Who Benefits from Public Utilities?

Who Benefits from Public Utilities? *

PETER HARTLEY Monash University,

Clayton, Victoria 3168 and

Princeton University. Princeton, New Jersey 08544

CHRIS TRENGOVE Monash University,

Clayton, Victoria 3168

We model the determination of output, factor payments and prices within publicly ownedfirm, assuming thefirms are managed by utility-maximizing employees monitored by vote-maximizing politicians. The choice of a public monopoly to supply the output is most suited to further the redistributive aims of thepoliticians, but will also be favoured by employees who can capture some rents.

This paper discusses the choice, within publicly owned ‘utilities’, of factor inputs, factor payments, prices, and the level of output and its distribution among different consumer groups. The firms in which we are interested are monopolies which supply electricity, natural gas, postal services, telecommunications, and so on. We d o not focus on the various efficiency arguments, such as the possible existence of natural monopoly, which have been used to justify the existence of public utilities. Rather, we restrict attention to the redistributive possibilities of supplying output through public monopolies. Our concentration on t h e redistributive element is justified by its ability to explain certain features of utility behaviour which are not consistent with the alternative view that public utilities are engines of economic efficiency.

Economists who have examined tariffs charged by publicly owned utilities have usually discovered that the tariffs are not closely related to calculated

We would like to thank participants in seminars given at Monash University, the University of Adelaide, the University of Queensland. the Australian National University and Princeton University, and in particular Jonathan Pincus, George Fane, Harvey Rosen and anonymous referees for useful comments on earlier versions of this paper.

marginal costs of supply.’ In our own examination of the electricity supply and telecommunications industries in Australia we have observed that tariffs are often justified on the grounds that they reflect average, rather than marginal, costs.

Additional inefficiencies are introduced by cross- subsidies from some groups of consumers to others (for example, from urban to rural consumers). Also, (apparently disfavoured) groups with low elasticities of demand (such as commercial establishments purchasing electricity for lighting) are charged in excess of the average costs of supplying them. Some consumers not rationed by price are rationed by other, probably less efficient, means. Examples include long queues to obtain telephone service and lower reliability of electricity supply for non-metropolitan customers.

Other investigators of utility industries in Australia have argued that there is considerable evidence of over-manning, and other indications

’ See, for example, T w e y (1968). Pelman (1971) and Rees (1976). In Hartley and Trengove (1984) we discuss the differences between SECV tariffs and the marginal costs of supplying electricity in Victoria, Australia. Trengove (1982) discusses the operations of Telecom Australia including the relationship between tariffs and costs.

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164 THE ECONOMIC RECORD JUNE

that inputs are not being chosen to minimize costs. Engineering expertise appears to be more valued within the organization than is commercial expertise. Wages and working conditions for employees often appear more generous than in private firms.

We examine two major types of restriction on trading opportunities that are useful for achieving politically desired distributional outcomes, though at the cost of some of the above inefficiencies. The first is the granting of monopoly status, that is, a restriction placed on product market trading opportunities. This is particularly useful when the purpose of political intervention is cross- subsidization. The second type of restriction relates to the capital market, or the fact that the utility is publicly owned. The absence of explicit shareholders is important in deriving an underlying bias towards average cost-pricing. Capital is in effect assigned a zero’ weight and profits are diverted to other factors of production and to consumers.

I Monitoring State Enterprise Taxpayers might be thought of as ‘owners’ of

public enterprises. However, non-tradability of ownership rights reduces incentives for the citizen- owner to monitor State enterprise profitability. Furthermore, the absence of an organized market where rights to the profits are continuously traded raises the costs of obtaining information on managerial performance. With lower benefits accruing to any individual monitor and with higher monitoring costs, the nominal ‘owners’ of State enterprises are less likely to require profit maximization than are the actual owners of private firms.

In addition, monitoring the profitability of State- owned utilities is unlikely to be a private interest of elected representatives. The ‘economic theory of democracy’ does not constitute a settled body of thought.’ Nevertheless, there is some agreement that a representative political system based on majority rule is likely to result in government policies which favour a coalition of minorities at the expense of voters not in the coalition. Political parties can gain (and hold) office by proposing and implementing inefficient policies so long as the costs are dispersed across many voters and the policy provides significant benefits to politically

Mueller (1979) provides a useful guide to this literature.

influential groups. Following’ Peltzman (1976) we shall suppose that

the political process (for simplicity, ‘politicians’) maximizes political support given by

G1,l > 0, G1,2 > 0; G2 > 0

where CSI is the consumer surplus of group 1 derived from consumption of the utility product, CS2 is the consumer surplus of group 2, T is the excess of utility revenue over costs, and M is government expenditure on monitoring (see discussion below). The term r - M represents the political cost of altering the government’s budgetary balance - and hence the interests of marginal taxpayers or recipients of general revenues. The first two arguments of G represent the differential political influence wielded by consumers of utility output.‘

We also make the key assumption that politicians determine prices, while the utility decides how much to supply at those prices. While the real world is unlikely to be characterized by such a simple dichotomy, it could be argued that prices are easy for politicians to monitor and control, whereas levels of service provided are not nearly so amenable to third party supervision, given the number of dimensions along which the product specification can be varied. For example, the level of service to customers can be reduced by making them queue, providing them with older technology, lowering product reliability, o r reducing maintenance support. Such non-price rationing will be represented in our models by a quantity of service supplied which is less than the quantity demanded at the specified price.

If utility managers choose to ration supply, the politicians may then attempt to increase consumer surplus by limiting the extent of rationing. We shall assume that, by monitoring the enterprise, they are able to reduce the degree of rationing to some minimum level determined by the amount of their

’ We should note, however, that Peltzman includes firm profits in the political support function to represent the self-interest of the regulated firm, whereas we include profits to represent the interests of taxpayers. ‘ Our approach is unsatisfactory to the extent that no

attempt is made to detail the workings of the political ‘black box’ represented by G. One study which does this is Denzau and Mackay (1980), though the institutional structure i t seeks to analyze is rather different from the one conceived of in this paper.

1986 PUBLIC UTILITIES 165

monitoring activity. The use of appeals tribunals, ombudsmen, or personal review by politicians, as mechanisms whereby dissatisfied customers may seek redress for service which they feel is inadequate, might all approximate what we have designated ‘monitoring’. To assess the merits of each claim will be costly whatever review procedure is chosen.

To the extent that political monitoring of public enterprise is ineffective, we would expect the rationale of utility operations to coincide more closely with the goals of its employees (managers and/or workers). The simplest objective function of workers, as assumed in the literature on the ‘labour-managed‘ firm, is just w. the common wage. More generally, following the literature on the behaviour of trade unions, we assume the workers, or their union representatives. aim to maximize an objective function V(w,L), aV/aw > 0, aV/aL > 0, where L is the n u d e r of employees.

Following the work of Niskanen (1968, 1971) and subsequent writers, managers of the enterprise are assumed to benefit from output (and hence labour force) expansion. While Niskanen originally assumed that bureaucrats aim to maximize the budget of their bureau, he demonstrated in a more recent article (Niskanen, 1975) that his original assumption is equivalent t o assuming a desire to maximize output. Our preferred interpretation, which is consistent with the arguments in Niskanen (1975), is not that managers derive utility directly from a large labour force. Presumably the reverse is the case, since large workforces demand more administrative effort. Rather we assume managers receive increasing levels of non-pecuniary benefits as output increases. We demonstrate in an appendix that the model can be modified to cope with a more general formulation of the production of non- pecuniary benefits.

The overall objective function of the utility,

will represent both the direct preferences of managers and the interests of workers or their union representatives. Our assumptions about’ E and Yimply that a m a w > o and aF/aL > 0. We shall also assume that F is sufficiently concave to ensure that the solution to the first-order conditions below is a maximum.

Throughout the analysis we shall assume the capital stock is fixed and shall therefore be discussing the short-run determination of prices,

output and employment.’ In the main body of the paper, we shall assume that labour is the only factor of production which can be varied in the short run, so that total costs are WL and output is given by the short-run production function, Q(L).‘ We assume Q(L)/L increases monotonically up to some value L and then decreases monotonically to 0 as L -. - , Q(0) = 0, and Q(L)/L -, Q(0) as L -, 0 with 0 < Q(0) < - .

II One Consumer Group To familiarize the reader with the basic model,

we first analyze the case where politicians are interested in a single consumer group and allow the utility to spend all the revenue it raises. Naturally, this rules out the possibility of cross-subsidization from one group of consumers to another (to be examined in Section 111), which may well be a major political motivation for supplying output via a public monopoly. Nevertheless, we show in this section that the welfare of consumers might be increased by transferring utility profits to them through setting prices equal to average variable costs and expanding output beyond the efficient level. Such an outcome implicitly involves a subsidy from taxpayers who would then be called upon to finance subsequent capital expenditures. In Section IV of the paper we discuss the trade-off between political support from consumers and taxpayers in more detail.

Our general approach is first to enumerate the constraints which face politicians and utility employees, and then to establish some propositions which describe certain features of the solutions to the constrained optimization problems. Then, with the aid of these propositions, we give a qualitative description of the alternative model solutions. We d o this by employing the heuristic device of imagining the politicians commencing with a very high price, which they progressively lower in an attempt to benefit consumers and/or taxpayers. Their attempts to gain political support will eventually be limited by either a reduction in utility output and the instigation of rationing or the requirement that utility employees at least be paid the going market rate.

’ An extension of the model to account for the investment programs of public utilities is left to subsequent research. ‘ The assumption of a single factor of production N I ~ S

out the possibility of inefficiency from the use of inappropriate factor mixes (X inefficiency). This assumption is relaxed in Appendix A.


FIGURE I

Let the price charged to all consumers, and set by politicians, be p and (downward -sloping) demand at that price be Mp). Thus, M p ) represents the maximum quantity of utility output that consumers wish to purchase at the price p . Given p , utility managefs will choose w and L to maximize F(w,L) subject to the cmstraints

where wo is the competitive wage for labour employed by the utility’ and, for monitoring expenditures M, H(M) (ff < 0) represents the total of ‘sufficiently’ well established instances of inadequate service which will justify the taking of punitive action against utility employees. As a result, those employees ensure that H(M) is not exceeded. The demand constraint (2) reflects a constraint imposed by the market - namely that the most output the utility can sell is the amount demanded by consumers at the price set by

’ I t should be noted that w may be increased above competitive levels by ‘feather-bedding’- that is, by lowering the work effort needed to attract a given wage (which could well be wo)-as well as by the explicit payment of higher wages. In so far as the equilibrium outcome involves a wage in excess of w ~ , there will be queues for utility jobs. This is also the outcome in models of the behaviour of trade unions, where such queueing is associated with ‘structural unemployment’.

politicians.’ Similarly, constraint (3) is imposed by competition in the labour market.’

Figure 1 represents the constraints (1). (2). (3) and (4) in the (w.L.) plane and also shows a sample indifference curve for the function F. Since F is increasing in w and L, any unconstrained maximum for the utility cannot lie in the region (OJ 7. Hence, even though the production function might display initial short-run increasing returns, the enterprise will not operate in that region unless D(p) is smaller than the level of output, Q(L*). In such a case, output would be set equal to demand and there would be no rationing and no governmental monitoring activity.

More generally, the following proposition is evident from Figure 1.

Proposition I The budget constraint (1) will always hold with

equality. The maximizing w and L chosen by utility employees will then fall into one of four regions:

a) the monitoring constraint is binding b) the demand constraint is binding c) the wage constraint is binding d) only the budget constraint is binding.

Proof: If wL. < pQ(L) then w may be increased without

changing constraints (2) and (4) while leaving (1) and (3) satisfied. Such an increase in w would raise F. Hence wL = pQ(L).

Then if any of the monitoring, demand or wage constraints is binding, that constraint, together with

‘ A referee suggested we allow the utility to produce more than is demanded since ‘from casual observation it would seem that public utilities over-produce’. As we shall see below, the model already allows for over- production in the sense that the marginal cost of production can exceed the marginal benefit of output. More to the point, if we allow the utility to produce more than is demanded, we must ask what is done with the excess output. It would not be in employees’ interests to replace output at price p with output at a zero price. ’ We might also expect politicians to be concerned if

utility employees earn wages too far in excess of the competitive level wo, and so include a monitoring constraint on w - wo analogous to the output constraint (4). Workers queueing for utility jobs might complain to politicians just as rationed consumers do. However, such complaints would result in pressure to increase employment and output, as in the current monitoring constraint, not to decrease wages. Further, as we shall see below, the monitoring constraint (4) gives politicians control over maximum wages paid in addition to minimum output. This is also clear from Figure 1.


wL = pQ(L), will determine w and L. Q.E.D.

Observe for later reference that in the case of an interior solution, w and L will be chosen so that

PQ/W = 1 - 9 ; W L = pQ(L) ( 5 )

where 9 = LFL/wFw represents the marginal trade-off in F between the size of the workforce and the wage. The utility’s marginal cost of production equals w / Q , so the left-hand side of (5) can be interpreted as the ratio of price to marginal cost.’o

Now consider the way the utility operates from the politician’s perspective. We assume the politician chooses a price, p. and monitoring expenditure, M, to maximize

G = G(Q(L@,M)) D- l(q)dq 0s- - pQ(L@,M)); u - M),

subject to the constraint

M > O (6)

and also subject to the knowledge that, for a given p and M, the utility employees will choose L@,M) and w@,M) according to the constrained maximization problem outlined above. In particular, the politicians are constrained to keep w(p,M) 2 wo. From Proposition 1, the budget constraint ( I ) always holds with equality so that dp,M) 0 , and therefore &/ap = ar/aM = 0 .

The Lagrangian for the politician’s problem may be written

G + XM + p ( w - W O ) ,

with first-order (Kuhn-Tucker) conditions for a maximum

G ~ { ( D - I(Q) - p ) Q a u a p - Q} + pawlap = o , (7)

G ~ W - * ( Q ) - P)Q a L / a w - c2 + x + aw/aM = 0 , (8)

(9) XM = 0 , where X > 0 ,

I* Thus if F does not depend on L (the indifference curves in Figure 1 are horizontal), the utility will choose L and w so that p equals marginal cost, unless the monitoring constraint is to the right of L or the demand constraint is to the left of L’.

and p(w - wo) = 0 , where p 2 0 . (10)

First observe that politicians will only find it of value to monitor if marginal changes in monitoring have some effect on the utility’s choice of L and w:

Proposition 2

M = 0 unless the monitoring constraint is binding.

Proof:

are determined by We use Proposition 1. In region (b), w and L

wL = pQ(L) and Q(L) = D@).

In region (c), w and L are determined by

WL = pQ(L) and w = WO.

In region (d). w and L are determined by (5). In all three cases, therefore, aw/aM = aL/aM = 0. Then from (8), X = G2 > 0 so that M = 0.

Q.E.D.

If the politicians are monitoring the utility, they will have two ‘instruments’, M and p , to control two ‘effective targets’, w and output (or employment, L.). Thus, when the politicians are monitoring, we would expect them to be able to achieve their targets:

Proposition 3

then wages will be driven to WO.

Proof:

L will be determined by

If the politicians choose to monitor the utility

If the monitoring constraint is binding, w and

W L = pQ(L) and Q(L) = D@) - H(M).

Hence, aL/aM = - H / Q > 0 ; aw/aM=(w/LQ’) ( W - PQ) I o as L. s L* ,


Accordingly, p must be positive, implying w = WO.

Q.E.D. Now note that when the monitoring constraint

is binding, M > 0 so X = 0 and

aw/aM = c2 + G ~ ( D - ~ ( Q ) - p).(12)

Equations (1 1) and (12) combine to give

G2/Gl = H'(w/Q-D-'(Q))/(l -(D'/Q) (w/Q-p)) = -pH(cu - c/p)/

( 1 + t D/Q(c/p - 1 ) , (13) where a = D - I(Q)/p > 1 is the ratio of the price which would obviate the need for rationing, to the actual price set (given that supply is set at Q), and c = w / Q is the marginal cost of increasing output. M, p and L are therefore determined from (1 ) . (4) and (13). Condition (13) equates the (taxpayer) benefits from reductions in monitoring expenditure to the cost of reduced consumer surplus implied by the associated output and price changes.

Before discussing the relationship between various possible types of solution, we must first consider the way in which changes in p alter the utility's maximization problem. As is illustrated in Figure 2, an increase in p both shifts the constraint WL = pQ(L) outwards and changes its slope. The increase in (the absolute value of) the slope corresponds to an increase in wages foregone for any increase in employment and produces a substitution effect encouraging the employment of fewer workers at higher wages. At the same time, the increase in revenue implied by the outward shift of the budget constraint enables both w a n d L to increase. Overall, the supply of output as a function of p , which depends monotonically on the induced change in L, can be either upward or downward sloping depending on F and Q.

A further alteration to the utility's problem arises from the shift in the demand and monitoring constraints (to the left for an increase in p). If the utility is strictly constrained by the demand constraint (2) or monitoring constraint (4), the supply of output exactly follows the constraint. Otherwise, movements in the constraints have no effect on utility behaviour.

If the managers select an interior solution given by ( 5 ) rationing l L occurs. If utility employees have

The way in which consumers are rationed, that is, by choking off weakest demand first. is already dictated by the expression for consumer surplus used in the function, G. Generally, politicians will prefer consumers to be rationed in other ways, and the 'two consumer case' of Section 111 demonstrates one such alternative.

wages T

c C. Labour

FIGURE 2

a sufficiently strong preference for labour utilization rather than higher wages, the supply of output will increase with p . Politicians would then be able to reducep until wo is encountered, or until the gain to consumer surplus from price reduction is matched by the loss from quantity reduction. If the supply of output increases with decreases inp , politicians will reduce p until w falls to WO. Formally, we can show:

Proposition 4

(region (d) in Proposition 1) then If equilibrium occurs in the interior region

a) if the supply of output is downward sloping at the equilibrium p. w = wo

b) if the supply of output is upward sloping at the equilibrium, p, either w = wo or consumer surplus will be at a local maximum.

Proof:

If equilibrium occurs with Q(L) < D(p) then D-'(Q) - p > 0 from the assumption that demand is downward sloping. T h e n if auap < 0 ,

( D - ~ ( Q ) - p ) ~ . auap - Q .= o and then, from (7). p aw/ap > 0 . Hence p > 0 and so from (lo), w = WO.

Similarly, if aL/ap > 0 , then either p > 0 , so w = woor

( D - ~ ( Q ) - pi. Q. a u a p = Q. (14)

Equation (14) is the condition for a small change

1986 PUBLIC UTILITIES I69

I I > Q Quantrty

FIGURE J

in p to produce no change in consumer surplus, and is represented graphically in Figure 3. A small increase in p, A p , will reduce consumer surplus by Q A p . It will also raise output by nQ = Q .a . This increase in output will increase consumer surplus by (D-’(Q) - p) Q .a . Equating these values we arrive at (14).

It remains to establish the nature of the solution when utility output is constrained by demand. Then politicians will choose p to maximize consumer surplus and hence will make p as low as possible:

Proposition 5

If equilibrium occurs in the region where utility output is constrained by demand then w = wo. Also, the elasticity of demand, E , and the elasticity of output with respect to L, EQ, must be small enough to ensure

l/EQ + 1 / E > 1 .

Proof:

= p and hence from (7) When output is constrained by demand, D - ‘(Q)

Hence p > 0 and w = wo.

Also observe from (1 5 ) that if equilibrium occurs in the region where output is constrained by demand, aw/dp > 0 . But in this region, w is determined by

w = pD@)/Q- ‘ (D@))

so dw/ap > implies l / ~ + 1 / ~ > I Q.E.D.

Propositions 1 to 5 now enable us to characterize the various possible solution types. We d o this by considering the response of utility employees as politicians progressively attempt to lower the price

Suppose p is set high enough that output is constrained by demand. If 6 is greater than I , decreases in p will increase revenue, while if E Q is high a large increase in output can be achieved with a small increase in employment. In those circumstances, decreases in p will tend to increase w. Politicians would in that case reducep until the elasticities declined and w then fell to wo or Q(L) < D@). In short, from Proposition 5 , the only equilibrium with sales constrained by demand is one where w = WO. With wages at the competitive level, WO, setting prices equal to average cost in the region of decreasing returns to scale yields a lower price, pu, and a greater output, Qo, than occurs with marginal cost-pricing (point A in Figure 4). In these circumstances, consumers a re unambiguously better off than they would be under marginal cost-pricing (point (Pc,Qc). We might attribute this gain to the failure to consider the cost of using the (given1*) capital stock. This is, consistent with the absence of explicit claimants to utility profits, which, under marginal cost-pricing, would equal the shaded rectangle in Figure 4.

With output exceeding the efficient level, L will also exceed the efficient level, so that utility employees are also better off under average cost- pricing. However, given the output to be produced, production is always efficient, there being no possibility of ‘X inefficiency’ to occur with just one factor of production. (In Appendix A we discuss a case where inefficiency in production may arise through the choice of an inappropriate factor mix).

If, as politicians reduced p , output decreased, or increased at a rate less than demand, while w remained above WO, then there would be no equilibrium in the region where sales are

of output.

With the requirement that the utility raise sufficient revenue only to cover current operating costs, the utility will not have funds to finance any capacity expansion or replace depreciated capital. The model of Section IV examines the consequences of requiring the utility to raise some revenue from current operations to at least partially finance capital costs. However, we have not examined the inter-temporal resource allocation (or capacity expansion) problem in the present paper.

170 THE ECONOMI

I

constrained by demand. Further reductions in p would produce a substitution effect toward L and away from w on the part of utility employees. If wand L are normal goods for them, there will also be an income effect tending to reduce both w and L. Hence, w will fall as a result of both income and substitution effects, while the change in L will be ambiguous.

I f L, and hence output, increases with reductions in p, the politicians would continue to reducep until w fell to WO. This outcome is represented by point B in Figure 4. We shall show in a moment that B must involve an output less than Qc. This outcome will be inferior to the Qc,Qc) solution from the point of view of the managers. For consumers, price is much smaller than pc, but output is smaller than Qc, with opposite effects on consumer surplus.

On the other hand, if reductions in p lead to decreases in L , and hence output, the politicians may not reducep until w falls to wo (Proposition 4). The reductions in output might reduce consumer surplus to such an extent that the politicians choose to reduce p no further. In the equilibrium C in Figure 4, wages, w, may exceed WO. It is clear that labour is benefited and that management does not do as well as under average cost pricing at the competitive wage. Output will fall short of demand at the current price so that consumers will be rationed. On the other hand, consumers will face a price below pc and thus might prefer the public monopoly outcome to marginal cost-pricing, despite the fact that workers are capturing some wage rents.

The outcome when politicians choose t o monitor the utility is represented as point D in Figure 4. The

C RECORD JUNE

politicians will be faced with a choice between D and one or other of points B and C. To choose, they will need to calculate whether consumer surplus will be improved by monitoring, and, if SO, whether the cost to the taxpayers is justified. If monitoring is worthwhile, its extent will be determined from condition (13). Improving on point B by monitoring will only be possible if output expands, requiringp to rise. In fact, output expansion will have to be sufficient t o compensate consumers for the price increase. From (13), D-'(Q) must exceed c in the monitoring equilibrium at point D. Hence a monitoring solution necessarily involves production below the efficient level, but at a price below bothp, andp,. As noted above, this also implies B involves an output less than Qc.

We can also see from (13) that as the monitoring technology becomes asymptotically efficient (that is, as arbitrarily small monitoring expenditures allow H to be pushed arbitrarily close to zero), o r as the influence of taxpayers becomes negligible (G2 tends to zero), point D will coincide with Qc. Production will be efficient, with the entire profit rectangle being transferred, in lump-sum form, to consumers.

The simple model discussed in this section has demonstrated how some of the alleged behavioural characteristics of public utilities discussed in the introduction might be explained. First, the tendency toward average cost-pricing is consistent with the equilibrium A in Figure 4. Such an outcome will be more likely when the elasticity of demand is low, the short-run production function displays lower degrees of decreasing returns, and employee preferences are more biased toward higher wages rather than increased employment. Alternatively, the utility could be characterized by extensive use of non-price ratining, possibly with monitoring of its operations by politicians. The equilibrium C in Figure 4 will be associated with wages in excess of their competitive level. In all cases consumers appear likely to prefer the public monopoly outcome to marginal cost-pricing, but any gains they obtain will be at the expense of taxpayers who will be required to fund future capital investments.

III Two Types of Consumer Consumers of utility output will generally have

different demands for service, cost of service and political influence. When consumers differ in their degree of political influence, the redistributive possibilities inherent in supplying output via a


public monopoly are increased.” In this section we discuss the case of two

distinguishable consumer groups, each of which can be charged a distinct price. As before, we permit the politicians to set prices, and a level of monitoring, while the utility determines output and wages. Although it might be possible for politicians to monitor the degree of rationing to each consumer class, we will restrict attention to the simplest case where they are able to monitor only total output.

There are three main results of this section. First, when a group of consumers is the beneficiary of a politically motivated cross subsidy they will frequently be rationed by the utility. Second, when consumers are a favoured (disfavoured) group, the size of their implicit subsidy (tax) typically will vary inversely with their elasticity of demand. Third, with an increase in the number of consumer groups from one to two the politicians become interested in two more variables - the price paid by the second group and the quantity supplied to them. Our assumption that the politiciqs are able to monitor only total output relative to total demand implies that the number of instruments at their disposal does not increase commensurably with the number of targets. As a consequence, workers may obtain wage rents even when the monitoring constraint is binding.

UtiIity optimization

We now assume the utility maximizes F subject to a budget constraint

two demand constraints,

and the monitoring condition,

I’ It is only when there are two or more consumer groups that the aims of politicians, as represented by the political support function G. depart from maximization of consumer welfare (though possibly at the expense of taxpayers). “ Of course, an increase in the number of instruments

will provide more control to the politicians, but then the number of targets can be raised to again reduce their ability to achieve all their goals.

Each demand is assumed to depend on its own price only and the production of each output is similarly assumed inde~endent .~’ A common wage is paid t o both sets of employees.

Once again, a number of propositions can be established as to the nature of the various solution regions of the utility’s constrained optimization problem. In fact, the increase in the number of constraints (from three to four) and decision variables (from two to three) generates a larger number of solutions to the utility’s constrained maximization problem. In some of these we may derive certain conclusions about the relative magnitudes of the ratios of price, pi , to marginal cost, ci = w/Qi , - that is, the extent of subsidy - for the two groups. We leave the detailed statement and proof of these propositions to Appendix B and here simply state the qualitative conclusions.

Proposition 6

When politicians are monitoring the utility and both groups are rationed, the difference in prices charged will fall short of the difference in marginal costs. However, the group which is less expensive to serve will face a smaller ratio of price to marginal cost and will in this sense be cross-subsidized.

Proposition 7

If the utility is subject to monitoring, but only one group is rationed, there will be a tendency for the more subsidized group to be the one rationed. This tendency may be offset if the more subsidized group has a higher marginal cost of being served.

Proposition 8

In the case where there is no monitoring and just one group is rationed, the rationed group must be the more subsidized group.

Proposition 9

In the full interior case, where there is no monitoring and both consumer groups are rationed, there will be no cross-subsidization.

I’ These assumptions can be relaxed, but at some cost of additional mathematical complexity, and without adding much insight.


Proposition 10

When neither consumer group is rationed the politicians can determine w, L1 and L2 independently of employee preferences. (Here the requirement that the utility raise sufficient revenue to cover its (short-run) costs acts as an additional instrument of control for the politicians.)

Politicians’ optimization The politicians will choose p1, p2 and M to

maximize

subject to the constraints A4 2 0 and w@l ,pz,M) 2 wo . Although there appear to be numerous possibilities, th:e structure of the politicians’ optimization problem can still be discussed in terms of the response of utility employees as politicians lower the output prices. Once again, we first consider those cases which do not involve any monitoring.

Suppose that both p1 and p2 are initially set so high that the outputs to both groups of consumers are constrained by demand, and moreover that

where GI , 1 is the marginal political support, and E i the elasticity of demand, of consumer group i. This is just the condition which ensures that the marginal contribution to political support from both consumer groups is the same, given that there is no rationing. As long as w exceeds wo, from Proposition 10 the position of both groups can be improved through price reductions. Therefore, prices will be reduced in such a way that (20) continues to hold until either w reaches wo or rationing of consumers commences.

If wo is reached without rationing having been instigated we have a case corresponding to the competitive-w age/average-cost-pricing solution of Section 11, but augmented by (20) so that the interests of the two types of consumer are appropriately balanced. Observe that the benefit received by any consumer from political

intervention is measured by the extent to which the marginal cost of supplying him exceeds the price he must pay. If both consumer groups have approximately the same demand elasticities, then group 1 will be advantaged, relative to group 2, when G1,1 > G1 2, that is, when group 1 is politically more infhential. This tendency will be strengthened (or offset) if the demand of group 1 is more (less) inelastic than that of group 2. Further, as the political influence of group 2 dwindles to zero it will face a price (exceeding marginal cost) determined by the usual monopolist’s profit maximization condition.

However, as the prices are lowered, the utility may begin to ration one or other consumer group. Supposing that this is group 1, we know from Proposition 8 that at this point its ratio of price to marginal cost must be smaller than that for group 2. That is, the more subsidized group is the one which is rationed. As long as group 2 remains unrationed, its position will be improved by further reductions in p2. However, the public utility may begin to switch resources from the production of group 1 output to the service of group 2 -that is, aLl/ap2 may be positive. In addition, loweringpl further may begin to contract the supply to group 1. Depending on the net effect on Q1 of reductions in both prices simultaneously (all the time maintaining equality between the marginal contributions to political support) either wo will be reached or it will no longer be prudent for the politicians to lower prices because of the negative effect on group 1 consumer surplus. In this case the two conditions

together determine the optimal degree of price lowering. while wages will exceed the competitive minimum wo. Note that as G1,2 approaches zero, the effects of price reduction on the surplus of group 2 become irrelevant, and (21) and (22) describe turning points for group 1 consumer surplus with respect to both p1 and p2.

Another case results if both groups of consumers are rationed. Ratios of price to marginal cost will be equalized, so that cross-subsidization will be absent (Proposition 9). Simultaneous reductions in price may now begin to have a negative effect on either output through both own-price and cross- price effects. When the total effect of these on one


or other of the consumer surpluses reaches its turning point (assuming wo has not already been attained) the optimal prices will have been determined; in fact, we may well have Gl,2/G1,1 = (Q1 - ( D C 1 - p1)Ql aLl/aPl)

/(DF - P2)Q2aL~/apl ) and (23)

with wages exceeding WO. If the second consumer group has no political stature the result is as in the rationed case just mentioned-(23) and (24) define the turning points for group 1 consumer surplus.

Finally, the politicians may find it worthwhile monitoring when consumers are being rationed. The amount of monitoring is calculated to equate the marginal political influence of taxpayers to that of both consumer groups.

If, despite monitoring, both groups are rationed, wages can exceed WO. Politicians may limit the extent to which they reduce p 1 or p 2 because of adverse effects on the supply of output to one group of consumers. This may enable w to exceed W O . In the absence of other monitoring instruments, utility workers benefit by attracting a wage above competitive levels.

When only the more subsidized group, or the higher cost group (say group 1) is rationed, the impact of monitoring will be to limit the extent of rationing to that group. Since reductions in p 2 will always make group 2 better off (Proposition 7), p2 will be reduced until wages are driven to WO.

Optimal prices and monitoring expenditure are derived from

and

As G1 2 goes to zero, (25) shows that revenue is raised from group 2 according to the monopolist's profit maximization rule. And as G2 approaches zero, group 1 supply tends to the efficient level ( a 1 = c l /p1 ). With both taxpayers and group 2 consumers politically insignificant, group 1 would find itself the recipient of a transfer - efficiently delivered-of all of the (unpriced) utility profits

together with the (maximized) revenue raised from the second group.

IV Taxation and Subsidization So far our model has incorporated the political

trade-off between consumer surplus and taxation in two distant ways. The trade-off is explicit whenever monitoring expenditure is non-zero. It is also implicitly embodied in the assumption that utility costs match revenues so that any capital investment is funded by taxpayers. However, politicians are likely to have available explicit tax/subsidy instruments to enable them, if they so desire, to ensure that the utility raise sufficient revenue from its current operations to fund necessary capital investments.''

We revise the budget constraint in the model of Section I1 to

wL. < (P - T)Q(L), (27)

where T = tp is the per unit tax levied on output (equal to a tax on turnover at a rate oft per cent). From the utility's point of view a change in T has effects equivalent to an equal but opposite change in p except that the demand and monitoring constraints ( M and D in Figure 2) are not altered. Therefore, if the utility is constrained by demand, or is monitored, changes in Twill affect only wages whereas changes in p will affect both wages and output.

The politician's problem now has an additional first-order condition corresponding t o the additional decision variable. The politicians choose p , T and M to maximize

Q(L) G( s! D- '(q) dq - pQ(L); TQ(L) - M)

subject to w 2 wo , M 2 0 . The first-order conditions become

0

c l { ( ~ - - P)Q a L m - Q} + ~ ~ ( 7 - g a m p } + aw/ap = o , (2s)

I * Ideally, we would endogenize the level of capacity expansion to meet increases in demand. However, this would take us beyond the present analysis.


and

G ~ { ( D - 1 - aL/aT) + G2{TQ‘ dL/aT + Q } + p aw/aT = 0 . (30)

Just as with Proposition 2, i f the utility is not constrained by the monitoring condition, then aL/aM = aw/aM = 0 and equation (29) implies that A4 is zero.

As before, we consider what happens to wages and output as politicians reduce p . First, so long as output is constrained by demand, decreases in

decease wages and leave supply unchanged.

Tu -

-

L I * Qo Q

price increase output, while increases in taxation FIGURE 5

Politicians will therefore lower p i d raise T so that if ultimately a demand constrained solution eventuates it must be the case that w is driven to WO. Formally, from (30), with aL/aT = 0, aw/aT < 0 , p > 0 so w = WO. All that remains to be determined is the politicians’ optimum balance between ‘high’ taxes and ‘low’ prices. This is found using conditions (28) and (30). together with the first-order conditions for the employees’ maximum problem:

G2/Gl = 1/(1 + E(c/p - 1 ) ) (31)

where c is the elasticity of demand. Notice that as GI approaches zero, that is, as the political importance of consumers becomes negligible, condition (3 1) reduces to the first-order condition for choosing p to maximize revenue.

Whenever the utility chooses an interior solution it is easy to show:

a u a p = - aL/aT and swap = - aw/aT .

This in turn implies (from (28) and (30) that

GI = G 2 .

Condition (32) ensures that p and T a r e chosen to equate the marginal contributions to political support from consumers and taxpayers. Now if aL/ap is negative wages will again be driven to the competitive level. If, on the other hand, the ‘supply curve’ becomes upward sloping, then price will be lowered until condition (14) pertains, and again T is chosen t o ensure t h a t (32) applies. Diagrammatically, the ‘supply curves’ (Figures 5 and 6) for non-zero values of Tcan be derived from

those for T = 0 by noting that, in interior equilibria, changes in Tare exactly offset by equal and opposite changes in p .

Suppose that, when T is zero, political support is maximized by a choice of p = PO as depicted in Figure 5. Since, in the absence of monitoring, our previous model held no implications for the relative values of G I and G2, we might suppose that when p = po and T = 0, G2 exceeds G I . That is, the marginal contribution to political support from a one dollar tax reduction exceeds the marginal contribution from a dollar increase in consumer surplus. GI and G2 may be equated by levying a (positive) tax on the utility while simultaneously raising the price of output. All the while, utility employees will be unaffected because w and L will not change. Consequently, the incidence of the tax is totally upon consumers, and the existence of the taxing instrument allows political support to be maximized by transfers from consumers of the utility product to taxpayers. Of course, if when T = 0, GI exceeds G2, then the optimal ‘tax’ will instead become a subsidy.

If supply is upward sloping, as in Figure 6 , then a similar argument may be applied to demonstrate how, by imposing equal and opposite changes on p and T, the condition (32) may be attained. Once again, provided that the demand constraint is not encountered, utility employees will feel no impact of the tax (or the subsidy).

When politicians find it worthwhile to monitor, an argument along the lines of Proposition 3 again implies that wages are set at WO. Whereas previously, taxpayers could only be advantaged by reductions in monitoring expenditures, at a consequent cost to consumers, now the availability of a tax offers the possibility of improving the


I I >

Q Qo FIGURE 6

position of both groups. This might occur, say, by a rise in price together with an increase in monitoring (to raise supply) so that the net changes to both consumer surplus and to the government’s budget surplus are non-negative. It can then be shown that these net changes are maximized when

(33) G ~ / G I = ( I + ED/Q(a - 1)/(1 + E(c/~ - 1))

and

Finally, observe that political support could well be maximized by the setting of a zero price and subsidizing the entire wage bill of the utility. Derivation of the circumstances under which this ‘civil service’ variant of the model is applicable requires inclusion of the constraint that price should not be negative. Attainment of the zero price boundary may prevent the wage from being lowered all the way to WO.

Figure 7 illustrates, with supply upward sloping, the case where politicians find that political support is enhanced by continual price reduction accompanied by ever-increasing treasury subventions to the utility. The wage and the level of output can be maintained constant so that the total subsidy is passed on to consumers. Having reached the point where price becomes zero, however, it may still be the case that the marginal contribution to political support from taxpayers is less than that from consumers. Further increases in taxes will help to remedy this since they will lead

FIGURE 7

to reductions in the amount o f rationing. Simultaneously, they will generate increases in wages and the civil service bureaucrats will begin to capture a portion of the transfers.

Eventually, taxpayer tolerance to further subsidies will diminish sufficiently to just offset the political gains from increases to consumer surplus, say, at point A in Figure 7. Alternatively, the demand for the unpriced bureacracy output might be totally satisfied (point B). In either case wages will exceed the competitive level and there will be queues for the civil service jobs.

V Concluding Remarks The models discussed in the paper display two

major characteristics. First, they assume objective functions for politicians and State enterprises which deviate from profit maximization but attempt, instead, to reflect the different incentive structures inherent in State-owned enterprise. Second, they allow the two sets of decision makers to have control over distinct decision variables. The models are able to explicate a number of real world attributes of these institutions, such as: * demand is frequently rationed by means other

than price;

a major focus of the monitoring effort of politicians is their endeavour to force the utility to supply output, at the specified price, without excessive demand rationing, or other forms of product quality degradation;

* utility workers may earn wages above the competitive level, though monitoring efforts on the part of politicians can in some cases eliminate these wage ‘rents’;


When utility prices are used as a means of cross- subsidizing different consumer groups, those benefiting from the subsidy will frequently be subjected to quantity rationing by the utility;

when consumers are a favoured (disfavoured) group, the size of their implicit subsidy (tax) will vary inversely with their elasticity of demand;

the interest of managers in the consumption of non-pecuniary benefits can lead to over- expansion of production and an inappropriate choice of factor inputs;

over-expansion of production can also be associated with a failure to valuecapital inputs in the absence of explicit shareholders;

because of the political imperative to reduce price, utilities operating in regions of short-run increasing returns will have prices equal to average costs, no wage rents and no demand rationing;

we show in Appendix A that the utility will generally have a' clear incentive to achieve engineering efficiency for a given factor input mix, but it will have a lesser need for expertise in the selection of efficient input combinations, and this will have implications for the way in which certain skills are rewarded within the hierarchical structure of the utility.

The model also has implications for the distribution of benefits arising from use of the public enterprise form to provide the service demanded by consumers. One way of measuring these distributional effects is to compare the outcomes for each interest group against their prospects in the event that prices were set equal to marginal costs and rationing eliminated. We argued that politically favoured consumer groups are likely to be advantaged but that employees and managers will also prefer a publicly owned monopoly to competitive private firms. When marginal taxpayers are a more diffuse group than consumers, they are likely to have less political influence and so be called upon to fund capital investments of the enterprise while consumers are offered output at subsidized prices.

Finally, it must be emphasized that the models analyzed in this paper describe a class of government interventions which are explicitly designed to achieve distributional results different from market outcomes, although at some cost because of inefficient resource allocation. The

origin of the institutions being studied ought to be related to the rearranged distributional outcomes. For example, in those instances where consumers appear to benefit little from public monopoly, yet workers receive wages exceeding the competitive level, our model might imply a degree of irrationality of political behaviour since politicians would then prefer a competitive market and possibly even private monopoly. Of course, this defect could be remedied by introducing the interests of utility employees explicitly into the political support function. Almost any outcome can be rationalized using a sufficiently complicated objective function for the politicians, but at the cost that the model then produces few refutable propositions.

APPENDIX A

Generalized Functions for the Production of Output and Non-Pecuniary Benefits

A disadvantage of our use of a single input to production (labour) and its direct inclusion in the utility's maximand, F, is that efficiency losses due to factor mixes cannot be modelled. This defect can be remedied by letting output be a (concave) function of labour and an additional input (fancy technology, overseas trips, carpeting, etc.); that is Q = Q(L,K). The non-pecuniary benefits, N , enjoyed by managers will also be a (concave) function of both these inputs and the utility will seek to maximize

F = F(w,N) = F(w.N(L,K))

if we now suppose workers wish to increase w but are uninterested in the employment of L or K." The input, K, is distinct in nature from L, because the factor rewards going to it (r) d o not explicitly enter the function F.

The structure of utility decision-making can be demonstrated by writing down its constrained maximization problem as a function of price, p.

S@) = max {F(w,N) + A, @Q(L,K) - WL - rK)

+X2(N - N(L,K)) } w, N. L, K

where

*@,w,N) = max {@Q(L.K) - WL - rK) L,K + MN -N(L.K) )}

The optimization can thus be split into two parts. First, L and K are chosen to maximize net revenues, subject

" More generally, the objective might be written F(w,Ne(L,K),Nm(L,K)) with Ne the non-wage benefits accruing to workers (or their union representatives) and Nm the non-pecuniary benefits accruing to managers.

PUBLIC UTILITIES 177 1986

K

L FIGURE 8

to a constraint that a given level, N , of non-pecuniary benefits are generated. Second, F(w,N) is maximized subject to the constraint that maximized (constrained) profits are greater than or equal to zero.

Figure 8 illustrates the first choice in the (L,W plane. A contour is drawn for a given value of N , and given the functional form of Q , a number of equal-profit ellipses can be drawn as a function of p and w. As w is increased, each ellipse will change shape and tangency with the N contour will occur with different levels of profit. The combinations of w and N which yield non-negative maximized profits will comprise a convex region in the ( w , w plane (Figure 9).”

Maximization of F subject to the constraint that the maximized (constrained) profits are greater than or equal to zero is then represented by the tangency between the ‘budget constraint’ set - which incorporates the optimal choice of L and K-and the indifference curves of F. The maximum will occur on the boundary of the set where profits are zero.

When the utility is constrained either by demand or by monitoring, L and K will be restricted to a Qo = Q@,M) contour. For each lower bound on output, Qo, there will be a maximum w(Q,-,) such that r 2 0 for at least one point on the Qo contour. The point of tangency between the zero profit ellipse for w(Q and Qo will determine a smallest feasible value of N(&. Decreases in w below w(Q,-,) will permit the maximum value of N to increase until we arrive at a tangency between the zero profit ellipse and an N contour on the Qo contour. Still further reductions in w will allow tangencies between Ncontours and zero profit ellipses at (L.K) combinations yielding Q > Qo. For these wages, the constrained frontier will correspond to the unconstrained one. Similarly, for an upper bound quantity constraint, feasible ( w , N pairs will fall on a locus starting at a minimum w(QO, and tangent

” The region can be shown to be convex if Q and N are concave as we have assumed.

W

I I I N

FIGURE 9

to the unconstrained frontier.” The feasible set of ( w , N pairs is thus given by ABCD in Figure 9.

Algebraically, the utility’s full interior solution is determined from

and

while constrained maxima must satisfy

Having slightly modified the nature of the utility’s decision, the maximization of political support will proceed as before. The four cases, (a) - (d), reviewed in Section 11, will all have their counterparts, with the conditions (Al) - (A3) replacing (5). As before, monitoring will only be conducted if the monitoring constraint is binding.”

In all equilibria, inefficiency will occur not only through an ‘average cost-pricing’ tendency and resulting over- expansion of output on the one hand or rationing and/or excess wage payments on the other, but also via the utility’s choice of inputs to enlarge its non-pecuniary benefits. A resource cost can be associated with this ‘X

I’ As Q varies, the maximizing (L.K. W,) from the constraine8problem wi l l trace out the locus of maximizing (L,K, w) choices for the unconstrained problem. The unconstrained curve is formed as the envelope of the constrained curves.

I* Furthermore, when the monitoring constraint is binding, reductions in price must increae output and hence also consumer surplus. Politicians will therefore reduce prices until wages are driven to their lower level wo as in the simple model.


inefficiency’, and it will equal, for a given level of production, the increase in total costs relative to the cost minimizing choice of inputs.

It is of some interest to note that our representative Siate enterprise will be principally concerned with determining its most desired set of inputs, and achieving ’technical‘ or ‘engineering’ efficiency with respect to that input mix (and also in balancing its budget). The utility has a demand for the achievement of technical efficiency, since within a given budget, increases in productivity will allow the purchase of more non-pecuniary benefits. We would expect to see engineering expertise correspondingly well rewarded. at lpst in comparison to the rather meagre rewards going to employees who attempt to alter the input mix and so achieve greater economic efficiency.

APPENDIX B

Two Types of Consumer-Proof of Propositions Define the Lagrangian for the employees optimization

problem as

F(wJ-1 + X@lQ + P ~ Q ~ - W I +L )) + ~ l ( D 1 + ~ ( D 2 - d 2 ) +.dQI + Q 2 - b l - D 2 + H ) .

The necessary conditions for a maximum are then

We may establish the following propositions:

Proposition 6

If the monitoring constraint (19) is binding and both consumer groups are rationed, then p1 - p2 I c1 - c2 and pl /c l 1 p2/c2 as c1 1 c A so p1 < c1 and p2 < c2. The signes of dw/apj , $Li/apj ; i,j = 1,2 are indeterminate.

Proof: If the monitoring constraint is binding and both

consumer groups are rationed, w, L and L2 are determined by (16), (19) and, from (BA - (B3) with Cl = p 2 = 0 ,

@1 - p2)/(~1 - ~ 2 ) = I - 6 < 1 . (BS)

Hence pI - p2< c1 - c2 if c1 > c2 and p l - p2 > cI - c2 if c l < 9. Also from (B2) and (B3),

@IQi - P2Q2)/(Q2 - q = YA > 0

s o p /cl I p2/c2 as l/c2 3 I/cl . These inequalities can tien be manipulated to show p1 < cl and p2 < 9.

Finally, totally differentiating (16), (19) and (BS) we can show dw/apj , aLi/ap.; i j = 1,2 are ambiguous in sign.

Q.E.D. J

Proposition 7

If the monitoring constraint (19) is binding, but only one group, say group 1, is rationed (so (1 8) is binding), then c1 > p Also, if c2 2 c1 then p /cl < p2/c2. Finally, a ~ ~ / & ~ < 0, aL,/ap, < 0, aLI/b,, = a~,/ap, = Oandaw/api > Oi=1,2.

Hence w - p l Q l > 0 or c1 > p1 . Also from (83)

(82) and

/12/~2 = ~ ( 1 1 ~ 2 - 1 1 ~ 1 ) - X@l/Cl - p 2 / ~ 2 ) > 0 . Then c2 2 cl implies l/c2 < I/cl and hencepl/c, <

P2/C2.

Finally, Ql(L2) = D2@2) will determine L2 as a function ofp2..Q1(L ) - DI@ ) H(M) will determine L I as a function o / p r and k , a n d w(L1 + L2) = plQ1(L1) + p2Q2(L ) will determine was a function of p I , p2 and M. Totalfy differentiate to obtain aw/ap,, aLi/apj ; i j = 1,2 .

Q.E.D.

Proposition 8

If the monitoring constraint is not binding and only one group, say group 1, is rationed (so (18) is binding), then the rationed group must be more subsidized in the sense thatpl/cl 5 p2/c2. AISO, swap., aL,/apjj= 1.2 can be either positive or negative whife aL2/ap2 < 0, a~,/ap, = 0.

ProoJ

p1 = 0. Then from (B2) and (B3) With the monitoring constraint not binding y = 0. Also

P ~ / C Z - pI/Cl = p 2 / ~ 2 X > 0.

Again Q2(L2) = D2b2) will determine L2 as a function


of p so that aL2/ap2 < 0. aL,/apl = 0. From (Bl) and b 2 ) ,

(LFL)/(wF,) = 1 - @ ] P j ) / w or p l / c I = 1 - +

be determined by p 1 and p2 independently of employee preferences and aL /a c 0 , aL2/ap2 c 0 , aLl/ap2 = aL2/apl = 0 , L 2 p i > o i=1,2.

ProoJ

Ql(L ) - D (p l ) will determine L l as a function of p l , Q2(1!.2)’’ d2(p2) will determine L2 as a function of ~ 2 , and w(Ll+L2) = PlQI(L1) + P Z Q ~ ( L ~ ) will

Totally differentiate to obtain aL,/ap. , aw/apj as

Q.E.D. Q.E.D.

which, together with

W L = P1Ql(LI) t- ~ 2 Q 2 (L2@2)) . will determine w and L1 as a function of p

J = 1 , 2 . stated.

and 6 . determine w. Totally differentiating we find dw/Jpj , ,3tl?8p, s 0 1

Proposition 9

If the monitoring constraint and both the demand constraints are not binding then p /cI = p2/c2. Again aw/ap. , aLi/apj ; ij= 1,2 can f e either positive or negative. .J

Pro0 f:

- (B3) In this case y = 0 and p l = p 2 = 0 . Then from (Bl)

p l Q 1 / w = P l / C ] = 1 - + and

p2Q2/w = p2/c2 = 1 - + These two equations along with

wU-1 +L2) = P1QlW1) + ~ 2 Q 2 C 2 )

will determine w , L1 and L2. Totally differentiating we again find aw/apj , aLi/ap. , i,j= 1,2 can be z 0 .

Q.E.D. J

Proposition I0 If both demand constraints are binding, yet the

monitoring constraint is not binding, w, L1 and L2 will

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