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TABLE 3. Elasticities with respect to expenditure and own price for purchases of 16 basic foodstuffs in metropolitan and rural areas of north-east Brazil

*B₄ is positive but not distinguishable from zero.
**B₂ is positive and leads to a positive estimated pace-elasticity.
Source: Table 1 and original calculations.

The first conclusion is that elasticities vary more, among income levels, in metropolitan areas than they do in rural areas. For example, the elasticity for sugar shifts by 0.57 in cities as expenditure quadruples but by only 0.27 in the countryside. For beans, the change is 0.88 in urban areas and only 0.18 in rural areas; for eggs, the shifts are 0.58 and 0.05 respectively. These differences may partly reflect the typically smaller budget share for food in urban areas, so that a given increase from a low total expenditure allows a larger proportional increase in food spending. So far as transfer programmes to combat malnutrition are concerned, the clear implication is that it is more important to discriminate or to target beneficiaries correctly in metropolitan areas. The desire to help the poorest families applies to both urban and rural areas, but the cost of mistargeting is greater in cities because the very poor will increase their food consumption by much more than those who are not so poor. In rural areas this difference is usually smaller; rice, however, is an important exception, the elasticity shifting by the same amount in both urban and rural areas.

The second conclusion is that income effects generally are more sensitive to income level than has previously been recognized, with elasticities sometimes being quite high when incomes are very low. It is true that these elasticities are of the order of 0.3 or less for many foodstuffs when expenditure is Cr$2,000 per person or higher. But among much poorer families, income elasticities are commonly 0.5 or more, approaching or even exceeding 1.0 for some important foods such as rice, pasta, sugar, meat, eggs, oils, and fats. This finding may partly dispel the paradox, noted earlier, that low income appears to be the chief cause of malnutrition and yet consumption responses to additional income have been estimated to be quite small.

A third conclusion refers to the much-noted tendency of poor Brazilian families to use extra income to improve the quality and variety of the diet, without necessarily increasing total calorie intake appreciably, even when calorie consumption is inadequate. This behaviour, particularly the substitution for cheap starches of more expensive foods such as sources of animal protein, seems to account for the low frequency of families that eat enough calories but are short of protein [10]. The results in table 3 confirm that very poor families show high expenditure elasticities for such desirable and relatively expensive foods as meat, eggs, oil, and fats. But they also show that those elasticities fall quickly as income rises, and that they are not always much higher than the elasticities for cheaper foods of vegetable origin.

Much of the qualitative improvement in the diet seems to be replacement of manioc flour (which provides nothing but calories) by rice (which also provides some protein). The elasticities for sugar, which is one of the cheapest sources of calories, remain high. It is true that consumption of calories expands rather slowly at incomes of Cr$2,000 per person or more, but it is apparently not true that the low calorie-elasticity is due simply to a shift to much more expensive foods. At much lower income levels, where manioc flour and cornmeal are not considered inferior goods, the total calorie elasticity is much higher.

Combining the first and third of these findings shows that the tendency to improve quality rather than to increase quantity is much more an urban than a rural phenomenon. Presumably part of the reason for this difference is the greater variety of foods available in cities, which either influences peoples' tastes by a demonstration effect or allows them to satisfy their already existing desires for a more varied diet. Price differences may also contribute to the relatively greater tendency to improve diet quality in urban settings. As table 1 shows, such inexpensive staples as rice, beans, cornmeal, manioc flour, and brown sugar were more costly in cities than in rural areas in 1974-1975, so the cost of shifting from them to other foods may have been less for urban dwellers. (White sugar, however, was costlier in the countryside.) A study of price differences a decade later reports that, in general, the traditional staples produced in the rural Northeast are cheapest where they are grown, whereas more processed foods, which typically are imported from other parts of the country, are cheapest in metropolitan areas [3]. This finding was true of pasta, pasteurized milk, soybean oil, and margarine in 1974-1975.

Price effects and subsidies

Own-price elasticities, calculated from equation 5 in the appendix, are also shown in table 3. In addition to implausible positive estimates of B₄ for brown sugar and pasta, which cause the elasticities to become more negative as income rises, there are positive estimates of B₂, which make it impossible to calculate price responses for pasteurized milk (in urban areas) and for margarine (in rural areas). The general conclusion to draw from these estimates is that consumption is quite responsive to prices, especially for rice, pasta, sugar, fresh milk, and cornmeal. In general, low-cost, calorie-rich foods show more price responsiveness than costlier, protein-rich foods. This suggests that subsidies concentrated on the former and limited to poor consumer are effective in stimulating calorie consumption.

These estimates of price effects are much more plausible than those obtained by Gray [4] using data aggregated across households for each region of the country. Her results are especially implausible for rice and manioc flour, probably because differences in eating habits are correlated with price differences for these two foods from one region of Brazil to another. She obtained own-price plasticities of around -5 for rice and -3 for manioc flour, and cross-price elasticities of about 4. In the present study, own-price effects were estimated to be around -1 and -0.5 (at incomes comparable to the lowest used by Gray), and cross elasticities, not shown in table 3, of about -0.4 (rice price-effect on manioc consumption) or -0.1 (manioc price-effect on rice consumption), confirming the superiority of rice as a food.

How does the price-responsiveness of consumption differ between metropolitan and rural areas? At low incomes (Cr$500 per person), price elasticities are generally larger-sometimes much larger-in cities. It is unlikely that these elasticities are due to a price change having a larger income-effect on urban consumers; they reflect much greater substitution effects, consistent with the greater variety of food available and the tendency to diversify the diet. As income rises, urban and rural price elasticities tend to become more equal, as there is a larger change in the value of the urban elasticity. (Rice, cornmeal, and salted fish are the only exceptions.) It seems that city-dwellers quickly become less sensitive to price changes for inexpensive staples, because as their incomes rise they shift away from those to more processed, and more expensive, foods. It also appears that price subsidies to poor consumers would be more effective in stimulating consumption in cities than in the countryside, and in fact the only Brazilian food-subsidy programme operates only in metropolitan areas.

Family size and consumption per person

Table 4 presents estimates of relative consumption per person (using equation 7 in the appendix) as a household expands from four to eight members, at three levels of total expenditure. In the case of a nuclear family with both parents present, this corresponds to an increase from two to six children. For ethical reasons, there is no point in asking whether a poor couple might eat better if they refrained from having any children at all: what matters is whether they have few or many.

The principal result shown in table 4 is the rapid decline in consumption per person of nearly all foodstuffs as the household is impoverished by the addition of members. The only exceptions are brown sugar and manioc flour, and then only in urban areas. Even at an expenditure level of Cr$12,000, consumption per head typically falls by between 20% and 40% as family size doubles. Only a fraction of this is likely to be offset by the lower food requirements of children than of adults. At lower incomes, doubling family size is likely to mean eating only half as much per person or per constant total family intake. (In the case of coffee, consumption per adult may be maintained as children are added to the family.) It might be expected that the decline in consumption would be faster for costlier protein-rich foods than for sugar and starches, so that calorie intake would be protected at the expense of protein. In metropolitan areas this is indeed the case for meat and fish, but the protein/calorie distinction is not very systematic. The consumption of eggs and of fresh milk, for example, does not shrink any more quickly than that of cornmeal, pasta, or beans. Except at very low incomes, both foods actually seem to be better protected than rice-perhaps because they are valued foods eaten in small amounts, whereas rice is a large share of total calorie intake.

TABLE 4. Relative consumption of 16 basic foodstuffs per person in families of five to eight members, compared to a family of four members, in metropolitan and rural areas of north-east Brazil

a.Calculation for rural areas based on a positive (but not statistically significant) estimate of B4.
b. Calculation for metropolitan and rural areas based on a positive (but not statistically significant) estimate of B4.
Source: Table 1 and original calculations.

The tendency to eat more calories compared to protein seems, nonetheless, to be slightly stronger in urban than in rural areas, because the decline in consumption of calorie-rich foods is usually less in cities, while the decline for protein-rich foods is sometimes greater there. That is, the composition of the diet seems to be somewhat less affected by family size in rural areas. There is no marked or systematic difference in overall food consumption per person between urban and rural areas as family size expands: the reduction occurs at comparable rates in both places. Sometimes a small change in consumption simply reflects a very low initial level in a small household: pasta is an example. Domestic production of food in rural areas can also mean that total food-intake is less affected, but comparisons of total and purchased consumption suggest that this effect is not very important. Of course, the comparisons in table 4 do not refer to an adequate or recommended diet, but only to what people actually eat.

Concluding reflections

According to what may be called the "ideology of malnutrition" in Brazil [7], poverty is the chief cause of inadequate food consumption and of the clinical manifestations of under-nutrition. It is admitted that disease and lack of hygiene contribute to malnutrition, but these conditions are also strongly associated with poverty. Only a minor role remains, in this view, for ignorance or poor food habits as causes of inadequate food intake [1]. Programmes that subsidize or donate food to poor families are generally based on respecting the beneficiaries' habits and preferences rather than on trying to change them [6,8].

The approach taken by the present investigation and its findings are consistent with this "pro-poor" ideology, at least in part. The variables studied- expenditure, price, and family size-are all poverty-related, and in the consumption functions estimated they are combined into maximum potential consumption per person and appear separately as well. The results show that consumption responds to all these variables, sometimes quite dramatically. This finding does not prove that consumers are spending their limited incomes efficiently in nutritional terms, because it is possible to be economically rational and buy a given diet at minimal cost, while still not buying an optimal diet [9] But it does show that poor households are quite sensitive to economic pressures and opportunities.

Poor families in big cities, however, respond differently than poor rural households to changes in these economic and demographic determinants of food consumption. In general, urban consumers at very low incomes are more sensitive to changes in income and in prices but do not differ greatly in their response to changes in family size. They also show a greater tendency than rural consumers to diversify their diet as income rises and to substitute more readily among foods as prices change. Both these tendencies reflect the greater variety of foods available in cities and, to a lesser degree, higher relative prices for the cheapest traditional staples. This greater responsiveness makes it somewhat easier to influence the volume and composition of the diet of urban dwellers by transfer and subsidy programmes to combat malnutrition. Unfortunately, this is true only in part, because the greater tendency to improve the quality of the diet rather than just to eat more makes the urban poor relatively more susceptible to malnutrition in the first place.

Appendix

The consumption function and its interpretation

The total quantity (Q) of a particular foodstuff consumed by a family during the reference period is written as a function of the total family expenditure (X), the price of the food (p) and the number of family members (N), as follows:

(1) log Q = B₀ + B₁ log X + B₂ log p + B₃ log N + B₄ Np/X

where B₀, ..., B₄ are the parameters to be estimated. This is the widely used double-log model with three explanatory variables, and a final which is the reciprocal of the maximum quantity per person the family could buy if everything were spent on that one food. This follows because X/p = Q is the maximum total quantity and dividing by family size gives X/Np = q, the maximum quantity per person. The function can be expressed in terms of the quantity actually consumed per person (q) by using the transformation

(2) log q = (Q/N) = log Q-log N = B₀ + B₁ log X + B₂ log p + (B₃ - 1 ) log N + B₄( 1/q)

and expenditure per person (* = X/N) can be used as an explanatory variable,

(3) log q = B₀ + B₁ log x + B₂ log p + (B₁ + B₃ - 1) log N + B₄(1/q)

Both these transformations modify only the coefficient of log N.

This function has been applied to food consumption for the Dominican Republic [6], with satisfactory results. Its chief advantage is that it recognizes the constraint embodied in maximum potential consumption Q or q, which makes the response of consumption to changes in any variable a function of all three explanatory variables, without forcing the response to be the same regardless of which variable (X, p, or N) has caused a change in q. The chief disadvantage is that the function does not correspond to a utility specification; it does not even allow the adding-up of consumption of different foods to reach total food intake. It also cannot be inverted analytically, so as to derive, for example, the level of total expenditure necessary to assure an adequate diet for a particular size of family, given the parameters.

The elasticity of consumption (total or per person) with respect to expenditure (total or per person) is

(4) E_Q,X = B₁-B₄(1/q)

which tends to the limit B₁ as expenditure rises and q ceases to be a constraint. Similarly, the elasticity with respect to price is

(5) E_Q,P = B₂ + B₄(1/q)

and tends to the limit B₂ as expenditure rises (or price falls toward zero). The sum of these two elasticities is constant at B₁ + B₂ and so is independent of q.

An elasticity can also be calculated with respect to family size, but this makes little sense because the number of members can change only by integer amounts. Instead, when a family size changes from N to N** members, the corresponding change in consumption is

(6) log (Q*/Q) = log Q* - log Q = B₃(10g N* - log N) + B₄(N*-N)p/X = B3 log (N*/N) + B₄(1/q* - 1/q) which depends on both the ratio and the difference of the two family sizes. The change in per capita consumption is given by equation 6, with B₃ - 1 replacing B₃

(7) log (q*/q) = (B₃ - 1) log (N*/N) + B₄(1/q*- 1/4)

Changes in total or per person consumption due to discrete changes in expenditure or in price can similarly be written as functions of the change in l/q and the ratio X*/X or p*/p.

Acknowledgement

I am indebted to Claudio Castro and Dorothea Werneck for access to the data; to Mauricio Leite Vasconcellos and Amaro Monteiro for creating the special file used; to Felipe Ruiz for the calculations; to Alan Berg, Claudio Castro, Osmil Galindo, Peter T. Knight, William P. McGreevey, Dirceu Pessoa, and Rosa Amália Araujo Viana for encouragement and helpful discussion; and to Nevin Scrimshaw and Judit Katona-Apte for suggestions. None of them bear any responsibility for errors of fact or interpretation.

References

1. de Aruda BKG. Alimentação e bolsões de pobreza. Brasília: Instituto Nacional de Alimentacao e Nutricao, 1980.
2. Filho MB, de Paula Barbosa N. Alimentacao e nutricao no Brasil, 1974-1984. Brasilia: INAN, 1985.
3. Galindo O, Musgrove P. Do the poor pay more? Retail food prices in northeast Brazil. Econ Dev Cultural Change (in press).
4. Gray CW. Food consumption parameters for Brazil and their application to food policy. IFPRI research report no. 32. Washington, DC: International Food Policy Research Institute, 1982.
5. Instituto Brasileiro de Geografia e Estatística. Estudo Nacional da Despesa Familiar: consumo familiar, antropometria; dados preliminares. 4 vols. Rio de Janeiro. 1977-1978.
6. Musgrove P. Household food consumption in the Dominican Republic: effects of income. price and family size. Econ Dev Cultural Change 1985;34(1):83-101.
7. Musgrove P. Ideologia, pesquisa y realidad de la situación alimentaria y nutritional en el Brasil. Cadernos de Estudos Sociais 1986;2:329-348.
8. Musgrove P. Que los pobres comae mejor: evaluación de programas destinados a mejorar el consumo alimenticio de familias pobres en el Brasil. Washington, DC: Pan American Health Organization, 1987.
9. Rosenberg E. Consumer behavior in relation to nutrition: a Brazilian case study. Ph.D. thesis. Nashville. Tenn, USA: Vanderbilt University. 1976.
10. Viacava F, de Figueiredo CMP, Oliveira WA. A desnutrição no Brasil: uma Análise do Estudo Nacional da Despesa Familiar (IBGE 74-75) pare o Nordeste, Estado de São Paulo e Estado de Rio de Janeiro. Petrópolis, Brazil: Vozes, 1983.
11. World Bank. Brazil: human resources special report. Washington, DC: World Bank, 1979.

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