I read somewhere that the "optimal" approach to buying a money-saving
appliance that you're not sure how much you'd use is to keep track of
how much you waste by not having it; when the total of waste reaches
the cost of the appliance, you buy the appliance. This way, your
worst-case expenditure is twice the cost of the appliance, and your
best-case expenditure is nothing. And, with this policy, it's very
likely that you'll buy the appliance if it will save you money, and
you won't if it won't.
This actually works for any constant factor of the cost of the
appliance. You could buy the appliance when your total potential
savings reach 75% of its cost, or 200%; the underlying principle is
the same. Depending on your priors (how likely it is you'll keep
doing what you're doing) and your time preference for money, it might
make sense to adjust the factor.
Presumably whatever benefit you'd be getting more cheaply with the
appliance is more valuable than the amount you're wasting by not
having it --- say, having a washing machine might save you $25 a week
in laundry-service costs, but having clean clothes to wear is
presumably worth more to you than the $25; and having a camper bus
might save you $100 a night in hotel-room fees when you travel, but
presumably if traveling isn't worth $100 a night, you wouldn't be
doing it before buying the camper bus.
Some other possible strategies have, in some sense, an unlimited
downside. "Never buy" can cost you an unlimited amount of money ---
$100 a night for all eternity, say --- and while "buy just in case"
won't cost you an unlimited amount of money, the ratio between the
benefit you get and the cost is unlimited. For example, you could
spend $40000 on a camper bus you never use. If you use it for just
one night, you'd have gotten better value for your money by spending
$10000 on a really nice hotel room. (Not that this is a reasonable
strategy.)
The buy-when-costs-reach-predetermined-multiple-price strategy omits a
couple of significant factors, though: the cost of owning the
appliance, and its lifetime. The cost of ownership can be substantial
if you have a small house and move frequently, or if it requires a lot
of maintenance. (This is much on my mind at the moment, because I'm
living in a small apartment --- effectively an efficiency with a
storage room --- and I've moved six times in the last seven or eight
months; and my refrigerator and bicycle need some serious
maintenance.) These are not too hard to add in to the model, though,
and you still have a strategy that guarantees you a worst-case
expenditure of a constant factor of the cost of the appliance.
RAID
----
Another case where a constant-factor extra cost gets you something
valuable is error-correction coding. For some constant factor in
coding expansion, you can reduce the probability of storage errors in
your data to an arbitrary degree. The simplest realization of this is
"disk mirroring", where you store the same data on both disks. If one
disk dies, the other still has your data. (In theory. Right now,
some of my data is on a RAID where one disk has died, and I haven't
gotten around to replacing the dead disk, so I could still lose my
data at any moment.)
Food buying
-----------
It's well known that you can buy sufficient nutrition for a
dramatically lower cost than a normal diet. On August 16th of last
year, after the national statistics bureau had created a furor by
deciding on a poverty line of about AR$6 per day, I went to Carrefour
on Independencia in San Telmo to price out some food and calculate the
lowest-priced macronutrient-balanced diet. Here's what I came up
with. None of the prices are sale prices.
| | Soybeans | Salt | Sunflower oil | Flour | Total |
|------------------------+----------+------+---------------+-------+-------|
| g/day | 200 | 5 | 33 | 430 | 668 |
| kcal carbohydrates/day | 54 | | | 1238 | 1292 |
| kcal protein/day | 280 | | | 155 | 435 |
| kcal fat/day | 420 | | 297 | 39 | 756 |
| kcal/day | 754 | | 297 | 1432 | 2483 |
|------------------------+----------+------+---------------+-------+-------|
| AR$/kg | 7.98 | 6.30 | 5.10 | 2.48 | |
| AR$/day | 1.60 | 0.03 | 0.17 | 1.07 | 2.86 |
| US$/day (at AR$4.50) | 0.36 | 0.01 | 0.04 | 0.24 | 0.64 |
(The whole spreadsheet, in Spanish, is at
<http://canonical.org/~kragen/comida.gnumeric>. Due to rampant
inflation, Argentine prices have gone up since then.)
The idea is that you boil the soybeans with a little salt, or maybe
sprout them, and use the flour, rest of the salt, and the sunflower
oil to make what are called "tortas de parrilla", a sort of unleavened
flatbread which is commonly for sale in the streets here, cooked over
charcoal in metal pans on shopping carts. You can see that the result
is hearty; what may not be obvious is that the soybeans provide enough
fiber and omega-3 fatty acids to avert what could otherwise be serious
nutritional imbalances, and that their protein is of an especially
high biological value, i.e. its amino-acid mix is close to optimal.
There are a couple of obvious questions about this diet:
- What about vitamins, minerals, other micronutrients?
- Don't you have to be rich to bulk-buy to get prices this good?
- Won't the lack of variety really suck?
- Isn't this going to be a lot of work?
- Isn't so much gluten going to be bad for you?
There's also the question of how much space you need for food storage.
### What about vitamins, minerals, other micronutrients? ###
The flour (whose extremely low price is, I think, a result of
government subsidies) is fortified with a variety of vitamins as
required by law. But all-in-one multivitamin pills cost about US$0.02
per day, or AR$0.09 at the time, and provide all the micronutrients
we're known to need. So it's possible to solve the micronutrient
problem very cheaply.
### Don't you have to be rich to bulk-buy to get prices this good? ###
Bulk buying is indeed necessary, although all the prices above are for
units of one kilogram or less. (You might be able to get better
prices if you buy in *real* bulk.) It turns out, though, that even if
you're actually so poor that you can't ever afford to buy US$5 of food
at a time, you can work up to bulk buying with a constant-factor-worse
strategy. If you're buying sunflower oil, say, by the 250mℓ bottle
and getting a 20% worse price as a result, you can gradually build up
a stock of sunflower oil by buying an average of, say, 10% more than
you need. 250mℓ might last you 7½ days, so buy a new bottle every 6¾
days on average, rather than every 7½. Every week, more or less,
you'll accumulate an extra 25mℓ of oil; after about six months, you'll
be able to buy the 500mℓ bottle instead of the 250mℓ bottle, and your
sunflower-oil investment will start paying dividends. Another year
later, you'll be able to buy a liter at a time.
You could argue that this is not a realistic view of life in poverty;
more typically you have no money coming in for a long time, like a
month or six months, and then you finally get some, which you can use
to buy things you've been putting off; and the critical thing to focus
on is not efficiency but resiliency, i.e. making sure you have some
way to get some food when you need it. This actually just happened to
me, and I went to the supermarket and bought two kilograms of rice,
some mayonnaise, butter, spaghetti, rice, *pears*, and so on, after
living for much of the last weeks on whatever dried foods I had stored
up and whatever my girlfriend bought for herself. But I'm getting
ahead of myself.
### Won't the lack of variety really suck? ###
The lack of variety is a more serious problem. It tempts you to go
off-budget and eat an AR$5 hot dog or something, because you just
can't face the thought of another lunch consisting of soybean
pancakes. And there may be health problems caused by such a
monotonous diet, even if they don't come from deficiencies of known
macro- or micronutrients; for example, there might be a pesticide used
on the soybeans that your body can tolerate if you're eating 200g of
dry soybeans once a week, but not every day, or you might be getting
some vitamin in a form that your body finds particularly hard to
absorb.
The same constant-factor-worse strategy applies, though. If you can
manage to buy 10% more soybeans than you're eating, then after a short
time, on some shopping trip, you can buy another nutritionally similar
low-priced food instead --- around here, that would be lentils, split
peas, or garbanzo beans, or possibly polenta or whole-wheat flour. As
long as you can keep buying a constant factor *more* than what you're
eating, whether it's 5%, 10%, 50%, or 100% more, the variety of foods
stored in your pantry will continue to increase, and therefore so will
the variety of your meals.
(Practically speaking, you might also want to spend some of that
constant factor on things other than macronutrients: spices, MSG,
onions, sesame oil, herbs to plant, and so on --- things that go a
really long way to rendering otherwise unpalatable dreck edible.
Tonight, for example, I ate about 100g (dry) of boiled split peas,
which were AR$8.50/kg and therefore cost about AR$0.85; I added an
AR$1 packet of dried soup stock, which is mostly MSG and salt but also
had some basil and garlic flavor, and it made a huge difference.
Ajinomoto has a line of mixed-condiment packages that are similar but
even cheaper. The one I used earlier today came in a package of 12
5-gram packets for AR$4.85, I believe, so each packet costs AR$0.40.)
This also gradually reduces the risk of hunger shocks where you have
nothing to eat for a few days, or weeks, because of an unexpected
expense, delay in getting paid, or jump in prices. That is, if
applied assiduously, the constant-factor-worse strategy eliminates
some serious risks to your food budget.
Building up a stock in this way also increases the probability that
you'll be able to buy food when it's on sale or even gratis.
This ignores, though, the cost of storage and the limits of lifetime
--- as the constant-factor-worse appliance-buying strategy does. If
you eat 200g of soybeans a day and buy 100% more, 400g (or, more
practically, buy 2kg of soybeans every five days), your stock of
stored soybeans will grow at 200g per day. If you somehow followed
this strategy for a year, you'd have 73kg of dried soybeans stored.
How on earth are you going to store 73kg of dried soybeans? And
stored flour will eventually go rancid, especially if it's whole-wheat
flour.
This *is* a real limit, but it's not as bad as it sounds, unless
you're bouncing from one temporary accommodation to another, as I am.
(In that case, maybe you should ask a friend to store your soybeans
and stuff in their house.) See below about space requirements.
Independent of how consistent or inconsistent your food buying and
income is, you can adjust how much of your constant factor is going
into building up a stock for the future and how much is going into
buying "luxury" foods that are more expensive than the bare minimum.
I think the optimum fraction for building up a stock for the future,
in the absence of storage and lifetime considerations, would be about
half of the total. As shown above, this is feasible if you're
spending more than about US$1.28 per day on food. The total
investment needed to build up a one-year stockpile would be about
US$234.
### Isn't this going to be a lot of work? ###
No, soaking and boiling soybeans and frying up griddle cakes is not a
lot of work. It requires planning and discipline, which can be
difficult, but it doesn't take much time or toil.
Buying 10% or 20% or 100% more food than you would have been buying
otherwise and bringing it home and putting it away is more work, but
it's not much more work. It's about 10% or 20% or 100% more work.
It's only a small constant factor worse.
### Isn't so much gluten going to be bad for you? ###
Most people digest gluten well. Some people don't. Some people are
so sensitive to it that they have to avoid it entirely or face serious
health problems. Avoiding gluten increases the cost substantially,
and because of the vitamin fortification, increases the risk of
micronutrient shortages. From the same spreadsheet, here's my
cheapest gluten-free version:
| | Polenta | Brown | Soy | Salt | Sunflower | Total |
| | | rice | beans | | oil | |
|--------------------+---------+-------+-------+------+-----------+-------|
| g/day | 240 | 180 | 200 | 5 | 33 | 658 |
| kcal carbos/day | 691 | 562 | 53 | | | 1306 |
| kcal protein/day | 108 | 58 | 280 | | | 445 |
| kcal fat/day | | 45 | 420 | | 297 | 762 |
| kcal/day | 799 | 665 | 753 | | 297 | 2514 |
|--------------------+---------+-------+-------+------+-----------+-------|
| AR$/kg | 5.56 | 5.17 | 7.98 | 6.30 | 5.10 | |
| AR$/day | 1.33 | 0.93 | 1.60 | 0.03 | 0.17 | 4.06 |
| US$/day (@AR$4.50) | 0.30 | 0.21 | 0.36 | 0.01 | 0.04 | 0.90 |
That is, cutting out gluten increases the price of the minimal diet by
about 42%, to almost a dollar a day.
### Won't food storage take a lot of space? ###
Earlier, I said that by buying a constant factor more than what you
eat, you will gradually build up a stockpile, which will allow you to
buy food only when it's on sale, buy food in bulk for better prices,
and keep a wide variety of stored food on hand to avoid dangerous
dietary monotony. But such a stockpile takes up space. Is it an
unreasonable amount of space?
I'll investigate this, plus the question of managing stored food
lifetimes effectively, in depth in another post. For now, the outline
is this:
These foods will last at least a year in storage. At the 600 to 700
grams of stored food per day described above, a year's supply is about
237 kilograms. That's a small enough amount of food that you could
store it under your bed, in your coffee table, or possibly in shelves
that already exist. So if you're not moving around a lot, it won't
take up an unreasonable amount of space.
240 kilograms is enough to have about four kilograms each of about 60
different foods, so it can provide plenty of variety.
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