meeting basic needs

Journal of Development Economics 18 (1985) 87-99. North-Holland

M E E T I N G BASIC N E E D S

The Trade-off Between the Quality and Coverage of the Programs*

Jos~-Pablo A R E L L A N O

CIEPLAN, Casilla 16496, Santiago, Chile

Received June 1983, final version received December 1983

This paper examines the conflict existing between the standard or quality of the subsidized social services offered by the government and its coverage when the amount of resources available is limited. A simple model is developed to study the trade-off and to estimate its magnitude. Some numerical simulations are carried out.

1. Introduction

The definition of the standard or quality of the social services to be offered by the government is made for every social p rogramme although it is not generally explicitly made. In the case of health, for example, it is necessary to define the weight which will be attached to primary care as opposed to more specialized treatments. Regarding housing policy, we have to establish what kinds of dwellings will have the benefit of a subsidy. In the case of education a decision has to be made as to the levels that the government will finance. In the case of social security, it has to be decided what percentage of wages pensions will represent and how long these pensions will last, etc.

Obviously, more is almost always preferable to less and when defining the type of services offered, a better quality service is preferable. The problem arises from there being scarce budgetary resources and from the fact that this means that a better standard is reflected in a less wide coverage. The better the type of service offered, the fewer the families who receive it. There is a clear trade-off between the quality of the services and the number of people attended.

When coverage is low it is the poor who lose. The studies carried out in developing countries on access to social services have shown almost without exception that when the coverage of social services is inadequate, it is the poorest groups which are not reached.

*This paper was written as part of a research program of CIEPLAN on Social Policies in Chile. It received support from the Inter American Foundation.

88 J.-P. Arellano, Meeting basic needs

Given the resources available, the higher the standard and the cost of the subsidized services which are provided, the smaller the quantity of these services which is actually supplied and the larger the number of poor households which are excluded. This situation is further aggravated by the fact that as the quality of the services offered by the government improves, they become more attractive to middle and high income groups.

Another mechanism to make consistent the amount of resources, the population in need and the quality of the services is an endogenous quality adjustment. We see this in the people queueing up for hours to be seen by a physician or simply rejected by the clinic because of lack of personnel. We also see it in the cases of irregular attendance at school, repeating and dropping out. These are examples of common reductions in quality that result from lack of resources coupled with an inadequate design of the standard of the services which are provided. Very often these endogenous quality adjustments are very inefficient and therefore welfare could be improved by an ex-ante definition of quality to make it consistent with the resources available and the existing needs.

The issue of the specification of the quality or standard of social services has been recently raised by the literature on the basic needs approach to alleviate poverty. It has been pointed out [Streeten (1981)] that 'The important question is frequently not how much public revenue is devoted to health or education, but how it is deployed and for whose benefit' (p. 6); and that 'The formulation of policy is . . . also often distorted by the excessive standards imposed by the professionals, whether engineers, doctors or teachers' (p. 148).

In what follows a very simple model is developed to analyse some basic interrelationships between quality and coverage. The numerical simulations carried out on this basis will show an important trade-off between quality and coverage. The next step would be to elaborate on the quality determi- nation. For that purpose one would have to go to the sectorial analysis, but that is outside the scope of this paper. Only a few general considerations are made in its final section. Most of the examples are drawn from the Chilean experience given that there are specific studies available.

2. The model

The simple model used in examining the quality--coverage trade-off is developed below. For the sake of simplicity, it is assumed that the social services studied are similar to other goods and services in the sense that they have a supply, a demand and a price. Of course, many times there does not in practice exist a market in which these services are traded and services such as education and medical care have economic characteristics very different from those of ordinary goods and services. This simple model is, however,

J.-P. Arellano, Meeting basic needs 89

sufficient tO illustrate the importance of the choice of the standard of the services to be supplied by the government.

We introduce the quality dimension of the service in its quantity demand and supply functions, as follows:

X d == x d ( f f d, q).

x " = XS(pL q),

where X o, X'=quanti ty demanded and supplied, q=index of standard or quality of the service, p°,p~=demand and supply prices. The variable q differentiates between the 'same' good or service with different characteristics, such as, for example, a house whose standards (size, materials used, siting, etc.) vary; or an 'education' whose length (hours of classes) differs. 1 This same analytical technique is used by Spence (1975) to introduce the quality dimension into a study of manufactured products which are imperfect substitutes.

We will assume that the supply and demand functions have constant elasticity with respect to price and to 'quality'.

X d ~-.~- o'~q - - ~p d , 0", t / > O, (1)

g s= - &4 +*lOL 6,~>0,

where

a = elasticity of demand price with respect to quality (= #a/~), q --price elasticity of demand, 6 = elasticity of supply price with respect to quality (= iO~/4),

= price elasticity of supply, = d X / X (percentage change).

(2)

In equilibrium,

O"=O s, (3)

£d= £.= £ = ((a-- 6)/~ + ~) ~. (4)

awe may think of different goods or services which are close substitutes among which we have to choose one, and then decide the quantity to consume of the service chosen. We rank the substitutes in order of preference and give a value of q to each of them (q increases with the degree of preference). Then, given prices and income we can determine a positive relationship between q and X d.


If there is a drop in the average standard of the services (q), the quantity consumed (X) increases if the reduction in its demand price is less than the reduction in its supply price (a < iS). This situation is illustrated in fig. 1.

/ .o //'q~. ~ /" "~~ ql

/ //1!" I " ' ' . . ~ 1 q O ' . I I ~ x

x O x I Fig. 1

< qo

The conflict between the standard of a service provided and its coverage can be looked at from two points of view: given the available resources, how does a change of standard affect the coverage of the service or, alternatively, given the coverage of a service, how does the standard of the service provided affect the total costs of the programme? The answer is, naturally, the same in both cases.

Here the case which will be taken is the effect upon the cost of a programme when it is decided to subsidize its consumption up to the point at which the target group; that is, the population most in need, is consuming a specific amount (XP=X*). Two groups are, therefore, distinguished: the target population (P) and the rest of the population (R). The behaviour of the two groups is assumed to differ mainly because of their different income levels.

In pursuing the stated objective, different types of subsidy can be used. Two are considered here. The first of these is a general subsidy, received by the entire population, on consumption of the service. This is carried to the level at which the drop in price is sufficient for the target group to achieve the desired level of consumption. The alternative is a 'specific subsidy' which is granted only to those families in need. This is achieved by distributing the service, or some sort of vouchers, only to those who fulfill the appropriate requisites. It will be shown below that the general subsidy is likely to be more expensive. The general subsidy has to be paid to a larger number of families and a higher subsidy per unit of product is almost always required to achieve X e =X*. A point in its favour is that it generally involves lower administrative costs.


Below, the effect of modifying the standard is looked at in each of these cases.

3. A general subsidy

The stated objective is

X * = X P ( p d, q). ( 5 )

For this to occur, the price paid by consumers (p-d) has to take the following value:

p-d = pP(X*, q), (6)

where XP(') is the demand function of the target population and pP(') is its inverse function.

The total cost of the programme (C,) is, thus,

C, = [X* + X R] { f [ X R + X*, q] - - f } . (7)

Substituting the demand function of the rest of the population (XR) 2 gives

Cg = IX* + X~(p -d, q)] { f [ X~(p 'a, q) + X*, q] - p-d}. (8)

Substituting (6) into (8) and differentiating with respect to q, we obtain

* R s R s R s dCg=(X + X )[.pxXpfq +pxXq +Pq-lfqq] dq

R R s d +[Xq + Xpp~(p - p )dq,

where the subindex denotes the variable with respect to which the partial derivative is taken (p~ = ~pS/ax).

Introducing the values of the elasticities and using the definition of the subsidy (s) gives

f -- (1 4- s) pd, (9)

f ( l + s ) yX Rt/R, R _, 07 a p X R }

2The index P indicates that the variable refers to the poor or target population group and R that it refers to the rest of the population.


The expression obtained shows that a reduct ion in the s tandard (q) makes it possible to reduce costs (or to increase X*) no t only because of the lower cost of p roduc t ion (measured by 6) but also - - when we assume that a s > tr p - - because of a drop in the consumpt ion of the non- target populat ion.

The drop in s tandard leads the non- target popula t ion to reduce its demand for the subsidized service provided by the state. This effect depends directly on a s , the elasticity of the demand of the non-target popula t ion with respect to q. To the extent that the popula t ion in need also reduces its demand, depending on tr p, the reduct ion in cost is smaller.

Table 1 sets out the values which ~/~ (or ,g*/~) could take. It shows the elasticity of the response of the costs of the p rog ramme (or its coverage of the target populat ion) to changes in the index of quality or s tandard (q), depending on the different values of the parameters. To carry out the simulation analysis, it will be assumed that q can be assimilated to the unit cost of the service or, in other words, that a d rop in q of 10% brings with it a 10% drop in average product ion costs. The supply price elasticity with respect to q (6) is, therefore, equal to 1.

It can be seen from table 1 that in the case of a p rog ramme grant ing a subsidy of 20% of the selling price of the service (s = 0.2), a reduct ion of q by 1% would permit a reduct ion in the total cost of the p rog ramme of between 2.8% and 11.4%. The lower limit occurs when tr p takes on its highest value and tr g its lowest. The opposite is the case for the higher of the two figures.

When the service is being provided almost free (s=0.8), a 1% reduct ion in unit cost makes it possible to reduce total costs, or to increase coverage, by between 4.4% and 1.1%.

Table 1 Elasticity with respect to q of total costs or coverage of a programme granting a general subsidy

[see eq. (10)].

6= 1, X~/X=0.7

e=0.2 e=0.1

qR = 0.2 qR = 0.5 qR = 0.2 q~ = 0.5

0-R 0-R o-R o-R

aP s 0 0.2 0.5 0 0.2 0.5 0 0.2 0.5 0 0.2 0.5

0 0.2 6.0 6.9 8.2 6.0 8.2 11.4 6.0 6.2 6.5 6.0 6.5 7.2 0.8 2.3 2.6 3.1 2.3 3.1 4.4 2.3 2.3 2.5 2.3 2.5 2.8

0.1 0.2 5.1 5.9 7.2 4.4 6.6 9.8 5.4 5.6 5.9 5.3 5.8 6.5 0.8 2.0 2.3 2.8 1.7 2.6 3.8 2.1 2.2 2.3 2.0 2.2 2.6

0.2 0.2 4.1 5.0 6.3 2.8 5.0 8.3 4.8 5.0 5.3 4.5 5.0 5.7 0.8 1.7 2.0 2.5 1.1 2.0 3.3 1.9 2.0 2.1 1.8 2.0 2.3


The case was also examined, although it does not appear in table 1, of the cost reductions when the target population is larger (XR/X is lower). There was found to be a tendency to reduce the impact of a drop in q when tr R is larger than aP. 3

4. A specific subsidy

The case studied below is that in which only consumption by the target group is subsidized. It is useful here to define the excess supply function which this group faces,

X E = X s - - x R : x E ~ E , q ) . (11)

The price~luality elasticity of this function is given by

aE_ fie + trR~lRXR/X ~E -- (12)

e + ~ X R / X ~ "

In this case, the total cost of the programme is

C s = X * (pE - - p-d). ( 1 3 )

Knowing the cost of a specific subsidy programme, it is possible to compare it with the cost of a general subsidy as found in (7). Remembering that in equilibrium pE(X*)=p~(XR+X*), the ratio of the two costs can be written

C___~g _ X* {p~[ XR(p 'd, q)+ X*, q3 -- p~}

C, X*{pS[XR(P ~, q)+ X*, q]-p-a}

XR {p~[ XR(p "d, q) + X*, q-I -- p-,i} X* {pS[XR(pE, q) + X*, q] -- p-d}"

(14)

This comparison of the costs of a programme which subsidizes the consumption of the entire population and of one which only benefits the population in need is interesting because it applies not only to policies affecting q.

Eq. (14) shows that if costs do not vary with the level of production (e= oo) or if the demand of the non-target group is price inelastic (qR =0), then the general subsidy per unit consumed is the same as the specific subsidy with the only difference in terms of total cost being that, in the case of the general subsidy, an additional sector of the population (X R) benefits. [The

3If XR/X=0.5, when s=0.2, the fall in total cost ranges from 9.8% to 3.5% and when s=0.8, from 3.8% to 1.4%.

A J.D.E-- D


first term of (14) is equal to one whilst the second term is positive.] On the other hand, when e < ~ and r/R>0, the subsidy per unit for the general programme is larger than when only a specific group is the recipient. [The first term in (14) is larger than 1.] 4 In this case, the total cost of the general subsidy is higher not only because it goes to a wider population but also because the subsidy per unit is higher.

Eq. (14) can be simplified by writing it in terms of elasticities. In order to do this, it is convenient to calculate ( p ~ - ~ ) in the case of the general programme (Ss) and in the case of the specific programme (S~).

C__As = S~X* + (S x - S,)X* + XRS~ + XR(Sg- Ss) C, S~X*

= &x* + ss)x* + xR[& + ( s , - &) Cs SsX*

c, ( 1 . " xR 1

C ' = ( 1 1 + ~ \ + T

(15)

Table 2 shows the ratio between the cost of a general and a specific subsidy for different values of the parameters. It can be seen, for example, that if the target group is small - - reaching around 30~ of the total population - - and the price elasticity of the demand of the non-target group is five times larger than the supply elasticity, then a general subsidy costs

Table 2 The costs of a general subsidy (Cf) as compared with a specific subsidy (C,) [see

eq. (15)].

c,/c,

X* e=0.2 e= 1 e=2

X * + X R ~/R=0.2 r/~=l t/R =0.2 v/R=l t/R =0.2 ~/R=I

0.7 2.8 8.5 1.7 2.8 1.6 2.1 0.4 5.0 15.0 3.0 5.0 2.8 3.8 0.3 6.7 20.0 4.0 6.7 3.7 5.0

4p~ >p-d and, therefore X~(p E) < XR(p -d) from which it follows that pS[XR(/~)] </¢[XR(p-d)].


twenty times as much as a subsidy directed only to a specific group with the per unit subsidy being six times larger than in the case of the general programme. The differences are less spectacular when the target group represents a majority within the population as a whole and supply is more elastic than the demand of the non-target group.

There are, however, important aspects which are not reflected in this comparison but which should be considered. Firstly, there is the fact that a specific subsidy usually implies higher administrative costs than a general one and these would reduce the cost difference found. In particular an expensive task may be the locating of the target and the means tests. Secondly, whilst a general subsidy means higher costs, it also benefits more families and this has a value which is implicitly left aside in the above analysis. A social programme, for example, needs political support and this may mean that a general subsidy is viable whilst a specific one is not so. These points are fundamental in designing policies and their omission from the above analysis of costs does not detract from their importance.

Returning to the analysis of the effect of changing q, eq. (13) is used to analyse the effect upon the costs of a specific subsidy. This is shown in (16).

The variation in cost or in the consumption of the target group when q changes is

^

Cs = [aE(1 + s) - a e3 q. (16) s

Replacing a E, we have

Cs=I {( fe + aRrlR ~--)( I + s) / (e + ~IRXR/X) }--aPI~. (17)

Fig. 2 shows an initial situation in which the quality of the services is qo and the subsidy necessary for the target group to consume X is AB. A reduction in q reduces the supply price (production costs) and the demand of the non-target group and these two effects both serve to increase the excess supply (X E) available to the target group with the result that the subsidy needed falls to CD.

Table 3 simulates the effects which a change in q would have on the total cost of the programme. When the original subsidy is of 20%, a cut of 1% in q would, depending on the values of the parameters, reduce the cost of the programme by between 1.79/o and 5.6%. The smaller reduction occurs when and a R are at their lowest and the larger reduction when a t" and r/R are at their highest. Something similar happens when the original subsidy is of 80%. In this case the costs of the programme fall by between 0.7~ and 2.1~o when q is reduced by 1~.


xS (qo) P ql < qo _xE (qo)

i )

N /

0o -" " " " ",,X,; ~ - - - - \ B

/ /" " ,~ l xR D'~N~ . P x* \ ~ xP(qo) X

Xp x (ql)

Fig. 2

Table 3

Elasticity with respect to q of total costs or coverage of a programme granting a specific subsidy [see eq. (17)].

6= 1, X~/X=0.7

e=0.2 e= 1

~/R = 0.2 r/R = 0.5 ~/R = 0.2 t/R = 0.5

0 -R ¢7 R 0 -R 0-R

s 0 0.2 0.5 0 0.2 0.5

a E= 0.59 0.67 0.79 0.36 0.49 0.68

~ = 0 0.2 3.5 4.0 4.7 2.2 2.9 4.1 0.8 1.3 1.5 1.8 0.8 1.1 1.5

aP=o.1 0.2 3.0 3.5 4.2 1.7 2.4 3.6 0.8 1.2 1.4 1.7 0.7 1.0 1.4

0 0.2 0.5 0 0.2 0.5

0.88 0 .~ 0.94 0.74 0.79 0.87

5.3 5.4 5.6 4.4 4.7 5.2 2.0 2.0 2.1 1.7 1.8 2.0

4.8 4.9 5.1 3.9 4.2 4.7 1.9 1.9 2.0 1.5 1.7 1.8

I t s h o u l d be n o t e d tha t a cu t in q is m o r e effect ive in r e d u c i n g costs , for

iden t i ca l p a r a m e t e r va lues , in the case o f a gene ra l subsidy. T h e dif ferences

b e t w e e n the t w o types o f subs idy t e n d to d i s a p p e a r as the size of the t a rge t

p o p u l a t i o n increases , s

5. T h e t r a d e - o f f in d i f f e r e n t p o l i c y a r e a s

T h e a b o v e ana lys i s sugges ts t ha t the spec i f i ca t ion o f the type o f services

offered by the g o v e r n m e n t is i m p o r t a n t for the cos ts a n d c o v e r a g e o f a socia l

p r o g r a m m e . U n f o r t u n a t e l y , w h e n de f in ing the s t a n d a r d o f qua l i t y o f socia l

5In the case of a specitic subsidy, when XR/X=0.5 and s=0.2, costs fall by between 2.2% and 5.7%. When s=0.8 they fall by between 0.9% and 2.1%.


services, its repercussions upon costs, coverage and possible 'leakages' are not taken sufficiently into account. The size of this effect may be rather important. It should, therefore, be explicitly considered when designing social programmes so that these achieve the greatest possible progressivity.

It is not our purpose here to try to determine the most convenient standard of the social services. That would require a sector by sector detailed analysis. We only offer some illustration of the decisions involved in the main social programmes.

One of the cases in which the quality-coverage trade-off is most evident - - and which fits most closely the model set out above - - is the housing programme. In recent years, there has come to be an increasing awareness of the difficulty of satisfying housing needs given the available resources and traditional standards. Studies have shown that the housing which is supplied is far beyond the possibilities of the poorest groups for it is housing of a high unit cost.

We have shown [Arellano (1983)] that the poorest half of the Chilean families cannot buy, without a substantial subsidy; the most economic dwelling which is offered by the government programmes. The same has been found by Grimes (1976) to happen in Mexico City and Bogota. At a country level, the incompatibility of dwelling standards and costs with the typical family income can be illustrated by comparing the situation in Chile with that in a group of industrialized countries. In Chile the dwelling cost was found to be about 2.5 times the average family income, while in six industrialized countries studied, the cost was 1.8 times the household income.

This inadequate quality specification explains in part the unsatisfactory results shown by the housing subsidies. Given the relatively high value of the dwellings subsidized, they were attractive to middle and high income groups, reducing the access to the population most in need.

A reform of housing policies has to include a revision of the standards of the subsidized dwellings. A neglected dimension in government programmes that could help in this revision is the quality specification that poor families give to the shelters they build on their own. The little evidence available, suggests that this may be a promising alternative [Arellano (1983)].

In the case of health services the quality inadequacy has been described by De Kadt (1974) in the following terms: 'In Chile, as in other countries and regions, the health system is, to a large extent, a "copy" of the one prevailing in industrialized countries where the "curative" aspects receives priority. The use of these imported schemes is i n a d e q u a t e . . , because they are unable to cure the illnesses that affect the poor people in LDC's, in particular the children. Secondly, they tend to worsen the distribution of health care . . . generating differences between urban and rural areas and within the cities . . . . '

The identification of inequalities in health care and in access to the medical system has led to an insistence on the importance of developing


primary care systems as compared with excessively specialized medical attention. See, for example, World Health Organization (1978).

As in the case of housing, so in the case also of health, there has been a proposal to make an explicit effort to modify q. This would be achieved by changing the type of establishments in which care is provided (first-aid posts as opposed to hospitals) and the type of professional providing the attention (para-medical as opposed to medical). These changes would result in lower unit costs and a reduced demand by non-target groups, with the latter effect being strengthened by the differences which exist between the ailments which affect poor groups and the rest of the population. An analysis of these policy alternatives for Brazil can be found in Knight (1981) and World Bank (1979).

Regarding education one of the aspects which is represented by q is the number of years of free or subsidized schooling which are provided. The cost of education to the family increases with years of schooling and hence attendance falls or, if truancy is to be avoided, heavy state subsidies are required. From this point of view, it is not desirable, for example, that university education should be free or heavily subsidized for, as the available studies show, it is difficult for students from poorer families to reach this level. Even, in fact, at the level of primary education, the type of programme and the number of years of schooling which it involves needs to be carefully evaluated so that it is feasible for the poor.

In many social security programmes, at least part of the benefits are financed by a deduction from the worker's wages and this means that the more the benefits offered, the higher is the payroll tax. The level of benefits provided is being represented by q. If these benefits are paid for with contributions made by the worker and if the cost is high, lower paid workers will remain outside the system in the so-called 'informal sector' which is not covered by social security. If, on the other hand, the system is financed out of general tax receipts and not out of wage deductions, the trade-off between coverage and q arises from the limited funds available. There is, therefore, in this area as well a conflict similar to that seen in the case of other services.

The social security systems existing in Latin America do not, however, take sufficient account of this fact and, in general, when protection against a certain risk has been established, the lines followed have been those of the industrialized countries. If we compare the replacement rates (pension as a fraction of wages before retirement) and family allowances in Chile with the situation in OECD countries, we find similar ratios. For blue-collar workers the replacement rate in Chile in 1979 was about 60% while in a sample of 12 industrialized countries it reached 56% in 1975. 6

6Chilean data on the basis of official figures examined in Arellano (1983). For the OECD, Haanes-Olson (1978). In Chile for a blue-collar worker who earned the minimum wage and obtained a minimum old age pension, the replacement rate was 72% in 1980.


It has been shown that the quality dimension which has clearly been inconsistent in the Chilean case as in other Latin American countries is the retirement age requirement. The early retirement prevailing during past decades has raised to 20 the number of retirees per 100 active workers. This proportion would have been cut in half had the retirement age been 60 years for women and 65 for men.

These examples serve to illustrate aspects of the design of social policies in which the conflict studied becomes important. Obviously, detailed analysis is required for each type of programme. This raises, amongst other matters, that of the 'appropriate technology' for supplying social services to the population in need. This question is not gone into here but it is unavoidable.

In order to design social programmes which fit the needs and possibilities of the developing countries, a creative effort has to be made and in this we believe that the organized participation of those who are to benefit is indispensable.

The aim of the above analysis is to find a better use, from the point of view of the poorest groups, for the available public resources. In many cases, however, it will not be enough to improve the allocation of existing resources. It will also be necessary to increase them if the basic needs of these families are to be satisfied.

References

Arellano, J.-P., 1983, Social policies and income redistribution in Chile, Ph.D. thesis (Harvard University, Cambridge, MA).

De Kadt, E., 1974, Aspectos distributivos de la salud en Chile, in: Bienestar y pobreza (Ediciones Nueva Universidad, Santiago).

Grimes, O., 1976, Housing for low income urban families (World Bank, Washington, DC). Haanes-Olsen, L., 1978, Earnings-replacement rate of old-age benefits 1965-75, Selected coun-

tries, Social Security Bulletin, Jan. Knight, P., 1981, Brazilian socioeconomic development issues for the eighties, World Develop-

ment, 1063-1082. Spence, M., 1975, Monopoly, quality and regulation, The Bell Journal of Economics 6, no. 2,

Autumn. Streeten, P., 1981, First things first. Meeting basic human needs in developing countries (World

Bank, Washington, DC). World Bank, 1979, Brazil: Human resources special report (Washington, DC). World Health Organization, 1978, Primary health care, Report of the International Conference

on Primary Health Care (Alm-Ata) Sept.

meeting basic needs

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