This paper is prepared for staff use and is not far publication. 'hevieus expressed are those of - the author and not necessarily those of the Bank. I1JTWNATICNAL BANg Fa RBC~SIRIICTIONAND I I 6 v ~ 8 E N l ' Econdcs Department Uorldng Paper No. 17 I June 17, 1968 I This papar report8 on an attempt to estimate the effects of incame, price and weather an the consuaption of water in urban areaa of developing comtriee and to derive hrcctional relationships between these factors and the dmmd for water which can be used for forecasting. The st* ia based on data far 38 cities in Africa, Asia and k t i n kmrica. The data were rrocessed by the Bankls of the p a s by %&an G. van der Tak, Jochen Schmedtje and Shlano Rentlinger, and the editorial assistance of Sanjaya -. Investment Planning Division Prepared by: Avigdor Meroz - Table of Cantents (cont'd) 3) Tatal hily Psr Capita Water Conamp tion (Including FubUo &drantrr) - Results of Linear W t i p l e Reperreion L) Price Klasticities a t V a r i o u Levels of &ice and hconre -Dcmus&ic O E D 5 ) Price Elaaticitiea at Variow Lvds of Price and Lcome-Total OFCD 18 6) Income Blasticitiea a t Various Levels of Price end Income-Total GPCD 18 - Cbarte 1 ) Average Yearly Quantity of !-later per Persane in Dwellings with ifate ~Wera,etc. 9 Apmndix Tableg 1) Total. GPCD ar.d Per Capita ODP 3 2) Mscamfort Index and Annuel Average Teraperatures 13 Average Tempsraturea B 4) .*%?I OPCD and Annual Avarage of L kdmm Daily Temperatures 9 5) Total GPCD and Annual Average of IB- Temperatures Above 60 F 10 6 ) Total G R D and Mscanfart Xndex 12 - * I A QuantiWtive Analysis of Urban Hater nRmand 1. fntr-ion The evaluation of urban -tar supply projoctrr euffms, aa does the evaluation of almolrt all public Wty projects, -om the great difficultlea of weeeing the bamftts that result from tbem. In tbe abseace of benefit e e t h t e s , uatm atlpplg wojecta bave to be JtwtU'iedcm the bada af the phyeical quantities of uatur repixed by a given population. Cbce the need fctr a certain amount of uat.er ia established, project preparation coneiste of Oiading tbe cheapest way of producing it in the long run. term the 'simple requirement technique', 'is a t present widely used for want of mbing better. It is defective in that it leave8 out of canaideration vaFiontl factare that affect tbe conauuptioa ol wa* beaklea tbe number of people t o be m d . In m i c u l a r , a) it provides no indication of whether or not tbe demand fw mter of the mdsting population has been cratib factcPI.ilg met, so that there is no way of judging whether tbe supply of water needs to be changed regarding existing W d t b) it doea not accaunt far increasing water demand per capita due t o rises in per capita incam; c) it does not account far changes in per cspita c a m t i o n dne to changes in tbe price of uatar; and E d) it dm8 not account far different levels a.per capita casufqtion in ctifferent climatic, cultural and - - religious conditions. '!Thus the tsinph re-ementat approach ehclrld ideally be c q l e - mented a t h varioaa sorts of e c m d c and nm-acondc infarmation in order . of uater in urban areaa of developing countries, and by means of multiple - 2 - r e g r e s s h analpsis t o derive h ~ c t i Q l a relaticmahipa between then vhich l can he uasd, to the extent perm;ltted by the lhdtatiars bposed by the data, far farecasting. 2. a It marrt be &eased at tbe outset that the &+%aare far From can- plete, both in t e r of ~scope and covarage over t-, ~ and are a b l e t o mar, Insom cases to eubetantial mar. C ~ ~ t ifigures were not, o n far instance, available in all cases fcrr each of the main categories (d~aeatic,cammrclal, ind~trid.and publie) separately; the rates charged fca. the different categories vere similarly not alwege given; lnccnae per capita far indlvkbal cities was not available, and so on. In many cases there uas no indication of the reliability of the figures, and consumption f-ea were subject to error because af poar nrsterlng and inadequate records, uhih reven\Y) figme8 were somtiD13a dietorted by inefficient accounting. The mdenesa of Lhe data naturally affects the d d i t y and quality of the analysis baaed upon t h , but a t the mament we can do nothing hithout having access t o better and m e complete informaticill. WortuuAtely, suc5 information does not e x b t in documented form, and w i l l have t~ be gleaned f'rorn the primerg sources. Classification of Consumption 7. * &ban water con-ion is usually classified lfor purposes of deelgn into four categories, dometic, carmercial, industrial and public, aach category baving i'fferent average and peak cMlstcaption characteristics. For our purposes, domestic c-im is the nrwt iqmtant type, since the figures show that it prepaaderates i n the total commption of uater in the citPes studied. C~rmercialand public '%es, emhracdng consumption by hospitals, churches, schools, reatwanto, hotels, offices end so on, bave been grouped together with industrial -&es of water, first because the data vere not available to Uet them s e p a r a w for each city, and secondly because indwtrial consumption is not gQnerally very large (Industries tending t o depend on their own water supplies in developing countries), so that no great distortion results fram this annlgamation. We are left, therefore, with two main categories, dometic consumption and 'other' c-im. 8. The domatic use of uater includes both indoor uses such as cirirklng, cooking, bathing and uaswng, and outdoor uses like sprinkling and supp- m b d n g pools. 'ihe latter la probably of d l significance in developing cormtriee, thwgh ve do not ban the da'h to separate the two use83 it is certaiuly of much less lnpcrtsnce than In countries W e the U.S. 9. a,batbklg In most developing cumtries a substantial part of water for wa~h- and dridsbg &a supplied by pubUc bydrant8. Since this nter is $upplied fie8 (ar a+,a naPrinaL charge) the factors governing its con- sumption w e Wcely t o be very d i f f m t from the conrmmption of dometic water which is suppUed to, and paid far by, private h~weholda. The quantLtative bpmtance of public hydrant consumptian is such (for Instance, far Singapare, Jbmn,BdroPbzrra, W, Ama, and tjoon, where per capita public hydrant cmsuuption, colunm 12 in Table 1 is 40-60$ of domestic per caplta conamption) (colunm 9) that it ma t o be treated aa a s p r a t 0 categmy in this study. We have, therefore, tried relations??ipabetween the acplanatcmy factors and uatu. conmvnption (domestic ~ l u s'other') with and without public hydrants. Use of Cross--ion Analysis * 10. In a study such as this, one has the choice of as- one or both Yse* of two techniqaea, cross-section analysis and time-series have used ollp the fanner, becaue the data available (Table 1 did not we p e t the nse of tke-series analysis. Furthennore, a the-series analysis may not have ahom clearly the adjastment in consumption due t o a charge in incame or price of uater, since auch adjustment my tab a fairly long period in which wates saving devices are adopted or new outlots installed. In crosz+section analpis, on the other hand, i f we can assuns that Uferent cities :we idmtical in habits', tastes and cUraatlc con&.i;icw affecting uater consumption, we can take different levels of consumption to represent different levels of lang-ran a d j u s t d t o differences in per capita income and the price of water. Clearly the assunprtion of fdentical tastes is a heroic one, an&c&itutes ane of the =jar weakneesea of cross-section analysis. ~evd-theless, it is essentjal, far without it we cannot get anywhere a t a l l , 'A can *mat actual differences in tastes, etc., a8 ldisturbances' the analysis, hnd hope their effect is not biased in any special dirktion. 11. Far a thorough analysis of the economic doterminants of water ckmmi we should id- have had the actual rates c k g e d for water to each t~pe of consulasr. There are various types of water rates -midmum charges per period, charges based on nrrmber of cannectims, rmtered charges, and so on - which may be classified into two groups, me contai.?ing cbarges that are directly related to the amount of water actually conawd, the other, charges - 5 - that are no5 so related. The l a t t e r are usuaily in the form of f l a t rates, independent of the amaunt of water used, ar a mixture of both types, Urn- ing far free water on the basis of flat rates up to a certain, usually U M ,amaunt and charging extra for further c ~ t i o n . 12. Clearly, only tb rates that depend directly on the amount of water canswd are relevant t o the quanSity of uater demanded; the othere cannot lave an effect an it because once the f l a t rate is paid the marginal unit8 of =tar are free, hm,detaihd data on different charges ware available in only a few cases, and we had t o me an apprcximation t o a general price instead of the real prices charged t o cansuraera under different rate system. Since the most commonly available and canparable data were the total quantity of water sold and t o t a l rwmw from these sales, the a s a x e revenue per unit of watar sold was chosen as the approximate price of uator, The t o t a l quantity of natar sold uaa so defined aa t o exclude uater which tns free or not paid for by the direct user (i.e. pubUc hydrant water, U t a r y quarters, stc.), and the t o t a l revenue was adjusted accard- ingly. Claarly such a m o d ~2imputing price to the water sold blurs the actuol difference8 betlrxen the two kinds of rates in different cities, and thus conceals t o some extent the true relatian between prices and demand; unfartunately,the paucity of data prevents a better analyeis. Derivation of Per Capita Incorn 13 Information was completely lac- m the incorms of conaumrs in dlffarrent cities, either h ~ r e c t l yin te-.-mu of per capita income or indirectly i n tens of relevant indicatars such a s electricity consuzuption, property b e s , teiephone amnections and so on. 2h had, therefore, t o make do with per capita GDP figures, uhich m e available for all the countries con- cerned, a8 indicatars of income in the cities. Ihcomes in cities may vary conaiderabb from <;he national average, particularly in developing countrien, ' and the variance may also be different in different countries. a- We tried to get arcnmd this difficulty by relating the size of %he city t o average household income (t&=n from fan#y budget surveye) in three camtries b e data were avaLlable (see A p p e n w1, but dthoot much success. There seemed t o be no definite r e l a t i hip between the two, so we did not adjust per capita GDP figures. I * Darivation of '&ather Index h- 1s. Since it seemed plaueible that variaticns i n weather would explain surm of the oariatiorlc in water use, variow weather indices were con- structed on actvice from experts from the U.S. Wether Bureau and from the klorld Bank- (see Appendix 3). None of them seemed, however, t o have a significant correlation uith t o t a l per capiaa water commption in ejmple - 6 - regression analyses.31 Thua, gqr of these Indices mag have aerved equally uell, or poarly, in the aubaequent analysis. All d w e acpreeeed in local m e n c i e s were reduced to a common basis by cmeraian into tbe U.S. d o U a t officlal exchanqe rates. No attempt m e aade to aqjwt tbeae ratxe far poerible -at ., Q QPwer- valuatioa. L. The Reffl.ees.ioaAnalysis Choice of Dependent Variables The moat Moss candidate far bhe dej-mdent m i a b l e was average rwr capita water conmmmtian (gallane par capita daFlg, since we were interested in individual response8 to the changes in econoudc and other conditions. Three gpcd quantities vere tried as &pendent variables: i. Totdl gpcd - total water consrmpltion, excluding public hydrant consumption, tilvided bp nunrbar of people served by individual cannections. This is given in c o l m (u)04 Table 1. ii. Total gpcd * - total water consumption, including consmaptim from public Wcirants, divided by t o t a l population. This i5 ahcin in colinrm (13) of Table 1. iii. Damstic gpcd - total dca~ehicwater consuqtion divided by the number of people served-by individual cacnections, i.e. excludinq public hydrants. (Colman 9 - af Table 1). - 'J 0 3/ A poor carrelstion 4 a d n p b regression does not necessarily imply - a pour correlation a multiple regreasion. Nevertheless, a simple 'e repessicm is &a us, m x m & c & w a r, I relatbnsNp exists %tween the two factors. In this case, purely , m the basis of ahgle regression, there ~s no definite reason for picking one in& over another. - i- It ia cons-011 excluding bydrants which is tbe most meaningful fcr aur purpsee, aince free uater cannot be acpcted t o reapand t o e c a n d c factors Ilke price and Income. Nevertheless we have incl.u&d ccafmption Including that frat public wantti ar, a dependant varAable ?n oas cd the trials fur the sake of cdnaJletsness. Domestic gpcd ~ w scalculated to gain same idea of the effect of the 6xplamta-y factors car pure4 household damand. It is of maro Umited elgnFficance than total gpcd, not aaly because of ths d 8 . r caverage but al.80because a Rmallg~.nIWbar af obsarvatians ~ r w eavaiLable (29 as cozqwed t o 40 for total gpcd). In developed countries a variable that baa rcometimes been wed i s 'per household' ua* c o n ~ t i o n 3/,far the racwoa that econdes of scale of per capita water c m t i o n occur ae the number of people in a household increaaae. kSe did not, however, possess the informatiaa t o rake such an analysis far a l l the countries studied here, though Flgme 1 lllwtratee hou damstic gpcd varies vith fand3y size md incape level. The inpUca- tions of this effect are discussed later (para. 9). The choice of explanatory factore uas primarily dlcbted by general econdc consideratiom and the availability of data. The main economic factors normally related t o demand are price and income (coltma 19 and 23 in Table 1); we tried simple regression between theso and the demand far water in order t o confirm that some definite relatio~lshipa&t between them in the f i r s t iasknce (see Appandicea 1-3). These 8impb regressions * 3/ For instance by 2ii. HOY8 and F.P. Linaueaver C &pact of Price on Residential Water Demmd and its Iielation t o -em 3esign and Price Structure", Water Resoarces Research, Vol. 3, No. 1, 1967. - Derived ficm the Statist,ical Abstract of Israel, Jerusalem, 1966 (p.203) 8- I c w J h d that no& economic relatiamhipa bold in this case. The eb@e renrecsion of consuxu~tioa(C 1 on pocics (PI ia: The 8-b regression oi caaetrrrqJtion (c) on income (Y) is: 23 Thsse regression c d f i c i e n t s are biased eathatee of the "truen r e m s o of consumption to price and income changes because water con- sumptian is expected t o be a function of both price and incom as well as I other variables. Mutiple regression ee given bedm should result in better 6Etimates of the "trueHresponso relationshipc. 2b. Ammg the other explanatory variables c a d were two indicoa of weather; aa rrrentianed above, there -asno r e a m t o pick these indicea over others on the basis of sirnple correlation. We picked the averam of comm-s&se groa;rda t o have scum effect rn uat& consumption, the second because it effectively combines htllrFdity and temperature (columns 21 and 22 in Table 1). 25 We used three o t h r explanatory variables: S, the nurcber of people I served by indoor end outdoar individaal connecti~lsas a percentage of the cityla total poplatian (calm 16 in Table l), P,the total &r of people served by all water slrppliea (columns 16 pPu l8 in Table 1)and R, a dmmy variable t o distinguish between two rate stmctmes, ukre a valw of crne I s assigned when the .rate of watq charges is related t o the ,volume of later consrmprtion and a value of zero is assigned vtben a flat rate is charged independent of water c m m i d n . 26. C l e a r l y other factors, such as habits, culture, religion, and 80 I on, have an effect on wap consaaprtian, bat these are not quantifiable and we had no choice butato ignore t b m . 'Xe also had LO infurmation on 3i!0 practic~din cases of sa demand, so we-had-to -*ire it. nearly the plctnre for denand ig rted when such rationing exists, but ve have reason t o believe C a t this distclrticm is quite mall, and tht rationing is of minor importace relative to total consumptian. 3J The rainfall-teqsrature index waa suggested by Be Qry in X o ~ g ! ! AVERAGE YEARLY WAN?ITY OF WATER PER PERSON IN DWELLINGS WITH WATER METERS, BY GROUPS OF NET INCOME PER FAMILY AND AVERAGE SIZE OF FAMILY (URBAN HOUSEHOLDS, ISRAEL, 1963/64) AVERAGE SIZE OF FAMILY - 10 - The r d t a of' the multiple regresalon presented in four grmykgor (The first three are linear functions), 5n which: i. The dependent variable is total coastmptica frun public hydrant8 Tahle 1 1 3 ii. The depaadent vuiabls is total gpcdu, including consumptian from public bydFanta (column 13 b~ Tablo l ) ~ iii.Thedependantvariableiadcwetiagpcdexcluding hydrants ( c o l 9~ 5n Table 1); v . The dependant varlable i a aa in (I) but the functional farm of' the equatian is log-linear. IZegreseioa results *am various conbinatians of variables far the first group (i) are presented in Table 2. Qdyprice and income had a significant effect on water ccuumqtion. Far aU the othar variables, the standard errors of the coefficimta are nearly eqval to ar mch higher than the response coefficients. Consequently, equation (i.5): - (i.5) Ct = 46.1 72.9 P + 0 . SY (1 vhere C t ~ c i ,arr:ludhg c a w t i o d from public hydrants, P price (US$ per 120 gallc+n)aradY = incame(GIl? per capita in US $), uaa chosen for ddng projectians of gpcd far various levels of iacome and price in Tables 4 - 6 below. This is also the most useful equation because Ctle dependent variable excludes uater ccxumptlan uhlch could not be expected to be raspormive t o price and because the regression ts derived r ' r ~a larger data base t2Pan the equations in subsequent groupings. Regression results from various cambinations of variables far the second grap of eqytians are pre-ed in Table 3. As would be expected, the price variable exptzlna leas of gpcd uhen c-im from public w a n t s is -hcltlatd. Ihe only clearly sigdficant variable in all equatiom is incame. 'Ltre d o l e set of q . L l tyielded rather l a r K i ~ tp' For ~?IIs and becauae the eqyaticms .?e dsrhmd froan only 17 reason observaticms, the equatl.ona in this g.0upb.g are not used for projectiw in the subsequent amlpia. - u- Though it would have been interesting to examine changes in damestic water c w t i a r , aa distinct from total consumption including that of industry colmcerce and government, the lack of data and amall number of obesrvations (29) led t o rather poor results in the regression analysis. Rro triala were made, one nith price,income and average nsximm temperature as explanatory variables, which s h d on4 price aa being significant, and the other with ahply price as the explanatory variable. (iii.1) cd 1 - 7 6 6- 9 . 3 P~ +~ 0.008 Y :d + 0.272 T (10.200) (0.006) (0.186) iie - 0.5m - (iii.2) Cd 39.259 - 52.170~ P (2 (10.570) r2 - o.lS5 where Cd is damestic consmptian, P price, Y income and T average maximum temrperature. In view of the regression r e d t s from the linear equations ~ 5 t h gpcd, axclnding public hydrants, aa the dependent variable (group i regressia~sl only two log-linear functions were estimated. U s i n g the same explanatory variables and data a8 i n eq.?atian (i$), the logarithmic regression equatims are as follows: (iv.1) 1% Ct = log 1.82 - 0.43* log P + 0 . d log Y (3) (0.10) (0.10) -2 R = 0.49 * * 9 (iv.2) log Ct = log a.3 0.46 - log P + 0.U log Y + 0.95 log T (0.09 (0.10) (0.74) - I= - 0.52 'J 's A s with tb linear equ$ion,temperature was again not significant a t a 5% = level (ar even a t a 1&level) in explakbg changes in water consmption. . L * Significant at lea& a t the five percent level. -14- We used the linear function for total gpcd (excluding public bdrants) in preference t o the log function for predictive purposes because the former has different elasticities a t different points of the function while the latter has the same elasticity throughout. Tbeareticallg we would expect the linear function t o be more valid, since we expect the elasticity of demand for uater t o change a t different levels of price and lncorae. Elasticities in income and price u. These are conaidered in trzrnt The price elasticity of total gpcd aa given by equation (1) is -0.113 at the average point of the function, at which gpcd is 42.5 gallons and prico is $~.26/1000 gallons. This means that at this point an increase, say, of one percent in price uoulcl result in a decrease of 0.43 percent in consungtiori, from &2.5 gpcd t o 42.3 gpcd. A t prices different from the price a t t t =average point, the elasticity uould change, being later at lower prices and higher a t higher prices. This is reasonable, since other things being equal, people can be expected to respond more to a change in price when the price is already very high than uhen it is low. According to the same equation (I), income elasticity for total gpcd a t the average points of per capita income, price and per capita daily conamption is 0. wkth income at $286, price at. $0.26/1000 gallons, and ccmsuraption a t 42pgpcd. In other m d s , an inmeaae in income of one percent with price rema- canstant will lead to an increase in gpcd of 0.33 percent. A t higher levels of income, elasticity would be higher than 0.33 and a t lower incomes lm than 0.33 2J. L Price elasticity of demand is the ratio of the percentage change in quantity damndad i n response t o a small percantage change in price; income elasticity is the ratio of the percentage change in quantity demanded in respollse to a small percentage change in incams. expenditures of homogeneous social groups an large categories of products are studied, the lmporhnt inference is that the incone elasticity is higher for the low income brackets than far the higher ones, and the reverse, that it declines when the level of income kcreases. When applied to one specific product, ravry exception to this general ruLe are, however, to be expected. This holds particularly trim In those cases where consumption is measured in volume terma and where, next to income, other factors such as family size, profession, etc., play a dominant roleu (Italics ours). From R. Ferber and P.J. Verdoorn,Resaarch Yethods in Econdcs and Business, The Macmillan Campany, New Yark, 1962, page U.5. - 25- Equation (2), using domestic gpcd (c31m 9 in Table 1 ) aa the dependent variable, yields a figure only for price elasticity, a h c e the income variable did not show aw significance in the trial. The price e h t i c i t y of d w s t i c gpcd is - s a t the average point whero price is $0.26 per 100gallons and 3onswnptim is 25.6 gpcd. 'lhe e'laaticity vlll rise a t higher price levels and f a l l at l o w ones, in the mannor sxplaine6 above. tho linear function. It is interesting to note in thia cmtext that How and Linaueauer 2' found the price dasticity of 5ota.l damstic demand (in the U.S. ) t o be -O.L&, while Fourt found it t o be -O.u, bc%hk.1 logarithmic functions. The virtual identity of the price elasticities yielded by these stndies itl certainly coincidental, because of the vaetly differhg conditione between developed and underdeveloped countries; the most fi enables us t o say is that there ,i.= d s f k i t e relationship between price and consumption of water a regardless of the atage of economic development. The results of the regression analysis can be sumwised thusr If we rule out the consumption of water from public hydrants, we find that hcom and price have a definite effect on water consumption, +inaccmdance with the principles af economic theory. 5. Evaluation of the Analysis I Though the regression analysis confirms what we would expect t o happen an the basis of ecmomic theory, the act- figures that result from the equations are aabject to many faults. - These fault8 are described belar: C I Op. cit. page 8. In Farecastiw the Urban Residential Demand for Water, an unpublished research paper, Vniversity of Wicago 1958. - 16 - Use of Crose-Section Analysis a sPlall nunbar of obaematicma end relatively large disturbing eit~mente ubich could not be campenseted for. Ye b v e mentioned these diclturbancee above, and need ady point cut their presence mny bve had a significant influence on the reaulte. Price Derivation The darivation of the price per gallon of water fraa total revenue and total quantity of water sold is a very cpstionable pr~~edure,because I it averages out the differencee in rates which are of crucial impmfxince to the analysis af price rseponsiveness. Furthermore, due to possible inaccurate reporting of both revenues and pantitlee the average price mag be quite different from tbe W average. The most i n p r t a t objection to t h h procedure is that it doe8 not distinguish between ratee tbt depend the quantity of water caasam~idand those which do not. In the latter case a change 3n rates does not have q effect an the qpmtity of water c o i d while in the former it does. lie are interested ?ncases wh81:e rates do differ with conmaptian, but the kLnd of infomt-Lon we possessed did not permit this distinction. Otw analysis d f e r e , i n conueqtience, h o r n the averaging and grouping of the two different types of ratee and the effect af price is ueakened. Incolne De.rivati0.n In a similar fashion, the effect of real incame differences is weabened by the use of per capita GDP figures far the incam variable. There are two reasons fo;. this: first, the Income levels in a city may divergq consiZerably from the national average; second, pdr capita GDP ccrmparisons ars themselves notoriously difficult t o use as indicators cf - L ~onversianinto Dollars - It has been -timed above thatmfficial exchange rates were used t o convert local m e n c i e e t o a cornman derbbator. These rat- are in casas distorted by inflation, government Interference or market rigiditlee; ccmseqpently, the values for countries with overvalued exchange rates would have been exaggerated and far countries with undervalued rates (if there are aqy) understated. Fami& Size Distribution I (as In Israel,- see para. 21 above), i n tbat a larger family k e s loas I the e& in the different cities &died. This is, howem, unllkely,-and reduces the significance of that particular trial. 47. In sam, therefore, the regreseion analysis suffers frcm various faulte in the data, and consequently Frcm faults In the mthodology, which - I of its tentative nature, without &h, val% being attached to the qua- I factars into accounti uhen forecasts of wter demand, rather than In the actual elasticities and functions that are de..ived. It also points clearly to the need for further research in this field to estimate these quantities more accurately, which can cPlly be done with vastly improved data collection anti coverage. I &9. For the sake of illustration, hauever, we have shown 3 tables with farecasts of elasticities for incarne end price, derived fr~mequations (1) and (2), far total gpcd and domestic gpcd respectively. Tablee and 5 show price elasticitg of demand a t various levels of price and incorn, the farmer for domestic gpcd, the latter for total gpcd. W e can see that a t given levels of income, price elasticity Incremea a t higher prices, while a t given m incanes. ThB underlined figures in all three tables ahow the average valw - 19- It i s nece-y t o stress the illustrative nature of these figures. They should not be interpreted as actual values to be used in practical cases; they merely serve t o show h~i:the technique can be applied with better data. b the abce tables as we move further fromthe Mderllned average values, the possibility of error (already k g e ) increases aponentially. Present methods of farecasting water denand, uhich ignare incorns and price effects, viU give results where such effects are significant. If, far instance, incame in a city is going to increase at a vary rapid pace for acme r e a m , the incam affects will add to the deound for water and the 'simple reqvImmnts1 technique may imderestbate future demand. If, on the other hand, the supply of new water villnecessitate a large Increase in pice, the price effect may reduce the demand far water and the project m y end up with excess capacitp. Neither of these m q happen, of course. bcosae may continue to grow a t a steady rate, and pricos may rise mrghdly, so that the 'simple requiremantsl approach may requba no furthsr elaboration. Cur calcUtions &ou tbt the elasticities are not likely to be very large, so that fairly big chmges In income and price w i l l be requlred t o produce noticeable changes in cor,sumption. It is, thorefare, possible that In ~lanycases the traditiaaral approach w i l l suffice.' This is not an argument for abandoning inccrce and price, and especially prica, althgether in dar#nd forecasting. There w i l l be cases where these factors are important for water supply projects, and these cases justify the dovotion of further effart t o a better evaluatim of their effects. The present study is nothing more than a prelinrinary skirmish before the main engagaaent . - &her Simple Carrelation Betwan Rice and Con- tian In appeadix figure 1 total gpcd l a plotted agalnat average revenue. The equation far the shple regrmmicu~of uator caPurmFpltion an amage revenue isr where C ie total gpcd and X la average reveaw per 1 0 gallam in US. . dollare. (The atandard error Fs giwn in pareathesea and r la the simple correLatian c d ficient) TOTAL DAILY PER CAPITA WATER CONSUMPTION AND AVERAGE REVENUE 100 90 8 0 . l a 70 . V) GPCD 62.8- 79.3( Arr. Rw.1 Z 20 - 0 10 20 30 40 50 60 70 80 U.S. CENTS PER THOUSAND GALLONS IBRD -3915 a representative of its annual incam) Y and the city's popkition X are ah- below. trans 3/ 8 cities; range af pqmlstian UX),000 to 300,000 the average i s 182,000. The relationship is negative and contrasts wit'\ ubat bad been expected. !he other two cases show positive relatlmchipa but the mgnitude is too small t o suggest any definite connection. India8 _2/ 4 citiea; range of populatiar 1.7 to 4.2 uiillicu~,the average is 2.8 mcllion. Japan: 1/ I47 cities; range of population 0.1 t o 8.9 milllcm, the average ia 647,000. Putting the cities into two grcnps, one uith popcbtlan under 1xdllim, the ather with populatian above 1milUan, the equations uill be: 1 ) 40 cities uith popalaticras in the range of 0.1 t o 1.0 mlllira, w i t h aperaee of 273,000. 3/ fian: 1 ) Snrvey of Cansmaer Zxpenditurea and Lcsse in 32 &ban Cities of Iran 1958/9 Bdhtin, Vol. 1, No. 2 u'nly-August 1W,Bank krkazf, &an. 2) Census Msi;rict Statistics of the Ist National Censns of Tran, 1956, k-aa General Ikprbmt of RibUc Statiatica. 2~ India* 1); cm~rmarpenditvres by Levels of &wehold Expenditure, The .L lktional Sample Survey No. 71, wwrmwat nt' mu, m ~ c n t t eLYW. - 2)gStatistical Abstract of the hdian Unicll. 1962, Deprhmt of Statisticsl; GaPemrment of kxlia. Japans Statistical Yearbook 1965, k s z u of Statistics, .Office of the R% litinis*. dmple re eaeton of avtaaga tsrapsratum (X) in ~shrenbeit&water con- e r n %) Lor - - O.U5 C 70.9 X Tbe canrelatiaa ia positive but not significantly different from zero. The graph IB in Appendix Pigure 3, end the figures in AppandF~.Table 2. sham daily teageratmesm y bo more clot& related to water c&immptim tban other indices. Tbe carrehtian is dwm in Appendix FigrPre b and the values are in Table 1 in tb main text. The equation is: ukm C stands for -a- c w i m aad X far annual average of mudmum daily tanpmattxrea. This Index is also not si@f5cantly correlated with water C a certain lekl, Mch was-suggested by weather axperta to b;, in the range af 55' - 65' F. ik m e d an equation with a base af 600 F, calculating the anrmal average af daily tempiatures above this base. Tbia carrelrrtion irr shown in Appanctix .Rigu=e 5, ani the equation is: s I whare C ?aconsumption and X ia the index of' daily everage temperatures above 60° F. The carrelation ia not significantly different from zero. 'Ihe figures are shown in Appendk Table 2. TOTAL DAILY PER CAPITA WATER CONSUMPTION AND ANNUAL AVERAGE OF MAXIMUM DAILY TEMPERATURES . 100 90 8 0 . · · · . 70 . 3 .. z 0 2 . . . . 60 . za 0 2 50. . . Q: GPCD 30.0+ 0.159(Tarnp) . V) I Z '3 2 . . 4 0 ; . .. . (3 2 .. 3 0 . . . 20 . . I f . . .. . - - . 10. s I - 1 * h w 0 60 70 80 90 100 TEMPERATLIRE (DEGREES FAHRENHEIT) IBRD -3918 APPENDIX -lo- FIGURE S s a . TOTAL DAILY PER CAPITA WATER CONSUMPTION AND ANNUAL AVERAGE OF DAILY TEMPERATURES ABOVE 60' F 100 90 80 70 5. ;i 0 2 60 Z 9 a w $0. a V) 2 GPCD * 58.7- 0.895( Tamp) 0 I!40 d vi. 3 e 30. - 20 I. - 1. * - e w 10 0 . 08 0 0 10 20 30 40 TEMPERATURE (DEGREES FAHRENHEIT) IBRD -5919 I . - -1l- - rature and Zelative Hrmiditgt This is called the ~dbccmfcrt index1 by theT+ ~eatharBureau. It assume8 base lavels of 500 F for temperature and 0.55 for relative humidity u. The correlation is shown in Appendix Figure 6, and the eqmtian iat - C 21r.O + 0.256 X - (0.5) R 0.09 u b r e X stands for the ldiscamfort index1t here too the correlation coefficient l a not significantly different from zero. The 1discaai'ox-t index1 figurea a m ahom in Appendix lgble 2. e) Rairfall Tamperatwe Index; Qle of the M c e a used in the text is the rainf-~tmprature index, suggested miginally by de Hartuune in W 6 for measuring humidity in relation t o agricultural production. The index was: -Precipitation Temperature + 10 where teqmrature was in cdigradsa and 10 was added t o avoid negative values when average tanparatares fall to -10" C. This index was emplayed by B. OuTg (see para. 2& in main text) in warking out a ueather index for agricultural production analysis. The valus for this index are given in Table 1, in the text. 3/ %e index is DI T = - (0.55 - 0.55 H) (T-581, where T stands far temperature and H far relative tnmddiky. In this study, T was taken a s annual average of dally madmum temperatures and H as annual average of daily relative Wdity, measured a t noan. 4 I 0 -15- 17. 1B.Q Appraisal of the H8niZ.&trowlit- Ha* E b ~ b U c of the P'Uippine~~1964. 18. m, Appraisal of the Jbore Rim Hatar Project, 3ingepwe, Malaysia, 1965. 19. IBFUI,Appraisal of the Bs,jtxra Xatar Project, The g i n g h of Burundi, 1966. 20. IBHD, Appraisal of the Ibcca hter b~ly Sewerane Rolect, Province and of East Pakistan, -%ldstm, 1963. 21. IBilD, Appralsa'L of the Chittauong '&tar Srrpplg and Sewerasre Roject, Rovince of &st Pakistan, Pakla-, 1963. 22. ]BAD, Appraisal of the M o r e dater Suovly, Sswaraae and k a i n a ~ eProject, Phase I, .ht Pakistan, 1966. 23. IBiZD, Apmaisal of the Banaalore riatar 3 ~ ~ ands5ewe.ra~e Project, 3 India, Draft, J.966. 2b. IBHD, Economic &owth of Algsris, Problem and Roepectq, Vol. V I I I : ;Jater Supply and huerage, 1966. 25. DItD/IIEl, '&tar and m e Ilata, Cd~apilcdby the Water §Upply Division In the Projects Ibpartment from Varioas Sources. 26. mA,A~aiadLdtbeT.ipeiReRiorrPlUatar9rrpp~Roject,China,1961. 27. IDA, Appraisal of tbe ~ M R Uiiatar 3rrgplg Project, Nicb~agua, 1962. 28. IM, Agpraisal of tbe -*tor &moly Project, Hashemite Kingdom of Jordac, 1961. 29. IIB, El-oject for the Constraction of Watar &DF& &&oats In 39 cities in Chile, Technical Ebpart, BDnsx I. ~ i t x I 30. m ~ -0vemn-t , and -an of tb .&tar 9tlpp3g *stem for t& af Q?rro, Bollrin. 3. DB, Annliais TecPico de IsSallcitud & Pkranciaadento b~tltadamr la bprasa de A- Potable & Wto, wr. la A~II8cian&l Siskrr, - M a r . . 32. m, Ahshadento & lpiv Fbtable r Alcan-ll.do rn b e t a r o m w o , mxlco, marpas ~ c o . 33. MF, h t m t i o n a l Plnnncirrl Statistics, Snpphmnt to 1966/67 Isnuas. a. PIF, htemational Financial Statistics, Vol. Xp, No. 1l Nov. 1966. 3 . O.M.S., Amelioration e t Extension du 3ysteune dlamovisiannsssnt en Eau Patable, Dahamy, V i l l e de Cotaaoa, Bopert, Walter Dardel, Ing. Conaeil Aarberg, Sulnse, 1965. I - s. Quraishi, O. He, Wktar Dmmd in SrcrdsnmJAW, hly 1962, pp. 776-780 37. QrPaiahi, O* Hea r?krdi~ Uatsr in Swed+a", JAW, Oct. 1961, pp. U51-1259. 38. Ruble, E. H., nhdu&ri.l Notar Rquirrl.ant~~",JAWa, July 1965, p ~ 831-833. . I 40. IN, Yearbook of Natloaal bcomta Statlatics 1965. I - - - &l UN 3peci.l PPnd 'MiOah t E?ul fOP Accra ~ W.tm ~ I ~.