Sheet 1: About

	
	

		
N238: Economics for Food and Nutrition Policy
	
	

		
Food Choices: Prices, Nutrients and the Least-Cost Diet 
	
	

		


	
	

		
This spreadsheet provides all the data and formulas needed to calculate an updated version of the 'least-cost diet',  defined as the combinations of foods that meet nutrient requirements for the lowest possible total cost per day.  Steps for the exercise are detailed in the "Instructions" tab.  

	
	

		
Data on a person's nutrient requirements are in the tab marked "DRI data", and information on the foods currently available for home delivery near the Friedman School in the tab marked "Food Cost and Composition".

	
	

		
Formulas used to calculate total cost and nutrients from various combinations of these foods are in the "Guesswork" tabs, one to meet dietary recommendations for women and the other for men.  

	
	

		
Comments and feedback are welcome!
	
	

		


	
	

		
Will Masters 
	
	

		
Friedman School of Nutrition
	
	

		
william.masters@tufts.edu
	



Sheet 2: Instructions

	
	

		
N238: Economics for Food and Nutrition Policy
	
	

		
Food Choices: Prices, Nutrients and the Least-Cost Diet
	
	

		


	
	

		
What combination of foods can meet a person’s nutrient needs at lowest total cost? This ‘least cost diet’ problem is a helpful starting place for understanding the nutritional aspects of food demand.  The question arose as soon as nutrients were discovered in the early 20th century, and mathematical solutions were first developed during World War II for the purpose of allocating food rations and also formulating livestock feed.  
	
	

		


	
	

		
Least-cost diets, defined as the combinations of foods that meet nutrient requirements for the lowest possible total cost per day, are intended to capture only one aspect of human diets.  Actual people may not meet nutrient recommendations, if only because real-life food choices involve other objectives and constraints.  In this exercise, we use least-cost diets as a benchmark to reveal which nutrients are most expensive for people to obtain from locally-available foods, and use the differences between least-cost diets and actual food consumption to see what else drives food choice beyond just nutrients. For use in dietary recommendations, we would need to add other criteria for a healthy diet, and other factors affecting food choice such as preparation time, culinary traditions and personal preferences.
	
	

		


	
	

		
This exercise begins with guessing at and potentially calculating what would be a least-cost diet based on our local food environment in Boston, and then comparing that with actual consumption among very low-income people in Ethiopia.  One purpose of the exercise is to reveal how food prices and nutrient composition affect the cost of meeting recommended levels of nutrient intake.  Another purpose is to gain familiarity with the types of data needed to analyze food and nutrition policy, downloading data in its original form from authoritative sources, using Excel to calculate results and make presentation-quality tables. The data analysis skills involved are very helpful for many jobs, and we will build on this in four more data visualization exercises later in the semester.  Since some students have not had much (or any) previous experience with Excel, we encourage you to search for and watch the tutorials at lynda.tufts.edu, where you can sign in using your Tufts UTLN and search for the specific Excel version and skills that you need.  You are free to share Excel tips with other students, but the final tables and explanations of your findings should be your own work.  After building each table in Excel you should paste it into a Word document, in a format similar to the tables used in your class slides and many publications, as explained for example in www.press.uchicago.edu/infoServices/prep-table.html.  
	
	

		


	
	

		
When working with data it is especially important to watch out for definitions and units of measure. Your document must clearly explain what your numbers represent, with definitions for each acronym (such as DRI) and labels for each unit of measure (mg, kcal etc.).  Every table must have an appropriate title (e.g. “Table 1. A first guess at potentially least-cost diets in Boston”) and a footnote below the table describing the data (e.g. “Source:  Calculated using foods selected by the author using data downloaded from peapod.org and other sources explained in the text.”)  All tables and figures you make for this class should all have titles and notes of this type, with brief summaries in plain English immediately above or below.  Presenting your own calculations in this way is an important professional skill that leverages your understanding of the economic forces behind your data.
	
	

		


	
	

		
1.  A least-cost diet in Boston
	
	

		
The first part of this exercise focuses on the prices and nutrient composition of foods currently available in Boston.  The accompanying Excel file (N238_Ex3-LeastCostDietsInBoston.xlsx) provides information on 41 food products in five categories, designed to facilitate understanding and build intuition about the least-cost diet problem.  
	
	

		


	
	

		
1.1 Dietary reference intakes (DRI) values 
	
	

		
The first sheet of your workbook, labeled “DRI data”, contains U.S. Institute of Medicine (IOM) estimates for recommended lower bounds and upper limits on dietary energy plus 19 nutrients of general interest.  These have been already downloaded for you from the USDA Food and Nutrition Information Center, http://fnic.nal.usda.gov/fnic/interactiveDRI, and formatted in a way that clearly reveals target levels for energy balance, recommended daily intake or lower bounds and also upper limits or bounds for intake where relevant.  Thresholds chosen for this exercise refer to the mean level of height, weight and physical activity reported by the National Center for Health Statistics (NCHS) for women and men at 30 years of age in the U.S. as of 2007-10 (Fryar, Chu and Ogden 2012).  
	
	

		


	
	

		
For the purpose of studying the economics of food choice, we can limit our initial analysis to just these few nutrients and thresholds.  In actual practice for dietetics, additional food components would also be important such as specific amino acids for protein quality, fatty acids for lipid quality, dietary fiber and antioxidants. Thresholds for each nutrient would also be adjusted based on individual circumstances.  Students who are interested in diet quality and not already familiar with the strengths and limitations of DRI data should review their definition and usage in the original source document (IOM 2006).  
	
	

		


	
	

		
1.2 Food cost and composition
	
	

		
The second sheet of your workbook contains data on a selection of foods available for home delivery from peapod.com in the area around the Friedman School (zip code 02111).  A typical U.S. grocery store carries over 20,000 distinct food items, with prices and items fluctuating over time.  The specific selection of products and prices were obtained on January 7, 2018.  Each is the low-cost store brand version of a commonly consumed food that one might expect to see in everyday use by low-income households.  
	
	

		


	
	

		
To illustrate food choice, items are grouped into five broad categories for ease of comparison among products that might substitute for each other.  For each item, data shown are the price per package and corresponding price per serving, based on package and serving sizes that are shown in both natural units such as one apple or one cup of blueberries, and also metric units such as grams.   Data on the nutrients in each serving were downloaded from the USDA National Nutrient Database at http://ndb.nal.usda.gov, and are shown in their respective scientific units of measure such as kcal, g or mg.
	
	

		


	
	

		
1.3 Guesswork: How close to a least-cost diet can you get without higher mathematics? 
	
	

		
The remaining sheets allow you to enter the number of servings you might choose of each item.  When you enter a number in the highlighted cells, formulas in row 13 at the top of each column will then calculate the total cost per day, and the amount of each nutrient obtained.  Formulas then compare those hypothetical nutrient intakes to the DRI values, and the cells will change color to indicate nutrients that are at 100% of their limits (green), below recommended intake (yellow, in row 8), above upper limits (red, in row 9).  Dietary energy is both an upper and lower bound, so appears in both rows.  If the diet meets all DRIs, the only color visible in row 8 and 9 would be green. Nutrients that are not colored are not binding, so only those that are colored influence the cost and composition of the least-cost diet. 
	
	

		
 
	
	

		
Your first task in this exercise is guesswork, using your familiarity with these everyday foods to choose a mix of foods that might come close to meeting the DRIs at lowest cost. For example, it turns out that an average U.S. woman whose diet consists of exactly 22 apples would achieve energy balance and vitamin K sufficiency, but be deficient in many other nutrients and also have a level of carbohydrate intake above the upper bound of the recommended range.  She would also have many other problems, but for this exercise it is challenging enough just to keep track of these DRI values.  As you adjust the number of servings for various foods, you will see how the balance of nutrients changes, and how total diet cost rises and falls. 
	
	

		


	
	

		
Guessing at the mix of foods needed to exactly meet all DRIs is extremely difficult – and would be nearly impossible to do at least cost. You are not expected to actually meet that goal, but to make and describe a few guesses in a way that demonstrates the principles involved.  As in real life, the portion sizes used here are merely indicative, and you can choose any number or fraction of portions for each food included in a given diet plan.  The fun of this exercise comes from being able to alter diet plans quickly and observe their consequences for nutrient intake, without harming any people or lab animals and without spending actual money.  Experimenting with different quantities of various foods in this computer simulation allows you to discover for yourself some of the underlying principles that govern the relationship between food choice, nutrient adequacy and diet cost.   
	
	

		


	
	

		
Your written report should compare and contrast two distinct diet plans for a woman and two for a man.  These four plans need not actually meet all DRIs, since you’d need a lot more math to accomplish that, but your four plans should illustrate answers to the questions below and be summarized in:
	
	

		
-- Table 1, showing the number of servings of each food in the four diet plans, and their total cost per day; and 
	
	

		
-- Table 2, showing the resulting macronutrient balance in percent of daily recommended dietary energy and protein, and percent of the upper and lower bound of their recommended range for total fats and total carbohydrates, as well as the resulting micronutrient balance in percent of daily recommended intake and upper limits where relevant.
	
	

		


	
	

		
Table 1 can be constructed by cutting and pasting from columns A through D of the Guesswork sheets, including only the rows needed for the foods included in your chosen diets.  For Table 2, you will need to use Excel to “transpose” data from rows into columns, so that each diet is shown as a pair of columns with rows for that diet’s percentage of the lower and upper DRI values. If you wish to show all four diets on one page, you will have eight columns of data, so headings should be abbreviated and then explained below the table.  Rows will refer to energy balance, protein sufficiency, recommended range for fats and carbohydrates, then recommended intakes and upper limits for vitamins and minerals.  Feel free to divide these tables if needed, for example to show Table 2a and Table 2b on separate pages, with a brief title above each table and detailed notes below it that describe the original source of your data and provide any definitions not already stated in the title and labels for the rows and columns of your tables. 
	
	

		


	
	

		
Below the tables, summarize any insights from your guesswork in response to the following questions:
	
	

		
(a)    How does the number of foods affect the cost of meeting these DRIs?  In other words, what level of diet diversity helps you get closer to DRIs at lower cost, and what types of foods should be included?  To illustrate your answer to this question, the plans in your report should have different levels of diversity. 
	
	

		
(b)   Beyond diversity, what individual foods are most likely to appear in least-cost diets, and why?  Which foods are likely to be needed in relatively large quantities, and which foods could be consumed in small quantities?  
	
	

		
(c)    How do the differences in DRIs for women and men affect the least-cost diet?  In other words, what are differences in DRI values for macro- and micronutrients, and what are the corresponding differences in your chosen diet plans?  To illustrate your answer, the plans in your report should have some similarities but also differences between women and men. 
	
	

		


	
	

		


	
	

		
1.4 Optional:  Mathematical solutions to find the exact least-cost diet 
	
	

		
For this exercise it is not necessary but is fun to look ahead, and see how Excel uses mathematical optimization to find the precise quantities of foods needed to meet DRIs at lowest total cost.  If you want to do that, you would alter your Guesswork sheets as follows:
	
	

		
-- Under Review, choose “Unprotect Sheet” to permit modification; and
	
	

		
-- In the search box, find and add in the “Solver”, which then appears under Data | Analysis.
	
	

		


	
	

		
When you click on the Solver, Excel will have remembered the following settings, based on the total diet in row 13 of each sheet:
	
	

		
-- Objective:  
	
	

		
      Minimize the total cost of all foods included in the diet (cell B13); subject to
	
	

		
-- Constraints:
	
	

		
     Maintain energy balance, by setting total intake equal to needs (E13 = E4) [row 4];
	
	

		
     At or above lower bounds for all nutrients (F13 ≥ F5, G13  ≥ G5,…, X13 ≥ X5) [row 5]; and
	
	

		
     At or below upper bounds where needed (G13 ≤ F6,…, Q13 ≤ Q6,… X13 ≤X6) [row 6]
	
	

		
A checkbox in the Solver command includes additional constraints that food quantities cannot be negative. The command also specifies that the solution method is the “Simplex” developed by George Dantzig as a way to find a least-cost diet and also perform many other optimization tasks. 
	
	

		


	
	

		
If you are able to take this additional step, feel free to include a note in your report about how your guesswork compares to the solution found by Excel, revisiting questions (a), (b) and (c) from the previous section using the correct answers.  Among the interesting features of this solution is the time-honored role of potatoes, peanut butter and canned spinach in American culture, as well as the consequences of micronutrient fortification for how milk, white bread and pasta enter the diet. 
	
	

		


	
	

		
1.5 Comparison with the original least-cost diet of 1939
	
	

		
Whether or not you choose to complete section 1.4 using Excel’s Solver, you can compare your guesswork to the results of the original least-cost diet that was first estimated by Stigler in 1939.  You can quickly read about the original “Stigler diet” here:. https://en.wikipedia.org/wiki/Stigler_diet.  That page includes a link to George Dantzig’s fun story of how he improved Stigler’s method, but even without advanced math you can compare the foods selected by Stigler in 1939 with those you chose by guesswork.  Please add a brief comparison between Stigler’s original least-cost diet and your choice from the foods available today at current prices.  Did you choose the same foods as Stigler did for his project, almost 80 years ago?  How have the many changes in the U.S. food environment since 1939 altered the foods that you think would be included in a least-cost diet? 
	
	

		


	
	

		
2.  What do the world’s poorest people actually eat?
	
	

		
The second part of this exercise asks you to describe what people eat in the world’s poorest food environments, and compare that to your insights from part 1.  We do not expect even the world’s poorest people to consume exactly a least-cost diet, if only because many people do not actually meet their DRIs.  They may also spend more than the minimum required to obtain nutrients, because other factors also matter for food choice such as cooking time and digestibility.  
	
	

		


	
	

		
In the exercise we look at the average quantities per person per day of various foods consumed by a whole population.  This differs from an individual’s diet in part because it is the average over many people, and therefore includes more different foods than any one person might ever eat.  There are two possible ways to measure food consumption:  one is by asking people to record what they ate, and the other to infer what they ate by subtraction, as the balance obtained by adding up food production plus purchases minus sales, nonfood uses and waste.  Each method has well-known limitations but also strengths, and we’ll use both in this exercise:  first the national Food Balance Sheets computed by the FAO for all countries since 1961, and then a national Food Consumption Survey of the type conducted in most countries every few years.  We’ll focus on Ethiopia, which is one of the world’s poorest countries and is the focus of many development efforts.  By definition, a national Food Balance Sheet can provide only the whole country’s average per capita, while Food Consumption Surveys allow disaggregation to subsets of the population, in this case to compare poorer versus richer people within Ethiopia.  We can also compare the per-capita average from the two methods, to get a sense of their strengths and limitations.
	
	

		


	
	

		
2.1 FAO Food Balance Sheet (FBS) data
	
	

		
For FBS data, go online to http://faostat.fao.org. To make this site work, you may need to disable your browser’s ad blocker or content filter – e.g. mine is ublock. Once you’re in the FAOSTAT site:
	
	

		
o    Choose “Explore Data”, then “Food Balance Sheets”, and read carefully about what these data are by clicking on “Definitions and Standards” and “Metadata”. 
	
	

		
o    Under “Download Data”, for “Countries” choose both “Ethiopia” and “Ethiopia PDR” (they changed in 1992), under “Elements” choose “Food Supply (kcal/capita/day)” and “Protein Supply (g/capita/day)”, under “Items Aggregated” choose all of the categories labeled “+(Total)”, and under “Years” choose 2013 and 1961, then click on “Download Data”. 
	
	

		
o    To create a meaningful table, copy the sheet in your workbook (so as not to lose the downloaded sheet, in case you make a mistake), then delete redundant columns and copy the data so that 1961 and 2013 values are in adjacent columns. Notice that the “Aquatic Products, Other” category is missing for 1961 so that row should be added with a symbol such as “..” to show missing data.  (Also, note how fish consumption is so low that calories from it round to zero in both years, but that is an actual observation so should not be deleted.)  Then sort the block of data by “Element” and copy the data so that the two columns for protein in 1961 and 2013 appear adjacent to the two columns for energy in 1961 and 2013.  To make each label appear only once, you can add another heading row and merge cells so that a single heading for “Energy (kcal/person/day)” spans the columns for 1961 and 2013, and one heading for “Protein (g/person/day)” spans its two columns as well.  Finally, insert blank rows or horizontal lines between the Grand Total and Vegetal Products as well as between Animal Products and Cereals, and sort the rows for the individual food categories including Cereals by dietary energy in 1961. 
	
	

		
o    The result, which can be Table 3 of your report, should provide a clear visualization that compares per-capita quantities in 1961 and 2013 of calories and protein obtained from all foods, divided into plant-sourced vegetal foods and animal-sourced foods, and the major foods in each of those categories.  
	
	

		


	
	

		


	
	

		
2.2 National household survey data
	
	

		
For diet recall data, Ethiopia’s Central Statistical Agency (www.csa.gov.et) most recently conducted a nationally-representative Household Consumption Expenditure Survey (HCES) in 2010/11. Reports from the survey are most conveniently downloaded from this repository: http://catalog.ihsn.org/index.php/catalog/3123
	
	

		
o    To see the survey results, open the Analytical Report from here: http://catalog.ihsn.org/index.php/catalog/3123/download/46156
	
	

		
o    To understand the context, read the first ten pages of the report (Executive Summary, then Introduction and Summary); you may also be curious about aspects of the survey such as sampling methods and the questionnaire, as well as other findings beyond the dietary intake data.  In this case, diet recall refers to the previous three or four days, rather than the usual 24-hour, 7-day or 30-day periods used in other surveys.  
	
	

		
o    For this exercise, you can jump to Table 36 on page 75, which shows diet composition in terms of calories per adult per day from each major food category, for survey respondents in each quintile of income from poorest (quintile 1) to richest (quintile 5).  
	
	

		
o    To make a table for your report you may choose to retype their Table 36 data into Excel, or to save time you can paste an image from their PDF file. If you are on a Windows computer, you can use the “clipping tool” or a program like SnagIt. If you are on an Apple computer you can use command+shift+4 to screenshot, and then crop the image to insert in your own report.  As always, please include a brief title above the table and detailed notes below it with a full bibliographic citation and definitions of the data.  
	
	

		


	
	

		
After presenting your tables, please discuss the evidence you find regarding the following questions: 
	
	

		


	
	

		
(a)    What are the main similarities and differences in food quantities for the hypothetical diets you chose in Part 1 for consumption in Boston, and the real-life national average consumption levels you found in Part 2 for Ethiopia?  The specific foods in your Boston food basket may not fit neatly into the categories used in either the food balance sheet or household survey data in Ethiopia, but the comparison will reveal important similarities and differences.  Please include a brief description of how Ethiopian diets changed from 1961 to 2013 as found using the FAO Food Balance Sheets, and how diets compare among poorer versus richer Ethiopians based on recall data from their 2010/11 household survey.
	
	

		
(b)   What can you infer from the Ethiopian data about the macronutrient adequacy of their food supply, focusing specifically on total calories and protein per capita?  How is that likely to compare with micronutrient adequacy?  You need not actually calculate micronutrients in foods consumed by Ethiopians, and in any case these are measured with considerable error so you should focus only on your judgment about the likely differences between macro- and micronutrient adequacy, and any other aspect of diet quality you might notice in these data. 
	
	

		
(c)    Finally, please describe some lessons from the exercise for how interventions can lower the cost of meeting DRIs in Boston and in Ethiopia.  Even without knowing anything about variation among people, do the data discussed here offer any insight into how the food environment affects the cost of nutrient adequacy?  In particular, consider the difference between fortification (by which nutrients are added to foods before sale), supplementation (by which nutrients such as vitamin A are provided separately from foods), and food assistance (by which people are helped to obtain additional quantities of ordinary foods). What factors might lead to preferring one strategy over the other?
	
	

		


	
	

		
Please limit the whole report to under 1000 words, plus tables.  At the top of the first page please write your name and date, the course # and name, and the title of the exercise, save it in Word or PDF format. As always for this class, to help keep track of things the filename should start with your last name and also include your first name, course and exercise number, e.g.: "SmithJanet_N238_Ex3.pdf".
	



Sheet 3:  DRI data

	
	
	
	
	

		
Table 1. Dietary reference intakes for 20 selected nutrients in an adult population at CDC reference levels of height, weight and physical activity
		


		


		


		


		


		


		


		


		


		


		


		


		


		


		


		


		


		


		


		


	
	

		


		
Energy (kcal)
		
Protein       (g)
		
Fat 
(g)
		
Carbo-hydrate (g)
		
Vit. A 
(mcg RAE)
		
Vit. C (mg)
		
Vit. D (mcg)
		
Vit. B6 (mg)
		
Vit. E (mg)
		
Vit. K (mcg)
		
Thiamin (mg)
		
Vit. B12 (mcg)
		
Folate   (mcg)
		
Niacin     (mg)
		
Calcium (mg)
		
Iron         (mg)
		
Mag-nesium (mg)
		
Potas-sium (mg)
		
Sodium (mg)
		
Zinc (mg)
	
	

		
Female
		
2049
		


		


		


		


		


		


		


		


		


		


		


		


		


		


		


		


		


		


		


	
	

		
Recommended intake  (or lower bound)
		


		
61
		
46
		
231
		
700
		
75
		
15
		
1
		
15
		
90
		
1
		
2
		
400
		
14
		
1,000
		
18
		
310
		
4700
		
1500
		
8
	
	

		
Upper limit of intake (or upper bound
		


		


		
80
		
333
		
3,000
		
2,000
		
100
		
100
		
1,000
		


		


		


		
1,000
		
35
		
2,500
		
45
		
250
		


		
2,300
		
40
	
	

		
Male
		
2731
		


		


		


		


		


		


		


		


		


		


		


		


		


		


		


		


		


		


		


	
	

		
Recommended intake  (or lower bound)
		


		
71
		
61
		
307
		
900
		
90
		
15
		
1
		
15
		
120
		
1
		
2
		
400
		
16
		
 1,000 
		
8
		
400
		
4700
		
1500
		
11
	
	

		
Upper limit of intake (or upper bound
		


		


		
106
		
444
		
 3,000 
		
 2,000 
		
100
		
100
		
1000
		


		


		


		
1000
		
35
		
 2,500 
		
45
		
350
		


		
2300
		
40
	
	

		
Source: Recommended intake and tolerable upper limit obtained from USDA Interactive DRI Calculator on January 7, 2018, at https://www.nal.usda.gov/fnic/interactiveDRI/dri_results.php
Values for total fat and carbohydrates are lower and upper bounds of the recommended range.  Energy requirement is for daily balance with no weight gain or loss.
Data shown are for 30 year-old adults, based on the mean of the U.S. population from NHANES data for a woman at weight=168.5 lbs, height=63.7 inches, physical activity=sedentary and maternity status=not pregnant or lactating, and a man of weight=195.7 lbs, height=69.2 inches, and physical activity=sedentary.
Note:  Original source is Institute of Medicine (2006), Dietary Reference Intakes: The Essential Guide to Nutrient Requirements. Washington, DC: The National Academies Press, online at https://doi.org/10.17226/11537.  Heights and weights are from Fryar, Cheryl D., Qiuping Gu, and Cynthia L. Ogden. Anthropometric reference data for children and adults; United States, 2007-2010.  National Center for Health Statistics. Vital Health Stat 11(252), online at   www.cdc.gov/nchs/products/series/series11.htm.