Everyday Systems

The other day on Writer's Alamanac there was a piece on the Stigler Diet developed as a mathematical model rather than an eating plan.

There's a diet named after Nobel laureate economist George Stigler. The Stigler Diet is actually a mathematical model for the cost of subsistence eating — a linear programming problem on how to get the most nutritional bang for your buck. Specifically, Stigler's math problem was this: Say you have a man who weighs 154 pounds. Out of 77 foods commonly available, how much of each one should be eaten daily so that the man gets the right amount of nine essential nutrients — at the cheapest cost? The nutrients Stigler took into consideration: calories, protein, iron, and some vitamins.

The solution to the optimization problem: In one year, that man should consume 370 pounds of wheat flour, 57 cans of evaporated milk, 285 pounds of dried navy beans, 23 pounds of spinach, and 111 pounds of cabbage. In 1939, dollars, this would cost about 11 cents a day. Today, it'd be close to $1.75 per day. Stigler was subjected to a barrage of ridicule for suggesting this dull and bland diet, and he tried to remind people that it was just a mathematical model. He issued a statement: "No one recommends these diets for anyone, let alone everyone."

Yikes! That's a lot of cabbage. And I like cabbage, especially sauted with green onions till soft in butter and mashed with potatoes. But this diet does go to show that you don't have to spend a lot on food.

I like beans and that's a lot of beans, too, more than twice as many pounds of beans than cabbage! They're both staples in my depression era diet, but certainly not as much as he suggests!

I love stuff like this. If I'd known about it in college, I'd probably have followed it (I was on-and-off an unscientific home brewed version of this to save money for glass ceiling violations). So probably good I didn't.

Reinhard

If you followed this diet, you'd be the world's largest source of natural gas.

*snicker*

No, I'm not very mature, why do you ask?

Nicest of the Damned wrote:If you followed this diet, you'd be the world's largest source of natural gas.

*snicker*

No, I'm not very mature, why do you ask?

snort

Nor am I, NotD. All this talk of cabbages and beans made me think the same thing....

Blithe Morning wrote:

Nicest of the Damned wrote:If you followed this diet, you'd be the world's largest source of natural gas.

*snicker*

No, I'm not very mature, why do you ask?

snort

Nor am I, NotD. All this talk of cabbages and beans made me think the same thing....

Cabbage and especially beans are a big part of my diet, and the natural gas exists for about a week -- then no more than "normal."

wosnes wrote:Cabbage and especially beans are a big part of my diet, and the natural gas exists for about a week -- then no more than "normal."

Your intestinal flora may vary. I've been trying to eat more beans since about the first of the year, and I still try to avoid closed, not-well-ventilated spaces.

Nicest of the Damned wrote:

wosnes wrote:Cabbage and especially beans are a big part of my diet, and the natural gas exists for about a week -- then no more than "normal."

Your intestinal flora may vary. I've been trying to eat more beans since about the first of the year, and I still try to avoid closed, not-well-ventilated spaces.

I think you have to eat them regularly. If I stop eating them for a while, there's a gassy period when I start eating them again. If I eat them nearly daily -- no problems. It has something to do with the starches in the beans and the intestinal flora, but I can't remember the exact explanation. All I know is the more I eat, the less I toot!

I have been eating beans, cruciferous vegetables, and the like for 30 years and the gasiness has just gotten worse. I've used beano, intestinal bacteria supplements, and have tried lots of different cooking strategies. I guess it's convenient that I'm single. I try to plan my eating of them, because they are good fiber, to coincide later with less social activities.

BTW, BlitheMorning, I didn't see potatoes, green onions and butter on the list. but I agree they would go well with cabbage!

oolala53 wrote: BTW, BlitheMorning, I didn't see potatoes, green onions and butter on the list. but I agree they would go well with cabbage!

Was there a more complete list that I didn't see? Supposedly there were 77 things, but I only saw a dozen or so.

wosnes wrote: Was there a more complete list that I didn't see? Supposedly there were 77 things, but I only saw a dozen or so.

My curiosity was piqued! So I searched on Google Scholar and found if not the original article by Stigler then one published shortly thereafter (cited below).

Since I'm working on my master's I have access to Jstor (yay!) and was able to read the article in its entirety.

From list of 77 common foods provided by the Bureau of Labor Statistics (1), Stigler found that 15 met his initial nutrient/price requirements.

At this point, he wrote:

... reducing the procedure is experimental because there does not appear to be any direct method of finding the minimum of a linear function subject to linear conditions. By making linear combinations of various commodities it is possible to construct a composite commodity which is superior in all respects to some survivor, and by this process the list of eligible commodities can be reduced at least to 9

The list of 15 is below with the 9 in bold. If this were a paper, I would label it Table 1.

Wheat Flour
Evaporated Milk
Cheddar Cheese
Liver (beef)
Cabbage
Spinach
Sweet potatoes
Dried lima beans
Dried navy beans

Oleomargarine
Green Beans
Potatoes
Dried Peaches
Dried Prunes
Onions

Interestingly enough, he noted

The BLS list is a short one, and it excludes almost all fresh fruits, nuts, many cheap vegetables rich in nutrients, and fresh fish. It is beyond question that with a fuller list the minimum cost of meeting the National Research Council's allowances could be reduced, possibly by a ubstantial amount.

The reason for this is that many of these items were seasonal and therefore cheap in season and not usually available out of season. Unlike today where I am going to eat tomatoes from Mexico for lunch.

(1)13 The commodities are described in Retail Prices of Food, 1923-36, Bureau of Labor Statistics, Bulletin 635, October 1937. The price quotations are averages of 51 large cities in 1939 and 56 cities in 1944; they were taken from the Monthly Labor Review, October 1939 and December 1944.
=============================
The Cost of Subsistence
George J. Stigler
Journal of Farm Economics
Vol. 27, No. 2 (May, 1945), pp. 303-314
(article consists of 12 pages)
Published by: Oxford University Press on behalf of the Agricultural & Applied Economics Association
Stable URL: http://www.jstor.org/stable/1231810

There's an Excel spreadsheet at
http://excelcalculations.blogspot.com/2 ... mming.html that lets you explore The Diet Problem

You can add or remove foods, change the nutritional bounds, and get Excel to find the least-cost diet.

I don't know of anyone who's actually followed this method though. It usually results in unpalatable diets, and usually has to be adjusted for a taste factor.

You may want to read this paper which describes the original computational implementation of The Diet Problem, and the author's half-hearted attempt at following the suggested diet

G. B. Dantzig, "The Diet Problem," Interfaces 20:4, July-August 1990, 43-47.

Nicest of the Damned wrote:If you followed this diet, you'd be the world's largest source of natural gas.

*snicker*

So you could save money on food AND energy bills