices be calculated?
What rate of discount should be employed investment decisions?
This Lecture is addressed to the questions. We begin
with pricing policy, taking as reference point the first-best marginal cost
pricing principle (described in more detail below). In section 15-2 we examine
some of the arguments that may be advanced to justify departures from marginal
cost pricing. These include the problem of financing public enterprise
deficits, the implication of monopoly elements in the private sector, and the
impact on the distribution of income. In part, this treatment exploits the parallel
between public sector prices and commodity taxation, and we do not repeat the
earlier analysis (e.g., of the distributional effect). However, we also draw
attention to the differences that may arise, and the fact that a simple
translation of algebraic result may obscure significant features of the
problem. We then consider the production decisions of the public enterprise,
and in particular whether the shadow prices inputs should be identical within
the public sector and whether they should be equal to the market prices of
inputs. Should British Steel use the same discount rate (for a given degree of
risk) as British Gas, and should these rates be equal to an appropriate market
rate? The question of the desirability of “production efficiency”, and the particular
application to the social rate of discount, are the subjects of sections 15-3
and 15-4.
Marginal Cost
Pricing Principle
The
principles of public enterprise pricing have long been the subject of
discussion, and particular reference should be made to the tradition in France,
dating back the work of the Ecole des Ponts et Chaussees in the early
nineteenth century (Ekelund, 1973). Much of this literature has argued in
favour of marginal cost pricing, a case thet was put forcefully by Hotelling in
his classic paper.
the
optimum of the general welfare corresponds to the sale of everything at
marginal cost. This means that toll bridges … are inefficient reversions: [that
taxes on incomes, inheritances, and site values] might well be applied to cover
the fixed cost are products of these industries. The common assumption … that
“every tub must stand on its own bottom” [is thus] inconsistent with the
maximum of social efficiency. [Hotelling, 1938, p. 242]
In short, Hotelling argued that prices should be set
at marginal cost and that any resulting deficit, in decreasing cost industries,
should be financed by taxation would be lump-sum. This case for marginal cost
pricing must be seen therefore as a first-best argument. As we have emphasized
in earlier Lectures, there are reasons why there may be limits on the use of
lump-sum taxes and why government may have to rely on distortionary taxation
(indeed, the taxes actually referred to by Hotelling are likely to finance
deficits has to be raised in a way that is distortionary - so that for those
economic activities price does not equal marginal cost – then there is no
presumption that optimal pricing within the state enterprise will entail
marginal cost pricing. If the desired distribution cannot be achieved by
lump-sum means, the public sector pieces may have to be used as an instrument
for this purpose.
The departures from marginal cost pricing in a
second-best world have been subject of much of the postwar literature. Thus,
the behavior of the public enterprise subject to revenue constraint (e.g., that
they should break even) was investigated by Boiteux (1956). He derived a
formula for optimal pricing (see Section 15-2) that appears to be virtually
identical to those derived in the treatment of Ramsey tax problem (Lecture 12),
e.g., that there should be equi-proportionate reduction in consumption, a long price had been equal to marginal cost. That
the formula appear similar by Hotelling. There is however the significant
difference that each state enterprise may face a budget constraint that in separate
from that faced by others.[1] So
while we can exploit the earlier result, we need to bear in mind the special
features of the position of the state enterprise and its relations with
government – to which we now turn.
Control over
Public Enterprises
The
formal similarity between the problem of taxation and public enterprise pricing
provides considerable insight, but fail to do justice to the complexity of the
questions arising from the relationship between the state enterprise and
government, and before presenting the analysis we should comment briefly on some
of the relevant issues.
On central question is the nature of
the “directives” from the government to the “state enterprises”, and degree of
autonomy of the latter. There are varying degrees of autonomy. At one extreme,
the enterprise may be run like a government department (as is sometimes the
case with the Post Office); at the other, the enterprise may be an autonomous
corporation like IBM or ICI, with the state receiving the profits like the
other shareholder (this is true, for example, of certain joint ventures). More
common is the intermediate case, where the public enterprise has independent
management, but is set objectives by the state and is subject to specified
constraints. The formal organizational relations may, however, imperfectly
reflect the degree of autonomy. The civil servants running the Post Office may
have freedom of action that the head of the sate steel corporation, who may
directed to locate his plans in certain areas, to build certain types of
plants. Etc.
In the design of the administrative
structure, a key role is played by the incentive informational problem to which
we have alluded on several occasions. The interesting questions raised are not
ones that we have space to explore here, and simply assume that the structure
is of the following two-stage nature. First, the government specifies the
objectives of the enterprise and constraint. For example, it decides on the
target rate of return on capital that has to be achieved by the industry and
magnitude of the state subsidy (if any). Second, the enterprise determines its
pricing policy so as maximize is objective function subject to the constraints.
For example, given that the National Electricity Corporation has to make
profits of $x, how should it determine the relative prices to households and
industrial user? The efficiency and equity properties of the outcome depend on
decisions made at both stages.
With this kind of structure, there
is no direct link between public enterprises. The National Electricity
Corporation does not take account of the effect of its policy on the National
Coal Corporation. Such interaction – affecting such matters as transfer pricing
– need to be taken into consideration by the government in laying down the
guidelines for individual enterprises, e.g., to allow for the fact that they
may be producing closely competing products (e.g., long distance train and air
service).
The two-level structure is one reason why the
parallel with the literature on optimum taxation is not complete. In that case,
there was a one-stage problem. If we apply the Ramsey result directly at the
level of the individual enterprise, then we are ignoring the fact that the
constraints are themselves the subject of choice. The profit targets for
different industries are set by the government, and take account of the
interdependencies. On the other hand, if we collapse the problem into one
stage, and treat all public enterprises as a single entity, we are ignoring the
fact that the design of decentralized guidelines is an important institutional
feature of the public sector.
In that follows, we pay particular attention to the
relationship between the two levels of decision-making, and the wider question
of the links with other instruments of policy. Do we, for example, want to keep
public sector prices low for redistributional reasons, and how does that depend
on the scope for redistribution via tax system? In the analysis we of necessity
have to leave on one side many important issues. We do not discuss the definition
of marginal costs and related questions such as peak load pricing. We do not,
in the models investigated, allow for uncertainty. The issue of incentives for
the managers of public enterprises is not addressed directly, nor do we
consider the information that is available to the government in its
decision-making. We assume, for instance, that it knows the technologies and
demand curves facing various industries, if this information is relevant for
the directives it gives to different firms. (Of course, if it had this
information, there would be bless need for decentralization.)
The analysis here is concerned with the publicly
owned enterprise. In a number of countries, particularly the United States,
industries such as telephones, electricity, and railroads, are typically
privately owned but publicly regulated. There is again a two-tier structure.
The government imposes constrains on the operation of the industry, and the
enterprise maximizes subject to the constraints. The different is, however,
that the enterprise objectives are now private objectives, such as the
maximization of profits or sales. There has been an extensive literature on
regulation (see, for example Baumol and Klevorick, 1970; Bailey, 1973). We make
no attempt review this literature; we do however note an passant some of the
main results. Finally, we shall have nothing to say about the relative merits
of private ownership, with and without regulation, and direct public ownership
and control. These issues are critical, but a full discussion is beyond the
scope of these Lectures.
15-2 DEPATURES
FROM MARGINAL COST PRICING
this
section we consider the departures from marginal cost pricing that may be
implied by need to finance deficits, by the existence of monopoly sewhere, and
by redistributive goals. We assume initially that all individuals are
identical, relaxing this when we refer to redistribution.
The Enterprise
with a Profit Target
The
simplest situation is that of a single public enterprise, producing one nal
product in quality Z (in per capita terms), in a otherwise competitive economy
(where the vector of per capita private outputs is denoted by X). all
individuals have identical utility functions U(X,Z,L), where L is the quantity
of labour supplied per person. Labour is
taken to be the numeraire. We denote by q the vector of prices of private
sector product and by p the price of the public output. The production
constraint assumed to be of the form
Ω
≡ F(X) + C(Z) – L = 0 (15-1)
There
F(X) gives the labour requirement in the private sector, and (Z) that in the
public sector. It is assumed that the production set is convex, the condition
for profit.
∏
≡ q . X – F(X) (15-2)
(e.g.,
value of the net output minus labour cost), is maximized a necessary condition
for which is that qi=Fi, where the latter denotes the
derivative of with respect to Xi. it is assumed at this stage that
there are constant return to scale in the private sector. So ∏ ≡ 0. The
implication of pure profits are discussed later.
The public enterprise is assumed to
determine its price, p, to maximize social welfare, as measured by the indirect
utility function of the representative consumer, denoted by V(q.p). the
enterprise is constrained by the profit condition (per person)
pZ
– C(Z) + T > ∏0 (15-3)
where T denotes the subsidy by the
government and ∏0 the profit target. The subsidy is
assumed to the financed by lump-sum taxation, so that T enters the indirect
utility function. There are assumed to be no other taxes at this stage. The
solution to the pricing problem may be seen by forming the Lagrangean.
L = V(q.p.T)
+ λ [pZ – C(Z) + T -∏0 (15-4)
The first-other condition with respect
to p may be written using the properties of the indirect utility function (the
assumption of constant return to scale in the private sector means that the only change in V is that
arising directly from p):
-
αZ + λ [Z +
(p-C1)
] (15-5)
] (15-5)
where α is the private marginal utility
of income.
Suppose first that T is freely
variable, so that lump-sum taxation can be employed to finance any deficit. The
first-other condition with respect to T (using the fact that (provided 
is that
is that
-
α + λ = 0 (15-6)
From
(15-5) it follows that (provided 
/
a
necessary condition for optimally is that
/ a
necessary condition for optimally is that
p
= C1 (Z) (15-7)
i.e.,
price equals marginal cost. This is an illustration of the standard argument
for marginal cost pricing.
Where there are constraints on the
use of T, and the enterprise has an effective profit target, then the pricing
rule must be modified. Suppose that T
0, and that with
marginal cost pricing this is not sufficient to allow the enterprise to satisfy
(15-3). This situation is illustrated in Fig. 15-1, where the profit target is
taken to be that of breaking even. At the level of output where the price equals
marginal cost, there is the deficit indicated by the hatched area. In other to
meet the profit target, the firm has to reduce output to ZB, where
price exceeds marginal cost. As drawn in that diagram, the instruction to the
enterprise to break even completely determines its pricing policy. It sets
price above marginal cost to the extent necessary to avoid a deficit.
0, and that with
marginal cost pricing this is not sufficient to allow the enterprise to satisfy
(15-3). This situation is illustrated in Fig. 15-1, where the profit target is
taken to be that of breaking even. At the level of output where the price equals
marginal cost, there is the deficit indicated by the hatched area. In other to
meet the profit target, the firm has to reduce output to ZB, where
price exceeds marginal cost. As drawn in that diagram, the instruction to the
enterprise to break even completely determines its pricing policy. It sets
price above marginal cost to the extent necessary to avoid a deficit.
In
practice, public enterprises produce more than one produce, and this introduces
degrees of freedom in to the choice of pricing policy. Suppose that there are
two products Z1, Z2. There are typically many
combinations of the prices p1,p2 that will satisfy the
profit constraint. How should the 
Figure
15-1 Public enterprise with break-even
constraint.
m
depart from the marginal cost principle? There have been two main phools of thought.
One view is that the mark-up over marginal should very according to “that the
market will bear”, i.e., inversely with the pasticity of demand. Opposed is the
position that prices should be oportional to marginal cost, advanced by, among
others, Frisch (1939) and Allais (1948).
In other to consider the merits of these rival
views, we may modify the earlier analysis, so that maximization problem is now
represented by the Lagrangean :
L =
V(q, p1, p2, T) + λ [p1Z1
+ p2Z2
+ C(Z1, Z2) + T - ∏0] (15-8)
The
are assuming that the level of the lump-sum tax fixed. The first-other
conditions with respect to the prices, p1 and p2, are:
(15-9)
There
C1 denotes 
. The parallel
with the Ramsey problem should at this point be clear, if we write p1-C1
≡ t1, then these conditions are the same as those in Lecture 12 (see
Eq. (12-13)).
. The parallel
with the Ramsey problem should at this point be clear, if we write p1-C1
≡ t1, then these conditions are the same as those in Lecture 12 (see
Eq. (12-13)).
If we consider the special case
where demands are independent and there are no income effects, then,
re-arranging, we have for good 1
|
This familiar Ramsey result, that the
“tax” should be inversely related to the elastic of demand, supports therefore
the “what the market will bear” view rather than the Frisch-Allais
proportionality rule. This, and other implications, were brought out by Boiteux
(1956). The extent of devinations from marginal cost pricing depends on the
budget constraint. Where this is not binding (e.g., because lump-sum taxes can
be employed) λ = α
and p1 = C1. At the other extreme, as the required profit
approaches the maximum possible, λ
à α,
and the right-hand side of (15-10) tends to unity. This yields as limiting case
the price-discriminating monopolist, since marginal revenue equals marginal
cost implies
(
(15-11)
Where
is the elasticity of demand.
is the elasticity of demand.
As in the optimum tax literature, the
analysis can be extended to interdependent demands. This is left as an
exercise.
Exercise
15-1 Examine
the optimal pricing policy where there are two goods with interdependent
demands. How does the excess of price over marginal cost depend on the cross-elasticities?
Are there circumstances in which a price less than marginal cost may be
justified?
Profits in the
Private Sector
The
assumptions made to date (both here and in the earlier treatment of optimum
taxation) do not allow for pure profits in the private sector, which arise in
the competitive case where there are decreasing returns to scale. We now
consider the implications of the existence of profit for public enterprise
pricing and the relation to the optimum tax formulae.
With the introduction of pure
profits, we have be careful about the normalization of producer and consumer
prices (Munk, 1978). We write q for consumer prices, s for producer prices, and
for the present treat labour as commodity zero. Since the supply functions are
homogeneous of degree as commodity zero. Since the supply functions are
homogeneous of degree zero in producer price (including those of the public
sector), in the absence of lump-sum income, one can in that case normalize by
fixing one producer price and one consumer price. There is no loss of
generality in fuming one good to be untaxed (as in analysis to this point).
This is however no longer true where the consumer receives profit income, since
multiplying all producer prices by 5 implies that the profit income is also
multiplied by 5. The effect can be offset only by multiplying all consumer
prices by 5. The assumption of an untaxed good is not in this case inocouos. We
can normalize one producer price ore one consumer price.
The restrictions on commodity
taxation are particularly important then considered in conjunction with
restrictions on the tax rate on pure profit. Suppose that we set at unity one
producer price (that of labour). The profit of the private sector is (per
capita)
∏
= s X – F (X) (15-2’)
This is assumed to be taxed at a rate t,
so that the lump-sum income received by households is (1 –
) ∏( ≡ I). Such a tax can be seen to be
quivalent to a rise in all consumer prices by a factor of 1/(1 -), since demand
function are homogeneous of degree zero in consumer prices and
) ∏( ≡ I). Such a tax can be seen to be
quivalent to a rise in all consumer prices by a factor of 1/(1 -), since demand
function are homogeneous of degree zero in consumer prices and
[2]The
taxing of pure profit can therefore be achieved by uniform tax on all goods (and
labour)[3].
As a result, any restriction on profits taxation must summit both 
and the ability to tax all goods at uniform
rate. In what follows we assume that is fixed, and that there is one untaxed goods,
which is taken to be labour. The individual budget constrain is then, with a
sector Z of public sector outputs.
and the ability to tax all goods at uniform
rate. In what follows we assume that is fixed, and that there is one untaxed goods,
which is taken to be labour. The individual budget constrain is then, with a
sector Z of public sector outputs.
q
X + p Z = L + (1- 
(15-12)
(15-12)
Combined with the production constraint
and (15-2’), this yields the public sector budget constraint (per capita):
p
Z – C (Z) + (q-s) X + 
= 0 (15-13)
= 0 (15-13)
or
p
Z – C (Z) + q X – F
(X) – (1 – = 0 (15-3’)
= 0 (15-3’)
Let us now consider the position of the
public sector as a whole determining the prices to be charged were all goods
can be taxed except labour (and there is no poll tax or subsidy). The
maximization problem may then be formulated in terms of the lagrangean:
L =
V(q, p1, p2, I)
+ λ [ p Z
– C (Z) + q X – F (X)
– (1 – 
] (15-14)
] (15-14)
The first-other condition for the choice
of pk is
+ 
+ λ [ 
] (15-15)
The effect on profit given by (from
(15-2’))
(15-16)
From competitive profit maximization, si
= Fi, so that the first term on the right-hand side is zero,
and we can replace qj - Fj by qj – sj
in (15-15). We may also make use of the properties of the indirect utility
function, and observe that.
(15-17)
Where 
denotes the
compensated demand derivative and 
the income term (and there is a corresponding
expression for private good demand). The first-other condition (15-15) can then
be re-written as
denotes the
compensated demand derivative and the income term (and there is a corresponding
expression for private good demand). The first-other condition (15-15) can then
be re-written as
(
+ 
(
-
(15-18)
≡
0 (
(15-19)
(15-19)
This formula allows one to see the role
played by profits. The percentage reduction of consumption along compensated
demand schedule is no longer proportional for all commodities; there is a an
additional term representing the effect of profit. If raising the price of the
kth commodity the kth commodity
should be reduced by less than the lth
commodity[4].
The derivation of the first-order
conditions follows in the same way for the choice of indirect taxes (i.e.,
differentiating with respect to qk). there is however a significant
difference between the case of public sector pricing and that optimal taxation.
This is brought out clearly in the special case where there independent
demands, no income effect, and no joint production. In case, a change in the
public sector price has no effect on private sector profit, and the first-order
condition reduces to the familiar inverse elasticity from (as in (15-10)). In
contrast, in the case of a tax on a private sector product, the effect on
profits is given by (where
= 0 for m 
k)
= 0 for m k)
(15-20)
Substituting
into (15-19), with the cross-price and income derivatives set to zero (and
replacing Zk by Xk).
(
(15-21)
(15-21)
This
differs from the result given earlier for the no-profit case in the appearance
of the term in (1 - 
). Defining 
as before for the elasticity of demand, and
). Defining as before for the elasticity of demand, and
(15-22)
As
the elasticity of supply, we can re-arrange (15-21) as (where 0 = 1 – α/ λ):
(15-23)
This
is a generation of the result originally derived by Ramsey (1927). In which the
elasticity of supply now enters the termination of the optimum tax rate (he
implicitly assumed that = 0), and the other things being equal the tax
rate should be higher on goods supplied inelastically[5].
The difference between public sector pricing and optimal tax case is brought
out by the term (1 - ). in the public
sector, is in effect unity, all profits being returned
to the government, so that no supply considerations enter. In the case of
private goods, where the rate of tax on profit is less than 100 per cent, the
supply side has to be taken into account.
= 0), and the other things being equal the tax
rate should be higher on goods supplied inelastically[5].
The difference between public sector pricing and optimal tax case is brought
out by the term (1 - ). in the public
sector, is in effect unity, all profits being returned
to the government, so that no supply considerations enter. In the case of
private goods, where the rate of tax on profit is less than 100 per cent, the
supply side has to be taken into account.
A natural question at this juncture
is why governments do not impose 100 per cent profit taxes. Earlier we provided
some explanation as to why lump-sum taxes should not be the only source of
revenue. But, if profits taxes are non-distortionary, surely they should be set
at 100 per cent, and thus the questions with which we have been concerned cease
to be relevant? In practice, governments have not followed this Henry
George-like policy. Although in wartime a few countries have impose 100 per
cent surtax rates, they typically do not levy on a regular basis 100 per cent
taxes on profits and the incomes of fixed factors. The reason for this goes
back to the lack of information at the disposal of the government. Most importantly,
it finds considerable difficulty in distinguishing pure profits from the return
to capital, or the return to entrepreneurship. This is seen most clearly in the
case of unincorporated enterprise. If there were a 100 per cent profit tax, no
such enterprise would ever declare a profit it would always distribute the
“pure profit” as wages to entrepreneurs.
Monopoly and
Second-Best
The
existence of monopoly profits in the private sector gives rise to effects
similar to those just discussed, but also raises other significant issues.
Should the attempt to offset in effect? Do departures from marginal cost
pricing in the private sector provider grounds for deviating from marginal cost
in the public sector? In order to concentrate on this kind of question, we
abstract from the effects of profits by assuming a 100 per cent profits tax ( = 1). For the reasons just outlined this is
not realistic; it does however help separate the issues.
= 1). For the reasons just outlined this is
not realistic; it does however help separate the issues.
Suppose that we consider the choice
of public enterprise pricing policy where there are no indirect taxes and the
private sector monopolists have fixed prices, sj, where sj
> Fj. since = 1, we can write down the first-order
condition by analogy with earlier result:
= 1, we can write down the first-order
condition by analogy with earlier result:(= 
(
(15-24)
The pricing rule in the absence of
monopoly is now augmented by the term underlined in (15-24). This may be seen
as the change in revenue from the profit tax arising from changes in private
sector outputs include by a rise in pk (holding sj and Fj
constant for all j). To see the implications, let us take the case of a single
public enterprise, producing goods whose demands are independent and where there
are no income effects. The usual elasticity formula is augmented by the
underlined term. If private firms price above marginal cost, and if their
output is an increasing function of the public price, then we shall on this
account want to raise the price above marginal cost. Conversely, if their
output is a declining function of the public price, then the underlined term is
negative. If 
= 0, which is effectively the case taken by
Green (1961), the deviation from marginal cost depends solely on the
divergences (sj – Fj) in the private sector. Intuitively,
it might be felt that the corrective pi/Ci ratio for the
public sector should lie somewhere between the maximum and minimum values of sj/Fj
in the private sector, but Lipsey and Lancaster showed that this was not
necessarily so. It is indeed possible that price could be below marginal cost
if “monopolistic pricing of commodities complementary to it produce negative
terms in the above sum [greater] an all the positive terms arising from …
monopolistic pricing of substitutes” (Farrell, 1968, p, 48).
= 0, which is effectively the case taken by
Green (1961), the deviation from marginal cost depends solely on the
divergences (sj – Fj) in the private sector. Intuitively,
it might be felt that the corrective pi/Ci ratio for the
public sector should lie somewhere between the maximum and minimum values of sj/Fj
in the private sector, but Lipsey and Lancaster showed that this was not
necessarily so. It is indeed possible that price could be below marginal cost
if “monopolistic pricing of commodities complementary to it produce negative
terms in the above sum [greater] an all the positive terms arising from …
monopolistic pricing of substitutes” (Farrell, 1968, p, 48).
The treatment just given is rather
special, relating to an “irreducible” astortion, were indirect taxes cannot be
employed to correct the deviant behavior. The analysis needs be extended to
allow for the use of indirect taxation – see Guesnerie (1975, 1978). We should
also note that lying behind this treatment of the implications of market
imperfections for public factor pricing is a view of the behavior of the
monopolist that is clearly not appropriate to oligopolistic markets, where
strategic elements are likely to be important. Further development of the
pricing rules requires a more boundly based general equibrium theory of
imperfect competition, and – as he have seen in Lecture 7 – this at present at
a rather early stage.
Exercise 15-2 in
the context of the model of imperfect competition described in Lecture 7 (pages
208-217), we examine the optimal policy of state enterprise supplying the
output Y. Should it charge more than marginal cost, on account of the mark-up
in the private sector? Suppose that one of the firms in the X sector is taken
oover by the public enterprise. What should be its pricing policy?
Redistribution
and Public Sector Prices
There
has been considerable debate about the role of the public sector prices in
redistribution, as illustrated by the following quotations:
By far the
simplest way of securing the distribution … desire is through the price system
… the only price a public enterprise or nationalized industry can be expected
to set is what we may as well call a just price-a price which is set with some
regard for its effect on the distribution of wealth as well as for its effect
on the allocation of resource. [Graaff, 1957, p. 155, his italics]
and:
subsidies to the
consumption of commodities are a particularly inefficient way of redistributing
income … the best way of making a particular individual better off is to give
him a appropriate sum money… It is thus
unlikely that consideration of the distribution of income should lead to an
optimal price below marginal cost. [Farrell, 1958, pp, 113-14, our italic]
In attempting to assess the merits of
these views, we can apply the same analysis as in earlier Lecture, introducing
the distributional characteristic of the public sector good, 
(Feldstein, 1972a). the application is
straightforward, following the same lines as in Lecture 12, and is left to the
reader as exercise:
(Feldstein, 1972a). the application is
straightforward, following the same lines as in Lecture 12, and is left to the
reader as exercise:
Exercise
15-3 Suppose
that individuals differ, being identified by superscript h. there is a single public
enterprise producing two products subject to a break-even constraint. Derive
the first-order conditions corresponding to (15-9). For the special case where
demands are independent and there are no income effect, show that the
first-order conditions corresponding to (15-9). For the special case where
demands are independent and there are no income effect, show that the
first-order condition reduce to
(15-25)
Where b is the social marginal valuation
of income and ? the covariance between bh/
and 
k.
and k.
From the example just given, it is clear
that there may be situations where redistributional reason dominate in the
determination of the structure of price (e.g., where 
and 
). In this sense, Graaff is correct. But the
result depend critically on the extent to which orther vary the poll
tax/subsidy element of direct taxation in such a way that = 1, then prices is set below marginal cost
only where > 0. If the social marginal valuation of
income falls with income, then is positive only for an inferior good. If the
good is normal Farrell’s conclusion is borne out.
and ). In this sense, Graaff is correct. But the
result depend critically on the extent to which orther vary the poll
tax/subsidy element of direct taxation in such a way that = 1, then prices is set below marginal cost
only where > 0. If the social marginal valuation of
income falls with income, then is positive only for an inferior good. If the
good is normal Farrell’s conclusion is borne out.
We can go on to consider the range of
pricing schedules open to the public enterprise. One commonly employed is the
two-part tariff, involving a fixed payment coupled with a price per unit. This
departs from a single price plus poll tax in that consumer choosing zero
consumption are not liable for the fixed element[6].
More generally, the marginal price may vary with the quantity. The feasibility
of such a nonlinear schedule depends on total consumption being observable. If
resale or repeat purchasing is possible, then quantity discounts or premia can,
respectively, be undone, For discussion of the optimal nonlinear schedule, the
reader is referred to Spence (1977), Willig (1978), Goldman, Leland, and Sibley
(1977), Roberts (1979), and Seade (1979).
15-3 CHOICE OF
TECHNIQUE AND PRODUCTION EFFICIENCY
In
this section we consider the choice of inputs for the public sector. The
questions discussed may be posed- in a somewhat over-simplified from-in the mix
of inputs used by each enterprise? Put another way, suppose that the government
set shadows prices for input and tells enterprise to minimize costs at those
prices. Should these prices be the same for all enterprises and all sub-units
of enterprises? What should be the relationship between these shadow prices and
market prices?
Production
Efficiency
The
questions just described are equivalent to asking whether there should the
production efficiency. Should the public sector be productively efficient in
the sense that the marginal rate of technical substitution between any two
outputs should be the same in different enterprises? Or should the railways
make the choice between coal and oil on a different basis from that faced by
the electricity industry? Should the economy as a whole productively efficient
in that marginal rates of substitution are the same in both public and private
sector?[7]
Intuitively, it seems plausible that
production efficiency is desirable. The Literature on the second-best has
however led one to be suspicious of such intuitive argument. Does, for example
the need to meet a profit target lead to input choice being different from
those made on the basis of market prices? Are distributional considerations
relevant in the choice of technique?
Our discussions indicate that the most one can hope
for is a result of the “separation” kind obtained in the Lectures on optimal
taxation. Where there are departures from first-best in one area, can we none
the less continue to hold? In the second-best conditions should have been
analyzing, if the government can impose 100 per cent profits taxation and tax
all commodities and factors, if the budget constraint of enterprises are
optimally chosen, then we will want to have production efficiency in the
economy as a whole. On the other hand, where these conditions do not hold, the
presumption in favour of production efficiency no longer obtains. Where, for
example, the budget constraints are arbitrarily fixed, we will want to have
efficiency within each enterprise, but there may be different shadow prices in
different enterprises.
The issue of production efficiency
was originally addressed in the classic paper by Boiteux (1956); he established
basic efficiency theorem for an arbitrarily given constraint. Diamond and
Mirrlees (1971) examined the question, using more general techniques, for the
case of unrestricted taxation and no pure profits and established the
desirability of production efficiency under fairly weak conditions. They
require only that the social welfare function be individualistic and that there
exist some good (with positive price) that is a “good” for all individuals.[8]
The argument runs broadly as follows. If the optimum were in the interior of
the production set, small changes in prices would still result in technically
feasible demands. On the other hand, lowering the prices of the good consumed
by everyone (strictly, a good that no consumer supplies), or raising the price
of the good supplied by everyone (strictly, non-satiation and positive response
of the welfare function). Therefore, given this condition, at an optimum
production must occur on the production frontier.
The extension of the analysis to
economies where there are pure profits and restriction on the set of admissible
taxes is studied in Stiglitz and Dasgupta (1971), Dasgupta and Stiglitz (1972),
Mirrless (1972a) and Hahn (1973). The result show that, if there are enough
instrument at the government’s disposal, and in particular if the government is
free to set any rates of tax (including 100 per cent) on the pure profit of
different producers, then production efficiency is desirable even with
decreasing return to scale in the private sector (giving rise to pure profit).
On the other hand, restrictions on the taxing possibilities of the government,
for example, limits on taxing pure profit or when a tax cannot be levied on
certain commodities or factors, may mean that production efficiency is not
desirable.[9]
We do not attempt to provide a
rigorous account of production efficiency; instead, we take an example that
brings out the role of several factors. We consider a set of public
enterprises, identified by an index j, each of which produces an output Zj
using inputs of two primary factors (types of labour) 
and 
according to the production function:
and according to the production function:
Zj = 
(15-26)
(15-26)
Where
Qj is assumed to be a
differentiable, well-behaved production function exhibiting constant returns to
scale (an assumption that can be relaxed). For each enterprise there is a
profit constraint
= 
(15-27)
Where wi denote the producer
input prices. On the assumption that the government can vary freely the taxes
on all goods and factors, but is restricted to taxing pure profits at rate, we
may derive the following first-order condition for the choice of input in the jth enterprise (where 
is the multiplier associated with the
constraint (15-27) and µ a multiplier (associated with an overall revenue
constraint) - see Stiglitz and Dasgupta (1971):
is the multiplier associated with the
constraint (15-27) and µ a multiplier (associated with an overall revenue
constraint) - see Stiglitz and Dasgupta (1971):
(15-28)
From this result we can see at once
that there are several sufficient conditions for production efficiency. If
there are no profit in the private sector, then the marginal rate substitution
between L1 and L2 in the jth public enterprises and equal to the private sector rate of
substitution. Profit taxes ( = 1), or if there lump-sum taxation such that
µ = α. Thus, of the government’s revenue requirements can met by a partial profit
tax, we may have < 1 but µ= α. Where these do not hold, but
the profit targets ∏? are set optimally, then will be equated for all j. in this case, the marginal rates of substitution are equal
within the public sector (since 
is equal for all j). all public enterprises use the same shadow prices.
= 1), or if there lump-sum taxation such that
µ = α. Thus, of the government’s revenue requirements can met by a partial profit
tax, we may have < 1 but µ= α. Where these do not hold, but
the profit targets ∏? are set optimally, then will be equated for all j. in this case, the marginal rates of substitution are equal
within the public sector (since is equal for all j). all public enterprises use the same shadow prices.
It should be noted that analysis assumes that the
government can levy a full set of commodity taxes and that it can tax all
factors in all uses. Otherwise, we may want to use distortionary factor taxes,
in some industry, as partial substitute for the absent commodity taxes.
Similarly, the fact thet we cannot tax labour in one use (e.g., household
production) does not mean that we do not want to tax it in other uses. Many of
the important instances of distortionary factor taxes can be related to these
condition; for incorporated sector may arise for the impossibility within the
unicorporated sector, the two factors must be treated the same.
Finally, we have taken no account so
far of distributional consideration, but they may also provide a reason for
productive inefficiency.[10]
Implication of
Production Efficiency/Inefficiency
The
efficiency/inefficiency result has several important implications; and it
serves to integrate the discussion of a number of different policy problems.
First, production efficiency within
the public sector implies that the transfer prices used by public enterprises
for sales within the public sector should be marginal prices, and hence not
necessarily equal to those charged to final consumers. The profit target should
be met on sales outside the public sector; to charge a mark-up on the transfer
of electricity to the public steel industry would lead to production
inefficiency (as would taxes on any intermediate transactions).
The second implication of the efficiency result concerns
the setting of enterprise objective related to input use. This applies
particularly to the requirement of a minimum rate of return (as with regulated
industries). Such rate of return constraints may be compared with the absolute
profit target considered above. It can be shown that for a given output a
cost-minimizing firm subject to a binding minimum
rate of return constraint produces, its output using a more (less)
capital-intensive method of production that with an absolute constraint if the
minimum rate is less than (exceeds) the market rate (Gravelle, 1976). By
contrast, a regulated private firm subject to a chooses a more capital-intensive
technique than the one that minimizes cost for the output level produced
(Baumol and Klevorick, 1970, Proposition 3). Where the conditions for
production efficiency do not hold, then it may well be desirable for the shadow
price of capital to differ from the market rate of interest, but such departures
need to be derived from an explicit analysis of the kind described above, with
full account taken of the instrument that government has at its disposal.
In a open economy, the possibilities for
international trade can be treated as private sector industries, and the
efficiency result implies that in evaluating public sector decisions the
international prices should be employed. This result holds not only when
commodity taxes are chosen optimally, but also when they are fixed arbitrarily
(Dasgupta and Stiglitz, 1974).
Finally, in the context of intertemporal decisions,
the efficiency result implies that the correct shadow price of capital (the
social rate of discount) is the producer rate inters. This is in contrast to a
substantial literature arguing that the social discount rate should be rate of
time preference, or some weighted average of this rate and the private rate of
return on capital. In the next section we take up this application in more
detail.
15-4 COST-BENEFIT
ANALYSIS AND SOCIAL RATE OF DISCOUNT
The
choice of the social rate of discount plays a critical role in cost-benefit
analysis, and we begin with a more general review of the issues involved.[11]
Cost-Benefit
Analysis
In
principle, cost-benefit analysis is straightforward. Any investment project can
be viewed as representing a perturbation of the economy from what it would have
been had the project not been undertaken. To evaluate whether the project
should be undertaken, we need to look at the levels of consumption of all
individuals of all commodities at all dates, under the two different
situations. If all individuals are better of with the project than without it
then it should be adopted (if there is an individualistic social welfare
function); if all individuals are worse off, then it should be rejected. If
some individuals are better off, and some worse off, whether we should adopt it
depends on how we weight the gains and losses of different individuals.
Although this is obviously the
“correct” procedure to follow in evaluating projects, it is not a particular
one; the problem of cost-benefit
analysis is simply whether we can find reasonable short cuts. In
particular, we are presumed to have good information concerning the direct costs and benefits of a project (its
inputs and its outputs);[12]
the question is whether there is
any simple way of relating the total effect. Thus, in the case of the choice of
discount rate, there is trivial sense. use the social rate of time preference
for evaluating benefits and costs accruing in different periods. This however
applies to total effects, and there is no reason to believe that these are
simply proportional to direct effects that are observed. If the ratio of total
effect to direct effects changes systematically over time, then we would not
wish to use the social rate of time discount in evaluating a project when
looking only at direct costs and benefits.
In a first-best word, with no
distortions and full scope for lump-sum redistributive taxation, if a project
is “profitable” on the basis of its direct effect using market prices,
then-with an individualistic social welfare function – it is socially
desirable. The problem of finding the correct shadow princes for cost- benefit
analysis arises from the existence of market imperfections and failures; it is
concerned with situations where one cannot necessary infer social desirability
on the basis of the profitability of the project. In the case of the social
rate of discount, the difficulties stem from differences between the private
rate return and rate at which society can transfer resources between periods.
The former is equal, in a competitive model, to the marginal physical rate of transformation of
output in one period into output in the next. The latter is the rate at which
to the government can make the transfer, or what we refer to as the marginal
economic rate of transformation.
In the applying this approach, we
need to begin with the reasons why a first-best cannot be attained. This
depends on the initial sources of market failure, and on the extent to which
government policy instruments can be employed to approach the first-best. As we
have seen in earlier Lectures, there is no more reason to believe that the
intervention is socially optimal at any point in time. Savings may be too low,
e.g., where individuals give less weight to succeeding generations that they
would collectively. Savings may be to high, e.g., because people can give as
much to their descendants as they would like but are constrained in giving to
antecedents. The direction of the misallocation may not therefore be clear, but
there is certainly no presumption that the market solution is socially optimal.
Social Discount
Rate in the Overlapping Generations Model
In
order to explore this in more depth, we make use of the overlapping generations
model described in earlier Lectures and which provided the basis for the
treatment of the optimum taxation of savings in Lecture 14. The main
modification is that there is now assumed to be a government capital good-the
social discount rate being the return on public capital. Total government
capital is denoted by G and enters the determination of aggregate output in
period u, which is assumed to be given by a constant returns to scale
production function:
Yu = F (Ku Gu
Lu Pu) (15-29)
where Pu denotes the total
population, Lu hours of work, and Ku the private capital
stock, at time u. the return to public capital accrues to the government.
output can be used interchangeably as either a consumption or capital good:
Yu = Cu + (Ku+1 - Ku)+ (Gu+1 - Gu) (15-30)
where there is assumed to be no
depreciation and no current government spending, and where Cu
denotes total consumption.
Initially we assume that all
individuals are identical; this is a crictical assumption which is later
relaxed. They live for two periods, working in the first, and the lifetime
utility of a representative member of the generation born at u is U (
, 
, Lu),
where 
denotes consumption in period i. total
consumption at date u is therefore, per worker,
, , Lu),
where denotes consumption in period i. total
consumption at date u is therefore, per worker,
(15-31)
where
n is the rate of growth of the population. The wage rate is wu
before tax and 
u
after tax, and price of second period consumption to generation u is pu.
The indirect utility function, Vu, is a function of u and
pu there are assumed to be no lump-sum taxes-although see below).
u
after tax, and price of second period consumption to generation u is pu.
The indirect utility function, Vu, is a function of u and
pu there are assumed to be no lump-sum taxes-although see below).
The level of capital goods at date u
is related to the savings of the order generation, and the capital market
equation may be written (see e.q., (14-53))
(1
+ n) ku+1 = Au - Bu (15-32)
Where
ku+1 is capital per worker, Au savings per worker, and Bu
the level of government bonds per worker. It is assumed that there are only two
assets in the economy-bonds and real capital. In particular, there is at this
stage no equity investment in firms. There are no “pure” profits. Again, this
is a critical assumption. From the individual budget constraint,
(1
+ n) ku+1 = u Lu - 
- Bu (15-33)
u Lu - - Bu (15-33)
Finally,
the production constraint may be expressed in per worker terms and re-arranged
to yield
(1
+ n) ku+1 = 
u + Lu (
,
) -
- 
-
(1 + n) gu+1+
gu (15-34)
u + Lu (,
) -
- -
(1 + n) gu+1+
gu (15-34)
Where
gu is government capital per worker (and we revert to f for the production function).
As in the previous Lecture, we
assume that the government maximizes the sum of lifetime utilities over
generations discounted by factor 
(where 
1);
(where 1);
(15-35)
We
introduce as before the state valuation function:
Ku, gu,
Lu Pu)
=
max
-
(1 + n) gu+1+
gu]+
(15-36)
(15-36)
Where
we have eliminated ku+1 between (15-33) and (15-34), and ku+1
in Γ(u+1) is given by the latter. The analysis of the optimal wage tax () and interest
tax (p) follows the same lines as in Lecture 14. Here we concentrate on the
effects of government capital. The first-order condition for the choice of gu+1
is:
) and interest
tax (p) follows the same lines as in Lecture 14. Here we concentrate on the
effects of government capital. The first-order condition for the choice of gu+1
is:
(15-37)
The
difference equations governing Γi are:
(15-38)
(15-39)
Where
fk, fg denote the marginal products of private and government capital
respectively. As before, we assume that an optimal policy exist.
Implications
Results
we
begin by considering the case where the government has full control over debt
policy. since Bu does not
effect Vu, the first-order condition is that ? = 0. It then follows
from (15-37) – (15-39) that
= 
)
and
= 
=
1 (15-40)
It
is immediate therefore that in this model, with identical individuals, all pure
profits taxed away and a completely flexible debt policy, the rate of return on
public capital must equal that on private capital. The social rate of discount
is private rate of return. The intuitive reason for this is that, with
optimally chosen taxes and debt policies, aggregate savings are fixed, and unit
of public capital displaces precisely one unit of private capital. And has no
further repercussions. From the difference equation (15-38), with 
= 0, the steady-state value of fk is given by (in steady
sate k, g, L and all other per capita variables are constant):[13]
= 0, the steady-state value of fk is given by (in steady
sate k, g, L and all other per capita variables are constant):[13]
=
(15-41)
If
the objective function is the total sum of utilities (so = (1+n)/(1+
)), the
steady-state rate of return is equal to the social rate of time preference.
This does not in general hold outside the steady state.[14]
= (1+n)/(1+)), the
steady-state rate of return is equal to the social rate of time preference.
This does not in general hold outside the steady state.[14]
These results give a straightforward
answer to the question of the choice of social discount rate. The assumptions
required are, however, of subious validity. The government does not use debt
policy primarily for purpose of intertemporal redistribution, as the above analysis
requires, and does not impose 100 per cent pure profits taxes; finally,
individuals are not identical.
The assumption about debt policy can
be interpreted more generally as applying to monetary policy: the issue of
money can have the same effect as Bu.
moreover, as noted is earlier Lectures, the use of differential lump-sum taxes
on the two generations equivalent to the use of debt. Thus a combination of
lump-sum taxes with zero present value has no impact on allow the government to
shift resources through time. Nevertheless, even when debt policy is viewed
more broadly, there may be situations where the government does not have
complete freedom to achieve intertemporal redistribution. Where this is so 0, and we have 9from (15-37) – (15-39)):
0, and we have 9from (15-37) – (15-39)):=
=
1+ (
(15-42)
If the government cannot use debt/monetary policy
freely for purposes of intertemporal redistribution, the social rate of
discount is not necessarily equal to the producer rate of interest. In steady
state, it is still true that 
the social rate of time preference, but 
< 0 implies fk > . the value of depends on the choice of tax instrument – see
the following exercise (based on Pestieau, 1974).
the social rate of time preference, but < 0 implies fk > . the value of depends on the choice of tax instrument – see
the following exercise (based on Pestieau, 1974).
Exercise
15-4 Derive the first-order conditions for the
choice of pu and u (by
differentiating (15-36)), and examine their interpretation in steady state
(making use of the difference equations in Γp and 
). use these
result to exspress the rate of return on public capital as a function of the
private return and consumer rate of interest. Show that where there is no tax
on wages fg is a weighted
average of the two rates, but that the weights need not lie in the interval
[0,1].
u (by
differentiating (15-36)), and examine their interpretation in steady state
(making use of the difference equations in Γp and ). use these
result to exspress the rate of return on public capital as a function of the
private return and consumer rate of interest. Show that where there is no tax
on wages fg is a weighted
average of the two rates, but that the weights need not lie in the interval
[0,1].
The model discussed above is parallel to that of
Diamond and Mirrless (1971), assuming constant returns to scale and hence no
pure profits.[15]
We have seen however that production efficiency may not be desirable: the
social discount rate is not necessary equal to the private rate of return. The
reason for this is that the government cannot-because of the assumption of
restricted debt/monetary policy-transfer resources at will between priods. It
cannot in effect trade freely on all markets. Where this restriction is
present, and ? > 0, then the marginal physical rate of transformation of
output in one period into output in the next (1+fk) is not necessarily equal to the rate of
transformation thet can be achieved by the government using a restricted class
of instrument (the marginal economic rate of transformation). This can be
viewed another way. Private savings are only channeled into private capital
accumulation; the government on the other hand is constrained in its ability to
influence private capital formation (where Bu
is fixed).
Finally, we allow for difference between people. If
the government is constrained in its ability too levy differential taxation,
then, even with 100 per cent profits taxes and complete control of debt policy,
the social rate of discount may deviate from the private rate of return for
distributional reasons. Moreover, if the distributional impact differs across
capital goods, then different social rates of discount ought to be employed for
different types investment.
15-5 CONCLUDING
COMMENTS
Our
treatment of decisions in the public sector has been highly selective, and
there are many issues that have been left on one side. We have not considered
peak load pricing or the interrelation between pricing and investment
decisions. No account has been taken of uncertainty or of rationed demand. the
discussion of cost-benefit has been very circumscribed. There is however one
shortcoming that we should emphasize: the lark of any explicit analysis of the
information available to the government and of the process by which it is
obtained.
This may be illustration by
reference to the setting of guidelines to public enterprises. Suppose that the
government possesses the same information as the producers (in both private and
public sector). Then clearly, it could solve the problem of optimal pricing for
the entire each enterprise and then face the enterprise with constraint of not
exceeding this level. The government does not however possess this quantity of
information: and if it did, it would hardly need to decentralize. We have
therefore to consider the mechanisms available to the government that enable it
to elicit the necessary information, and the motives of those in charge of the
enterprises. They latter will depend on the kind of considerations discussed in
Lecture 10 and on the specific incentive structures that are in effect. Thus,
there is an extensive literature in the field of economic planning concerned
with the effect of different incentive structures that are discussed in Lecture
10 and on the specific incentive structures that area in effect. Thus, there is
an extensive literature in the field of economic planning concerned with the
effect of different incentive schemes (for a recent review, see Johansen, 1978,
Ch 5). The problem is moreover close to that of the revelation of preferences
for public goods. In the next Lecture, we examine some of the procedures that
have been proposed.
READING
The
Anglo-Saxon literature on marginal cost pricing is usefully collected in Turvey
(1968); for an extensive account of the French literature, see Dreze (1972),
Kolm (1968, 1971) Rees (1968, 1976) and Turvey (1971). For discussion of the
distributional aspect, see Feldstein (1972a, 1972b). On the regulation of
public utilities, see the original article by Averch and Jonson (1962), and
surveys of the fields by Baumol and Klevorick (1970) and Bailey (1973). The
results on production efficiency are discussed in a Diamond and Mirrlees
(1971); for a broader treatment of the results in relation to second-best
theory, see Guesnerie (1978). There is an extensive literature on cost-benrfit
and the choice of the social discount rate-see Little and Mirrless (1974) and
the references given there.
[1] Informal
sense (as we note below) the taxation problem discussed earlier is special case
of the more general problem that Boiteux analysed: wehere there is a single
budget constraint for the whole public sector, and the level of revenue raised
for the public sector is set optimally (not, as in the Boiteux formulation,
arbitrarily)
[3] This
means in the optimal tax problem that, where the value of private profit
exceeds the government requirement, denominated appropriately, afirst-best
solution can be attained either by a pure profits tax or by taxing all goods
and factors, See Munk (1978).
[4]
in
the formulation given, it has been ssumed that all goods (expect labour) can be
taxed: the effect of the lagrangean (15-14)
[5] Most textbooks refer
to the formula that taxes should be proportional to ? (e.g., Pigou, 1947, p.
108). For further discussion, see Stiglitz and Dasgupta (1971, p. 170)
[6] This
feature of the two-part tariff is not captured in the empirical application by
Feldstein (1972b), who treats the fixed payment as a uniform lump-sum tax
[7]There is a closely
related question, which we should more properly have asked in the Lectures on
optimal taxation. Should the government impose differential factor taxes on
different industries within the private sector; i.e., should the private sector
economy be production efficient? See Stiglitz and Dasgupta (1971)
[8] Even this restriction
may be dropped if we allow trade taxes, i.e., taxes that are differentiated on
the basis of whether the individual is buying or selling a commodity.
[9] Also, we noted in Lecture
12 that, in the course of a process of tax reform, where only limitied steps
may be made, there may be situations in which temporary inefficiencies are
desirable even when the full optimum is characterized by production efficiency
– Guesnerie (1977)
[10] See Dasgupad and
Stiglitz (1972) and Mirrlees (1972a).
[11] The situation with
which we are concerned in this section are those where the government directly
undertakes the project; there are other circumstances in which the government
is called upon to license some private project (particularly in less developed
countries) or to provide some critical input (capital). Although many of the
same considerations arise, one must bear in mind the distinction between these
circumstances. In general, the criteria for evaluating project in these two
situations will be different.
[12] In practice
[13] As in Lecture 14, we
assume that an optimum, if it exists, converges to a steady state.
[14] It should be noted
that the discount factor relates to utilities,
not consumption-see Presteau (1974).
[15] The assumption of
constant return to scale encures that in steady state all relevant variables
are constant in per capita terms. It also means that, if
the return to the public capital (? Per worker in steady state) accrues to the
government, it is sufficient the new public capital formation (ng per worker).
Since the assumption ? 1 implies that ? n. if therefore the return to public
capital is appropriated by the state or 100 per cent pure profits taxation is
possible, then there is no need for distotionary taxes to finance public
capital formation.
Komentar
Posting Komentar