By necessaries I understand, not only the commodities which are indispensably necessary for the support of life, but whatever the custom of the country renders it indecent for creditable people, even of the lowest order, to be without.
Adam Smith, 1776(Reference Smith1)
Lower-income groups have poor diets(Reference Darmon and Drewnowski2) and suffer from higher rates of obesity and chronic disease(Reference Mackenbach, Stirbu and Roskam3). Food, health and incomes may be linked through food prices and diet costs(Reference Drewnowski and Specter4). Refined grains, fats and sweets are affordable, accessible and convenient(Reference Maillot, Darmon and Darmon5). By contrast, many nutrient-rich foods cost more and are consumed by more affluent persons(Reference Darmon and Drewnowski2). One barrier to the adoption of healthful diets by the lower-income groups may be diet cost(Reference Reicks, Randall and Haynes6, Reference Cox, Anderson and McKellar7).
Arguably, not all healthful foods cost more(8). Some nutrient-rich foods can be obtained at very low cost. Recipes and tips for healthy thrifty meals have featured ground turkey, chickpeas and condensed or powdered milk(9). Home-cooked lentil soup and inexpensive rice and beans have been proposed as suitable staple diets for the US poor(Reference Parker-Pope10). Nuts, seeds, legumes, cereals, carrots, potatoes and cabbage offer good nutrition at an affordable cost(Reference Darmon, Darmon and Maillot11). The search for affordable nutrient-rich foods is being aided further by the new techniques of nutrient profiling(Reference Maillot, Ferguson and Drewnowski12) and by the new metrics of nutrients per energy and nutrients per unit cost(Reference Darmon, Darmon and Maillot11).
However, many low-cost yet nutritious foods are rejected by the consumer. The present hypothesis is that such foods deviate from the current consumption standards; fail to meet cultural requirements, and may be socially or culturally inappropriate. The custom of the country – to borrow a phrase from Adam Smith – may place such foods or diets outside the accepted social norms. In striving to meet nutrient requirements at minimum cost, the search for lowest-cost healthful diets may have ignored the current eating habits of the population.
Mathematical optimisation models have shown for a long time that nutritious diets could be obtained at very low cost(Reference Stigler13, Reference Smith14). The USDA Thrifty Food Plan (TFP) model creates a diet that is as similar as possible to the current diet of low-income Americans, while simultaneously meeting a fixed set of nutritional and cost constraints(Reference Lino15, Reference Carlson, Lino and Fungwe16). Upper and lower bounds on food energy are based on the Institute of Medicine energy requirements, whereas nutrient and food group constraints are based on the Dietary Guidelines for Americans and on MyPyramid, respectively. The cost constraint keeps computer-generated diets below the target cost. To arrive at the optimisation solution, the TFP tolerates up to tenfold deviations from the current eating habits.
The present study reversed the situation in that the model minimised cost, while meeting different sets of nutritional and consumption constraints. Instead of meeting a single set of nutrition constraints, the model created food plans that met three sets of nutritional constraints of progressive severity. The intent was to determine whether healthier diets cost more. In addition, significant deviations from the mainstream French diet were progressively disallowed. Seven levels of increasingly stringent consumption constraints ensured that the final model had little tolerance for any deviation from the French mainstream eating habits. The intent was to estimate the cost of healthful diets that were also consistent with French cultural expectations and societal norms.
Methods
Dietary data, food composition database and food prices
The input data used in the present analysis were based on data collected in a cross-sectional dietary survey of a nationally representative sample of 1985 French adults (INCA; National Individual Survey of Food Consumption survey), aged 15–92 years, conducted in 1999 by the French National Agency for Food Safety(Reference Volatier17). Usual food intakes were estimated using a 7 d food record completed by all participants, aided by a photographic manual of portion sizes(Reference Le Moullec, Deheeger and Preziosi18). Participants who under- or over-reported their energy intake (284 men and 312 women), according to Black’s method(Reference Black19), were removed from the sample. The physical activity level assumed in the calculation of the threshold was 1·55, corresponding to seated work with low walking and leisure activity. The final sample(Reference Lino15) of 1332 participants aged between 15 and 92 years included 596 men and 736 women.
After excluding diet beverages, tea, coffee, dietary supplements and drinking water, a total of 614 different foods were declared as consumed by the participants. Their nutritional composition, expressed per 100 g of edible portion, and their edible conversion factors were computed from the INCA food composition database(Reference Favier, Ireland-Ripert and Toque20), the Suvimax food composition database(21) or from other databases(Reference Lamand, Tressol and Ireland-Ripert22–25). A column of French mean national 1997 retail prices primarily obtained from marketing research (SECODIP) was added to nutrient composition table. The prices were those paid by a representative panel of French consumers; therefore, the mean price reflected the most frequently purchased forms of each food. The prices were obtained for the foods ‘as purchased’, whereas the nutrient contents were based on the food ‘as consumed’. To adjust for preparation and waste and to have a common mode of expression for price and for nutrients, retail prices were converted into prices per 100 g of edible food, based on the edible conversion factors of each food.
The foods were aggregated into seven major food groups (meat, fruit and vegetables, mixed dishes and snacks, dairy, starches and grains, sweets and salted snacks and added fats), twenty subgroups (e.g. subgroups in the fruit and vegetable group were fruits, vegetables and dried fruits) and thirty-six families (e.g. families in the fruit subgroup were fresh fruits, fruit juices and other processed fruits). The recipes used to calculate the nutrient composition of mixed dishes were derived from the SUVIMAX food composition database(21).
Mathematical diet optimisation model
The principle of diet modelling with linear programming has been explained before(Reference Briend, Darmon and Ferguson26), and the characteristics of the optimisation models used in the present study were also published(Reference Maillot, Ferguson and Drewnowski12).
All linear programming models and statistical analyses were performed using the Operational Research Package of the SAS statistical software package version 9·2 (SAS Institute Inc., Cary, NC, USA).
Creation of twenty-one food plans per gender
Linear programming models were used to create twenty-one different food plans for men and women, meeting three sets of nutritional and seven sets of consumption constraints. All diets were isoenergetic as the model-fixed dietary energy at 9204 kJ/d (i.e. 2200 kcal/d) for men and 7531 kJ/d (i.e. 1800 kcal/d) for women. The optimisation process yielded a suggested food plan that consisted of quantities of different foods selected into the market basket from a pool of 614 foods (i.e. the number of foods in the food database). Total diet cost was minimised to obtain the lowest-cost food plans that fulfilled all the constraints introduced in each linear programming models and were presently developed to select twenty-one isoenergetic diets for each gender at minimal cost that differed in the nutritional (three sets) and consumption (seven sets) constraints.
Objective function
The chosen ‘objective function’ of the model ensured that the food plan basket was at minimal cost. Variables in the objective function were represented by the quantity of the 614 food items. Each item was linked to the nutrient composition and cost database.
The objective function Z was minimized:
where Qj was the quantity of food j in the modelled food basket plan; cj was the cost of 1 g of food j.
Nutritional constraints
Table 1 shows three levels of progressively more stringent nutritional constraints. Level A ensured that the food plans were consistent with guidelines for macronutrients. Level B ensured that the food plans were consistent with guidelines for macronutrients and with the French estimated average requirements for twenty-five additional nutrients(Reference Martin27). Level C ensured that the food plans were consistent with the macronutrient guidelines and with the recommended dietary allowances (RDA) for each of the twenty-five nutrients. Levels B and C introduced additional limits on the consumption of saturated fats, added sugars and sodium, and set safe upper limits on the consumption of nine additional nutrients.
Description of nutritional constraints introduced in linear programming models, separately for men and women
EAR, estimated average requirement; RDA, recommended dietary allowances.
*Constraint included in level A (achievement of macronutrient recommendations).
†Constraint included in level B (achievement of macronutrient recommendations plus estimated average requirements).
‡Constraint included in level C (achievement of macronutrient recommendations plus recommended dietary allowance).
Consumption constraints
Table 2 shows seven levels of progressively more stringent consumption constraints, based on the observed distribution of food intakes in the referent INCA population, calculated for men and women separately. These constraints were progressively applied to the seven major food groups, twenty food subgroups and thirty-six food categories.
Seven levels of consumption constraints introducedFootnote * into the linear programming models
* For a given level i of consumption constraints (with i varying from 1 to 7), the constraints included in the level i−1 are retained, and the constraint specific to level i is added.
Level 1 imposed no constraints on food choice. A Level 2 constraint was that the amount of energy provided by each of the seven major food groups fit between the 5th and the 95th percentiles of intake for that food group by the reference population. Levels 3 and 4 cumulatively extended that constraint to the twenty food subgroups and to the thirty-six food categories, respectively. Level 5 placed the upper bound on consumption, such that the amount of food in the optimised food plan could not exceed the 95th percentile limit for that food in the referent population. Level 6 introduced the additional constraint that foods consumed by only a small minority of the French population and therefore, by definition, not a part of mainstream eating habits, could not be a part of the optimised food plans. Accordingly, foods consumed by less than 2·5 % of the referent French population were removed. This led to the removal of 314 of the original 614 foods. Level 7 imposed the final and most stringent constraint that foods consumed by less than 5 % of the referent French population were removed from consideration by the optimisation model. That led to the removal of 429 of the 614 foods. All the constraints, cumulatively imposed at each higher level, ensured that the resulting computer-optimised food plan would closely resemble the mainstream French diet, with progressively less tolerance for any deviation from the current patterns of consumption.
Results
Figure 1 shows, separately for women and men, that the progressive application of nutritional recommendations increased the lowest achievable food plan costs. Plans that met the more rigorous nutritional constraints did cost more. Although food plans fulfilling all the RDA requirements (level C diets) could be obtained for as little as 1·50 €/d, the low cost was achieved only if consumption constraints were ignored (consumption levels C1 to C3).
Minimal cost of twenty-one modelled diets fulfilling increasing levels of nutritional constraints (
, A; 
, B; 
, C) and consumption constraints (1, 2, … 7). The number of foods selected for each diet at each set of constraints is indicated as well. Data are presented separately for men (a) and women (b)
Entering the increasingly stringent consumption constraints into the model led to dramatic changes in the resulting cost and variety of the optimised food plans. Not only did the food plans become more costly, but also the cost of a market basket of foods that was consistent with the mainstream French diet far outweighed the cost of meeting the nutritional constraints alone. The cost of food plans meeting consumption level 7 constraints (C7) was several times that of plans that tolerated more substantial deviations from current consumption patterns. The lowest achievable cost of level C7 food plans was 3·40 €/d for men and 3·20 €/d for women, almost ten times the amount calculated for the lowest cost level A1.
Furthermore, as indicated in Fig. 1, there was an interaction between nutritional and consumption constraints. As long as the model imposed no consumption constraints or tolerated a high degree of deviation, the difference in cost between the less nutritious and more nutritious food plans did not exceed 100 %. Once the stringent consumption constraints were imposed and the diet resembled more what people actually eat, the cost of healthier diets more than doubled, relative to less healthy ones.
The variety of foods in the market basket was also affected by the two sets of constraints (Fig. 1). The number of foods always increased from A to C, at each level of consumption constraints so that the higher-quality food plans were always associated with greater variety. For each level of nutritional constraint, the imposition of consumption constraints led to a greater variety of foods until level 5 with a drop observed at levels 6 and 7. It was then that the foods consumed by less than 2·5 % and 5 % of the total population were excluded, respectively. In most lowest-cost food plans, whole grains, lean meats, seafood, whole fruit and salad greens were missing altogether.
Table 3 shows the market baskets for women at different levels of nutrition and consumption constraints. In general, food plans that deviated most from the usual eating habits consisted of a small number of foods, provided in large amounts. Typically, those plans were based on grains, cereals, vegetable oils and sweets. Thus, the minimal cost level A1 plan for women consisted of only three foods: porridge, sugar and vegetable oil (Table 3). The minimal cost level C1 plan consisted of twelve foods (porridge, pasta, semolina, mashed potatoes, wheat germ, carrots, radishes, chicken livers, grilled herring, low-fat milk and vegetable oil). In other plans, nutritional adequacy was assured through large quantities of inexpensive carrots and low-fat milk, as well as organ meats (liver and brains) and herring.
Market baskets for food plans at different levels of nutritional and consumption constraints in women
Number of foods in the same subcategory (e.g. potatoes) is indicated in parentheses.
Discussion
Diet optimisation programmes are mathematical tools that are used to create healthful food plans at an affordable cost(Reference Stigler13, Reference Foytik28, Reference Darmon, Ferguson and Briend29). In the United States, such programmes have been used to set the official estimates of the lowest cost of a nutritious diet. For example, the official USDA food plans are generated by an optimisation programme that selects a diet that closely resembles the observed consumption patterns of the low-income population, while simultaneously meeting cost targets as well as nutrition and other constraints(Reference Lino15, Reference Carlson, Lino and Fungwe16). The lowest-cost USDA Thrifty Food Plan, most recently updated in 2007, is then used to set the benefit levels for the Supplemental Nutrition Assistance Program, previously known as food stamps. In 2007, the TFP cost per week was estimated at US $32·20 for women and $35·80 for men(30).
Mathematical models, faced with multiple constraints, do not always achieve a perfect fit. The new TFP market baskets are no exception: the USDA documentation acknowledges that they did not meet the vitamin E and potassium recommendations for some age–gender groups and did not meet the sodium recommendation for many age--gender groups(Reference Carlson, Lino and Fungwe16). To do so, the low-cost market baskets would have had to deviate very substantially from the typical consumption patterns (in the case of vitamin E and potassium) or would have required changes in food manufacturing practices (in the case of sodium)(Reference Carlson, Lino and Fungwe16). According to the USDA documentation, it was practically impossible to develop the low-cost TFP market baskets that met the sodium recommendation.
While nutrition and cost constraints of optimisation models have received most research attention, consumption constraints have not. In the TFP, the lower bound for consumption was set close to zero for most good groups, whereas the upper bound varied by food category, depending on average consumption(Reference Carlson, Lino and Fungwe16). Generally, the upper bounds were three to ten times average consumption. This was carried out, in part, to accommodate policy goals. For example, although the population average consumption for whole grains was near zero, the 2005 Dietary Guidelines for Americans specified that half of all grain consumption should be from wholegrains. As a result, the TFP had to tolerate high deviance from the usual eating patterns. According to the USDA documentation, the TFP basket for the family of four contained more vegetables (137 %), milk products (125 %), fruit (115 %) and grains (16 %) and less fats, oils and sweets (−83 %) than the observed consumption patterns of the referent group.
The present study set out to determine the cost of market baskets that were not only nutritious but also consistent with mainstream French diet. The present innovation was to let consumption constraints vary over a wide domain (seven levels), coming closer each time to the average French population diet. The upper bounds were not permitted a tenfold increase from average consumption; instead the upper bound was the 95th percentile limit for the population intakes. These limits were progressively applied to food groups, food subgroups and food families for a much tighter fit between the optimised food plan and the typical French diet. At the strictest level, foods consumed by less than 5 % of the population were excluded from the model.
Systematic reduction of the distance between current consumption and the optimised food plans led to higher monetary costs. What is more, those higher costs far exceeded those of a more nutritious diet. Nutritious market baskets that corresponded to the population eating habits cost several times more than market baskets that provided nutrition but ignored cultural requirements and social norms. It turns out that maintaining cultural norms was just as, if not more, expensive than improving the nutritional quality of the diet. The question arises whether other lowest-cost market baskets achieve their cost targets by ignoring or tolerating large differences from social norms.
Some similarities and differences with the official USDA food plans must be noted. Similar to the USDA food plans(Reference Bowman31), the study was based on retail food prices and not expenditures. Unlike the TFP, the objective function minimised diet cost instead of minimising the difference between the modelled diet and existing food habits. Unlike the TFP, the present model used only nutrient-based constraints and did not employ MyPyramid food category standards. Unlike the TFP’s use of fifty-eight food categories, the present market basket was based on >600 individual foods. In reality, each participant in the INCA survey consumed <50 different foods per week(Reference Volatier17). Tailoring the food plan to the eating habits of each individual is an alternative and more sophisticated approach(Reference Maillot, Vieux and Amiot32) that could yield different results. In the present study, consumption constraints were introduced and progressively reinforced, whereas in the TFP, consumption constraints were fixed and it was the cost constraint that was introduced at different levels of severity.
The present data shed new light on the argument whether nutritious diets cost more than less nutritious ones. Food choices are a part of social identity, and the ability to adhere to a socially acceptable diet is one of the necessities of life(Reference Chilton and Rose33). All too often, the low cost of powdered milk, ground pork, organ meats, beans, lentils, carrots and cabbage is cited as proof that low-income groups have full access to inexpensive yet nourishing foods. Persistent failures by low-income households to construct staple diets based around such foods have been explained in the past by a lack of motivation(Reference Dibsdall, Lambert and Bobbin34, Reference Henry, Reimer and Smith35), lack of nutrition knowledge(Reference Variyam, Blaylock and Smallwood36), lack of education or time or simply bad lifestyle choices by the poor(Reference Parker-Pope10). The present data suggest that the low cost of such diets is achievable only by tolerating a departure from social norms.
Studies on dietary change ought to take such norms into account. For example, intervention studies have persistently claimed that more healthful diets need not cost more and might even cost less(Reference Raynor, Kilanowski and Esterlis37–Reference Ottelin, Lindstrom and Peltonen40). On the other hand, observational studies of populations have associated freely chosen healthful diets with higher energy-adjusted diet costs(Reference Cade, Upmeier and Calvert41–Reference Townsend, Aaron and Monsivais48). It would be good to see whether the low-cost healthy diets that are introduced by researchers into schools and workplaces are sustainable in the long term.
Other factors, not covered in the present study, may involve time poverty and food preference. Studies have noted that many of the USDA recipes were time consuming when cooked from scratch, a situation remedied in the 2006 TFP that included more convenience foods(Reference Carlson, Lino and Fungwe16). Interestingly, the premise underlying the official USDA food plans is that all foods are purchased at stores and cooked and prepared at home. Arguably, using lowest-cost food plans to calculate food assistance for the poor does not take into account time constraints and the need (or right) to eat away from home, consistent with broader societal trends.
Conclusion
Food budgets of the poor are often insufficient to assure a balanced diet(Reference Vozoris, Davis and Tarasuk49–Reference Nelson, Dick and Holmes51). Even with efficient purchasing strategies(Reference McLaughlin, Tarasuk and Kreiger52–Reference Grant and Maxwell55), the food budget may not suffice for a diet that is both nutritious and socially acceptable(Reference Stewart and Blisard56). Although some nutritious foods are inexpensive, conforming to societal norms also has a price. Calculations of the minimum cost of a nutritious diet need to take social and cultural factors into account.
Acknowledgements
The present study was carried out with the financial support of the French National Research Agency under the projects ANR-07-PNRA-018, ALIMINFO and ANR-05-PNRA, 012, POLNUTRITION and with support from USDA CSREES Grant 2004-35215-14441 and NIH grant R01 DK076608. There were no conflicts of interest. M.M. and N.D. conceived the study, conducted data and modelling analyses, interpreted the results and participated in the writing of the report. A.D. participated in the conception and design of the study, interpreted the results and contributed substantially to writing the report. The authors declare no conflict of interest.
