World Bank Reprint Series: Number 157 Vinod Thomas Spatial Differences in the Cost of Living Reprinted with permission from J ozrnal of Urbant Economnics, vol. 8 (1980), pp. 108-22. JOLURNAL OF URBAN ECONOMICS 8, 108-122 (1980) Spatial Differences in the Cost of Living' VINOD THOMAS The World Banks Washington, D.C. 20433 Received Deceriber 18, 1978; revised March 20, 1979 A method is described for constructing spatial indices of the cost of a basket of basic "requirements" of food and nonfood categories. The proposed index for nonfood items is built up from household expenditure, since their prices are unavailable in most developing countries. Using Peru as a case study, it is shown that the cost differences have significant implications for measures of real income and poverly across regions and between urban and rural areas. Spatial differences in living costs have implications for estimates of income and measures of poverty within a country. Nevertheless, it is common to use money income in comparing living standards and a single money income threshhold in measuring poverty across location.s. These procedures, however, give a misleading picture of the benefits and costs of locating in various parts of a countly. Exactly how misleading depends on cost-of-living differentials. This paper describes a method for representing income and poverty differences within a cotn try more accurately than those based on money incoime measures. Focusing on the cost of basic requirenments of food and nonfood categories, a cost index of a basket typically consumed by the poor is built up. To bring ou t the imnportance of doing so, the index is used to deflate money estimates into real estimates. The cost-of-living index is also combined with inconme estimale.t to obtain measures of regional differences in poverty whiich are imore aiccurmte than those based on money income estimates. The country studied is Peru. The empirical analysis is based on a countrywxide budget survey called ENCA conducl(eL by Peru's Nfinistry of Agrictilture in 1971-1972 but publishiel after 1975 [9j.2 Uisinig inforniatitn given by this survey, per 'This paper is part of a larger study I did at the World Bank [141 in cooperation with Peru's Mini.ir% of Economics anti Finance. The study would not have been possible withouu the advice and support of ('arlos Amat y [eon ('havez and his research group at the Nfinistry. and Douglas Keare, John F'ngki%h, and Flkyn C(haparro at the World Bank. I acknowledge assistance from Nelson Valverde, John 1 4sk, and Joni Shaio, and helpful comments from Enrique Lerdau, George Tolley. and RWtard Webb. The views expressel1 are those of the author and not necessarily those of the World Bank (Group. 2The data given in this paper were obtained from the ENCA tapes by the kind courtecy of the Ministry of Economics and Finance and are given in a World Bank Workirng Paper, No. 108 0094-1190/80/040108 15-S2.00/0 (vpyr,ght i 1980 hy A,adcmic l'rcs., Inc. All nghLs of reprodnuction in any form rescrved DIFFERENCES IN LIVING COSTS 109 capita,income and expenditure are derived. In general, reported income (adjusted for income in kind) is lower than expenditure, especially for low-income groups in rural areas. This divergence perhaps reflects the failure of the sampling method to fully record seasonal fluctuations in income. Given this drawback, the paper relies on data on consumption expenditures rather than income. Expenditure data on food are broken down into specific categories and indicate both price and quantity. Data are also provided on consumption of homne-produced food and it is therefore possible to estimate the moiney value of this element of income. Expenditurc data on the main nonfood categories are available; however, they are not broken down into prices and quantities. ENCA classifies Peru into nine subregions. For ease of exposition, the regional comparisons repiorted in this paper will be confined to a four- region classification consisting of Lima, Coast (excluding Lima), Sierra, and Selva contLining. respectively, 23, 22, 45, and 10% of the country's population. To highlight the urban/rural differences, the paper also focuses on three distinct areas, differing in degree of urbanization. These areas are (i) Lima, the largest urban center, (ii) Urban Coast, the relatively built-up urban centers in the Coast except Lima (9% of the national population), and (iii) Rural Sierra, representing about the most rural situation in Peru (29%'c of the national population). 1. SPATIAL DIFFERENCES IN LIVING COSTS To correct money expenditure:s for spatial price differences and provide measures of actual consumption levclx,e regional conisumer price indices are required. The price index for any region j may be written as follows (Meesook [6]): n E VXm P, p = Y 100, ( I) EX'I,,, Pil,, where .X and 1' are quantities and prices, respectively. i are commodes, and in defines a regioni whose charactei-istics represent the national average. The :abuve price index rewritten in terms of relative prices, using 273. The basic information has now been published by the Ministry of Ag:riculhulre and the Ministry of Economies and Finance. 110 VINOD THOMAS expenditure weights instead of quantity weights, is given below: n EXi. Pimv pi n 0 Xim Pim Using data on prices and average shares of the various commoditie, in total expenditure, an overall price index for each region of Peru is calculated. First, the absolute prices of major food categories, taken from the ENCA survey, are converted into relative prices witni national average prices taken as 100 for each commodity. The relative prices of the various food commodities are weighted according to the importance of the com- modities in the budget to give a price index of food items. For simplicity, the national average expenditure weights are assumed for all regions. Next a nonfood price index, again with national average prices taken as 100, is calculated based on data on nonfood expenditure. Finally, using the shares of food and nonfood in the budget of the national average family, the two price indices for food and nonfood are combined into an overall price index for each region. The use of national expenditure weights as opposed to regional weights simplifies the procedure tremendously, while not affect- ing the results significantly. Ideally, consumer price indices should allow us to compare regional differences in the cost of achieving a certain level of utility. If people and locations were identical, a given basket of goods and services could be assumed to provide the same level of utility. Realistically, however, peo- ple's needs and tastes, as well as the quality of goods and services, vary from place to place, and it is thus difficult to define baskets of goods and services that are appropriate across a whole country, or to argu, that such baskets provide the same level of utility. A Food Price Index Some of these problems may not arise in the case of food, since nutrition levels can be defined in terms of calories and p -oteins. One can calculate a food price index that reflects differences in the cost of achieving a certain l-vel of nutrition recommended for each location. Of course, a variety of food baskets differing in their compositions, and hence prices and perhaps in utility, can provide the recommended level of nutrition. Ideally, perhaps, DIFFERENCES IN LIVING COSTS Ill a separate basket should be priced for each location that represents the revealed prefrences of the poor in that location. In this PL,. however, the same food basket is used for all locations. This basket consists of the items consumed by Rural Sierra's people at the 20th percentile in the income range. The quantity of food in the basket is adjusted to meet the nutritional levels recommended for each location by Peru's National Planning Institute [12]. A different food basket represent- ing the preferences of the poor for each location was not used, because data were available only for Lima, Urban Coast, and Rural Sierra. To the extent that the particular basket used is not revealed as preferred uni- formly across locations, tbe cost differences derived on its basis will be exaggerated. A Non food Price Indey Measuring and pricing the consumption of services and commodities other than food raises problems that will be met in most attempts to compare living standards within countries. Data on nlonfood expenditures are frequently available from household budget suL-rTes for a nuibnber of locations, but the quantities consumed may not be reported, or the commodity specificzitions may be poor, or inconsistent with the available price data. Even if some quantity estimates are available, "minimum requirements" of nonfood items are hard to define and measure, and as a result, regional variation in needs is difficult to assess. Quality differences of nonfood items are similarly hard to account for. If price data are available for at least some of the main nonfood categories like housing, clothing, and transportation, one may attempt to define "comparable" quantity units and build a nonfood price index directly on this basis. Peruvian data on nonfood prices do not permit this. Given these difficulties, a nonfood price index may be calclilated using some relationships of the Slutsky equation as presented by McCloskey [5] from data on nonfood expenditure. A detailed derivation is given in the Appendix. In the approach used, it is assumed that regional expenditure data refer to equivalent baskets of goods and services. In reality, however, considerable quality differences exist, because of this, it would have been better, had the data permitted, to construct the pricc indices on the basis of expenditure data for groups at similar positioiis in the incomle distributioni. The approach used in this paper is to think of differences in mean expenditures in any location from the country's average expenditures as the product of a price (lifferenice and quantity difference. The quantity difference is then explained in terms of a price difference and an income difference in a location conmpared to the national averagc. The index for any region j is constructed with region ni, whose per capita nonfood expenditure represents the national average, as a base. Any 112 VINOD THOMAS divergence in the nonfood expenditure of region j from the national average arises from both a price difference and a quantity difference for a uniform basket of nonfood items. N denotes the nonfood items; P and X again denote price and quantity, respectively. Let P.N be the average price of nonfood items in region j, weighted according to the proportions of the different items in regional nonfood expenditures, and let XN be the average quantity of nonfood items consumed in region j. The ratio be- tween the average annual per capita expenditure on nonfood items Z. in any regionj, and the national average, Zm, is then given by pNXN Z, Pj Xj Z= __r 3) Assuming that all regions have common price and income elasticities and common proportions of food and nonfood in total expenditure, any quantity difference between region j's nonfood consumption, XjN, and the national average, X,N, can be attributed to interregional differences in income, Y, and in the weighted average nonfood prices, PN, between m and any j. Thus jN =X + dX NAX , + dXm NpAp Xi Y.Ap.N (4) where AXY= Y - Y,, and APN= P/dP,4 is the change in the equilibrium quantity of nonfood consumption divided by the change in the price of nonfood, given mean income. It can be rewritten as dP,Z PNm m where qpis the own-price elasticity of the quantity of nonfood consump- DIFFFRENCES IN LIVING C'OSTS 113 tion. Thus, the difference in quantitv of nonfood consuimption between regions j and ni can be expressed acci.rding to (i) the interregional dif- ference in income multiplied bv the national averagc income elasticity of expenditures on nionfooil, antd (ii) the interregional difference in price (this is to be solved for) multiplied by the national average nonfood price elasticity. The income elasticity of noinfood consumption, 7qy in Eq. (5) and the own-price elasticity of nonfood consumption, riP in Eq. (6) cannot be estimated from nonfool expend(liture data. However, certain known rela- tionships exist between thie nonfood elisticities and the corresponding elasticities for food itemls as shown bv McCloskey [5]. The latter may be calculated from data on average income, and quantities and prices of food. Using these relatiionships, (5) and (6) mav be suLbstituLted into (4), giving the eq ULation yN N ,1 ± + (| + Stn SI ap G Sn Nay}j T-AP (7) where VS and S are the Qhmres of food and nonfood in total expeilditure, and a, and ap are national average income and own-price elasticities of the quantitv of food for the nation. Substituting (7) into (3). an expression may be derived for P,N: pN = [;z,+> 'JAY + S,| -- S,F{(-/uJ - S, a E) S,,ay}]i 5 N | a>. and ap may be computed by regressing logs of average quantities of food consumription on prices of food items and mean income levels. In order to calculate the P,'s, Eq. (1) is normalized assuming that P, = 100 and X,- = 7m /100. 'The required regional rnonfood price indices will then be given by the ratios P,N/ P N. Results The typical diet of the poor in Rural Sierra is much more expensive in urban areas: 3943 soles per capita per year in lima. and 3470 soles in Urban Coast, as opposed to 2650 soles in Rural Sierra. Among the three regions, the Coast shows the highest cost for this food basket: 3344 soles, 114 VINOD THOMAS compared to 2745 in the Sierra and 3060 in the Selva. The national average cost is 3155 soles per capita per year. Table I presents these cost estimates in the form of a price index for a "typical" food basket. To calculate the costs of items other than food, using Eq. (8), the income and price elasticities of food items (ay and op) were calculated from the ENCA data, at 0.7 and - 0.4, respectively. The results are not very sensitive to alternative values of these elasticities (Weisskoff [17]), Food and nonfood items each accounts for ,:., rut half the total budget in the country as a whole so that 0.5 was used for SF" aiAd S,. Alternative values for the share of food were also tried, based on expenditure patterns at the 20th percentile; 0.8 as in Rural Sierra, and 0.65 as in Urban Coast. These do not alter the results greatly. The use of national expenditure weig,hts as opposed to regional weights simplifies the procedure tremendously while not affecting the results significantly. The use of a national average income elasticity indicates the quantities that would be consumed in a hypothetical "average" location, at various levels of income. It will not fullv identify differences in the quantity consumed in a particular place th, t arise due to locationi-specific needs. The procedure used in this paper, for instance, will not fully reflect that part of urban people's higher consumption arising purely due to their being city dwellers--for example, the larger quantities consumed of transporta- tion, clothing, and safety devices. Such quantity differences, beyond those in the "average" location, will instead become part of the price differences. This feature of our method is reasonable insofar as this type of quantity differences does not enhance welfare (e.g., urban dwellers are not better off because they travel more). If, on the contrary, it contributes to welfare, the price index as calculated in this paper for urban areas will be biased upwards. The nonfood price index shown in Table I varies systematically among the Coast, the Sierra, and the Selva. Prices are highest in Lima and the Coast, followed by the Selva and the Sierra. They increase with the degree of urbanization: nonfood prices in Lima appear to be over 25% higher TABLE I Estimated Spatial Price Indices-Peru (1971) Peru Lima Coast Sierra Selva Urban Coast Rural Sierra Food: a typical diet 100 125 106 87 97 110 84 Nonfood: Based on Eq. (8) 100 157 102 72 97 125 56 Overall: Weighted average of food and nonfood 100 141 103 79 97 118 70 Based on minimum wage 100 140 106 79 99 104 72 DIFFERENCES IN LIVING COSTS 115 than in other big cities in the Coast and about three times those in the villages of the Sierra. the overall price index in Table I is a weighted average of the first two lines in the same table, as expressed in Eq. (2). The weights are the shares of food and nonfood in national expenditure. There exist considerable price differences between the Coast, the Sierra, and the Selva, and, not surprisingly, the urban areas in general seemn to be more expensive to live in, (Izraeli [4]), In an alternative attempt to construct a price index, information on the minimum wage established by Peru's Ministry of Labor was used. The last row in Table I presents the minimum-wage estimates in the form of an index with a national average of 100 as a base, This index shows dif- ferences between Lima and Rural Sierra, and between the Coast, the Sierra, and the Selva, which are remarkably similar to the previous results. To the extent that minimum wage differentials accurately reflect the income levels required to achieve comparable levels of living across loca- tions, they strengthen our earlier results. II MONEY MEASURES VERSUS REAL MEASURIS To bring out the significance of the cost-of-living differentials estimated in the previous section, two types of comparisons are made. First, money expenditures are deflated by the price indices to obtain more accurate measures of well-being across locations in Peru. Second, a national poverty threshhold is deflated by the price indices to provide a better basis for measuring spatial differences in pov erty. MAonev and Real Expenditure Annual per capita money expenditures and their breakdown between food and nonfood are given in Table 2. Mean expenditurz . differs consid- erably across locations within Peru. They vary systematically with respect to the degree of urbanization. The average consumption expenditure in Lima is nearly twice and in Rural Sierra is about half as much as the national average. Within total expenditure, nonfood items account for much more of the spatial differences than food items. Average total expenditure per capita in Urban Coast is 2.28 times as high as that in Rural Sierra, but food accounts for only 47% of this expenditure in Urban Coast compared with 65% in Rural Sierra. As a result, the average nonfood expenditure in Urban Coast is 3.5 times as high as that in Rural Sierra, whereas the differential for food expenditures is only 1.64. Housing and transportation expendituires accoLunit for much of this differential. Expendi- tures on these location-specific items are proportionately higher in the more urbanized locations (Tolley [15]). Together, they make up 29% of the 116 VINOD THOMAS TABLE 2 Annual per Capita Expenditure (Soles)--Peru (1971) Region Area Peru L[ma Coast Sierra Selva Urban Coast Rural Sierra Total expenditure 8558 16462 8412 5228 7041 10023 4404 Percentage in total Food expenditure 48 35 55 60 54 47 65 Nonfood expenditure 52 65 45 40 46 53 35 Housing 17 10 6 7 14 5 Transportation 12 4.5 4.1 5.6 5 3 Ratio of NF/F expenditures 1.1 1.9 0.82 0.66 0.85 1.1 0.6 Source: Calculated from F.NCA 1971. average expenditure in Liina, comnpared to 19%7o in Urban Coast and only 8% in Rural Sierra. The price indices estimated in Section I may be used to deflate the money expenditures to obtaini estinmates of real expenditLures. Table 3 shows the results of so dLoinig, and compares the real expenditures with the money expenditures. Measured in this way, the interregional differences in consumption appear much smaller and the rural parts of the country appear less disadvar;taged. Compared to a differential of 3.74:1 in money expenditures, the ratio of deflated per capita total expenditure in Lima to that in Rural Sierra is 1.93:1. Similarly, a differential of 3.15:1 in money TABLE 3 Actual and Deflated Expenditure-Peru (1971)' Region Area Peru Lima Coast Sierra Selva Urban Coast Rural Sierra Actualb Food 4129 5735 4627 3137 3802 4713 2880 Nonfood 4429 10727 3785 2091 3239 5310 1524 Total 8558 16462 8412 5228 7041 10023 4404 Deflated' Food 4129 4588 4365 3564 3920 4285 3190 Nonfood 4429 6832 3711 2904 3339 4248 2721 Total 8558 11420 8076 6468 7259 8533 5911 'In soles per capita/year. bFrom ENCA Survey (1971). cActual expeAditures on Food, Nonfood and the Total divided by, respectively, the first, second, and t1Wird rows in, Table 1. DIFFERENCES IN LIVING COSI'S 117 expenditure betwveen Liima and the Sierra as whole implies only a differen- tial of 1,77:1 in real terms. The differentials in the expenditure on food in real term.N is considerably less than those indicated by the expenditures in nm)ony terms. Table 4 presents these differentials in the forrm of indices with thce ntational average -as a base. While the m-oney me.asures suggest that people in Ln.imaI cosnsume 397 more and the Sierra 24%' less food thaL the national aveLrage, tile real expenditure nieasures tell a dlifferenit story, those in Lima consume 11%Ic more and those in the Sierra 14'; less food than the national average. The latter estimates in real terms are much closer to nea;sures of nutritional levels achieved in these regions. For instance, people in Linma on the average satisfy I 1%1' hiigher and those in the Sierra 6"' lower caloric needs compared to the national average. Phese measures underline the impor- tance of aflpl n,- spatial price differences to food Consumption expendi- ture data to obtain real differentials. Compared to food, the differentials in nonfood consumption are re- duced even more by going fronm a money measure to a real measure. The ratio of money expenditure on nonfood between Lima annd I Jrbhn Coast and between Lima and Rural Sierra are, respectively, 2:1 and 7:1, the same in real terms are, respectively, only 1.6:1 and 2.5:1. It is clear that a significant part of the urban expenditure in Peru should be attributed to the higher price of nonfood categories. Judging from the breakdowvn of nonfood expenditure in Table 2, it appears that the urban dwellers, conparecl to the rural people, spend much nmore on location-specific items like housing and transportation. Typically, the prices of these items rise with the increase in the degree of Lurhaniialion. Unless these price dif- ferences are corrected for, urban people %would appear to be better off than they really are. It may be concluded that altlhough Lima and the coastal region show a higher mean assumption in general than the rest of the country, these TABLE 4 Indices of Food Consumption- Peru (1971) Region Area Peru Lima Coast Sierra Selva Urban Coast Rural Sierra Money expenditure 100 139 112 76 92 114 65 Real expendiaurea 100 III 106 86 95 104 77 Caloriesbt 100 III 100 94 107 106 111 aMoney Expenditure divided by row 1, Table 1. bFrom Thomas [14, p. 29]. 118 VINOD THlOMAS differences are less than are implied by differentials in money expendi- tures. Only a part of the spatial differences shown in Table I is due to quantity differences, the remaining part is simply diue to differences in liv- ing costs. imqplictni ions for P0 r'l v Measures Spatial differences in living costs have serious implications for the measurement of the extent and location of poverty. An "absolute" measure of poverty level is the cost of buying a basket of "minimum" requirements of food and nonfood categories (see C'hiswick [2], Faber and NlUsgro%e [3], Orshansky [7], [8]). USHEW [16]). One approach to meMsuring poverty is to compare such a poverty threshhold to actual income (or expenditure) distributions across locations to obtain the percentage of population that fall below the poverty line. In the absence of spatial price indices, a single countrywide poverty line is usually used to measure poverty. By so doing. one tend's to give a misleading picture of poverty by overstating spatial differcnces, in general overestimating rural and underestinmating urban poverty. Row I in Table 5 presents one estimate of an "absolute" povertv level, built up from the cost at the national mean of buying certain "basic requiiremiients" of food and nonfood items (for dclails see Thomas [14]). By conmparing with the income distribution data for Peru [10, 11], the percentage of people below that poverty line is obtained (row 2). Spatial differences in poverty on this basis are sharp; while only about 4% of Lima's populaiion are poor according to this estimate, more than 50% in Rural Sierra fall in that category. In contrast to the countrywide poverty line, row 3 in Table 5 shows location-specific poverty lines ohtaine0 usintz price indlices for food and TABLE 5 Estimated Spatial Distribution of the Poor: National vs Location-Specific Poverty Linesa Regions Areas Peru Lima Coast Sierra Selva Urban Coa.st Rural Sierra 1. National poverty line 4575 4575 4575 4575 4575 4575 4575 2. Percentage below 28.0 3.8 19.2 42.5 29.4 9,6 53.4 3. L.ocation-specific poverty line 4575 6172 4792 3767 4437 5245 3445 4. Percentage below 28.0 8.1 20.5 35.8 28.6 12.3 41.4 5. Minimum wage 4767 6658 5100 3765 4753 4956 3445 6. Percentage below 28.5 9.8 22.4 35.8 30.5 10,7 41.4 a(Soles per capita/year) DIFFERENCES IN LIVING COSTS 119 nonfood. On this basis the spatial differ7-'nes in the percentage of popula- tion below the poverty line are much less (row 4 compared to row 2). For instance, 8% of people in Lima are now classified as poor while people in that category in Rural Sierra decline to 41%. Table 5 also shows the minimum wage figures provided by Peru's Ministry of Labor (see Table I also). The percentage of population below the minimum wage in each location is remarkably similar to that under the location-specific poverty line. To the extent that the minimum wage reflects the cost of purchasing a basket of basic requirements in each location, the results based on it support the use of the spatial price indices, as developed in this paper, to measure poverty. The poverty measure defined as the percentage of population below the poverty line does not fully reflect the extent of poverty. A better measure combines the percentage of poor with the magnitude by which they, on the average, fall short of the poverty line. Sen [13] has developed such an index of poverty and Anand [1] has further clarified its use. Thomas [14] applies such an index of poverty, first using the single nationwide poverty line and thenr the location-specific ones.3 The wide differences in the incidence of poverty based on a single poverty threshhold are once again significantly reduced by the use of location-specific poverty lines. Consequently, the implied benefits of locating in Lima and the Coast, in contrast to the other regions and rural areas, are reduced.4 APPENDIX: A NONFOOD PRICE INDEX A more detailed derivation of the nonfood price index than that in the text is presented here. The following notations are used: P weighted average price of nonfood X average quantity of nonfood Z average nonfood expenditure 3This index of poverty (I) for any location i. is given by I, = N,1/N, x (Y, - Y,P/YP), where N is the total population, Np the number of people below the poverty line, Y* the poverty line, and YP the mean income of the poor. 41t should be pointed out that the spatial price indices given in this paper do not reflect the differences in the availability of items that are not purchased, for instance, some public goods and services. There exist considerable disparities in the availability of public services in Peru. The rural areas in comparison to the urban centers lack these amenities. If one were to construct an index of availability of these items, the implied differences in their "cost" would probably be substantial, the rural areas displaying a higher "cost" than the urban centers. Depending on the imputed share of public services in total expenditure, therefore, some of the spatial differences in the living costs as presented in this paper would be reduced, and, as a result, the differentials in our earlier measures of real income and poverty between urban and rural areas increased accordingly. 120 VINOD THOMAS Y mean money income E mean expenditure 71Y income elasticity of nonfood uncompensated own price elasticity and cross price elasticity of nonfood ay income elasticity of food ap, at uncompensated own price elasticity and cross price elasticity of food Epj et compensated own price elasticity and cross price elasticity of food SF share of food in total expenditure SN share of nonfood in total expenditure m refers to a national average., j refers to a region, and A indica.tes a differential between j and mn. F and N indicate food and nonfood, respectively. P'NXN 7,,, P",'X X Zt Pm Xm Xi X' +dXN Y dXN pN A',N=-XN +- XY+ m-APN (ii) dYm dP,~ /1t = n (iii) dYm, m. dX N X N dP N (iv) In converting 7Y and 77p into thleir corresponding ay and Op, the following steps are used. The budget constraint for a two-good world of food. and nonfood is E = pFXF + pNXN. (V) Differentiating (v) with respect to E, holding prices constant, dE F dX + p14 dX N __ = p(vi) dE dY WY This can be rewritten as 1 = S Fay + S Nqy, (vii) DIFFERENCES IN LIVING COSTS 121 hence X= ( 1 - 5 Fa ) 1(Li SN' I FU)(viii) Similarly, differentiating (v) with respect to pN, holding pF and E constant, dE = xF dPF + pF dX + XN dP + pN dX (ix) dpN dpN dpN dP N dpN( Multiplying both sides of (ix) by P N/E and rearranging terms. =p t SN - S Fap) I(x 7qP=(SsNa)) (x) But a)) = 4 - S Nay. (Xi) Further, e= --. (xii) And ep = a, + SFay. (xiii) Substituting (xiii) and (xi) into (x) p= [ SN SF(-ap _ SFy) SN ay} (iv) Substituting (viii) and (xiv) into (iii) and (iv). and into (ii), Eqs. (7) and (8) in the text are derived. REFERENCES 1. S, Anand, Aspects of poverty in Malaysia, Rev. Income and Wealth, 23, No. 1 (1977). 2. C. U. Chiswick, "Measuring Poverty," IBRD Research Project No. 671-36, IBRD (March 1976). 3. R. Faber and P. Musgrove, "Finding the Poor: On the Identification of Poverty Households in Urban Latin America," Combined Studies on Latin American Economic Integration. ECIEL (June 1976). 4. 0. Izraeli, "Differentials in Nominal Wages and Prices between Cities," Urban Studies, 14 (1977). 122 VINOD THOMAS 5. D. N. McCloskey, "The Applied Theory of Price," Macmillan Co., New York, in press. 6. 0. A. Meesook, "Regional Consumer Price Indices for Thailand," Discussion paper, Thammsat University, Bangkok (December 1974). 7. M. Orshansky, Counting the poor: Another look at the poverty profile, Social Security Bull. (1965). 8. M. Orshansky, How poverty is measured, Monthly Labor Rev., 92 (1969). 9. Peru, Ministry of Agriculture, "The ENCA Survey" (1975). 10. Peru, Ministry of Economics and Finance, "Income and Expenditure Structure by Regions" (1977). 11. Peru, Ministry of Economics and Finance, "Structure and Level of Family Income in Peru" (1977). 12. Peru, National Planning Institute, "Estudio del Consumo" (1975). 13. A. K. Sen, Poverty, inequality and unemployment: Some conceptual issues in measure- ment, Econ. Pol. Weekly, Special Number (August 1973). 14. V. Thomas, "The Measurement of Spatial Differences in Poverty: The Case of Peru," World Bank, Staff Working Paper, No. 273 (1978). 15. G. S. Tolley, The welfare effects of city bigness, J. Urban Econ., 1 (1974). 16. U. S. Department of Health, Education and Welfare, "The Measure of Poverty," U.S. Govt. Printing Office, Washington, D. C. (1976). 17. R. Weisskoff, Demand elasticities for a developing economy: An international compari- son of consumption patterns, in "Studies in Development Planning," (H. B. Chenery, Ed), Harvard Univ. Press. Cambridge, Mass. (1971). 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