# Ok, some practical math:

sonhouse
Posers and Puzzles 14 Feb '06 20:59
1. sonhouse
Fast and Curious
14 Feb '06 20:59
You have a freezer, it can store food indefinitely, great freezer.
It takes an average of 200 watts (0.2 Kw) to run.
Electricity costs 10 cents a KWH (US\$) Now you buy a steak for
10 bucks. The inflation rate is 5 percent per year, that means the
price doubles in 20 years, so twenty years from now, that same steak
will cost 20 bucks. So here is the puzzle:
How long can you keep the food in the freezer before you start
spending more money on the electricity than the food? Obviously,
you spend a bit more immediately, but I am asking under those
conditions, how long will it take for the electical cost to equal the
replacement cost of the steak. Remember, the freezer can keep food
for decades as fresh as the day you bought it, its a perfectly reliable
freezer, never breaks down (Hmm, must not have any moving parts,
eh, ok, its a Peltier effect freezer, solid state type, you can get them
today). Anyway, what is the point in the freezer you want to decide
to eat the steak because it will soon cost more to keep it frozen than
to replace it.
2. PBE6
Bananarama
14 Feb '06 22:16
Originally posted by sonhouse
You have a freezer, it can store food indefinitely, great freezer.
It takes an average of 200 watts (0.2 Kw) to run.
Electricity costs 10 cents a KWH (US\$) Now you buy a steak for
10 bucks. The inflation rate is 5 percent per year, that means the
price doubles in 20 years, so twenty years from now, that same steak
will cost 20 bucks. So here is the pu ...[text shortened]... o decide
to eat the steak because it will soon cost more to keep it frozen than
to replace it.
The details of the question were a bit unclear, so I'm going to assume you want to compare:

1) The cost of purchasing a steak at \$10, plus the cost of freezing said steak for some amount of time "t"; and

2) The cost of waiting until time "t" to buy the steak and not freezing it.

I'm also going to assume you wanted the cost of the steak to increase continuously and doubling every 20 years. In that case, the cost of the replacement steak "y" is given by:

y = \$10*e[t*ln(2)/20]

where "t" is in years.

One more set of assumptions: the freezer runs all the time, and all the power being used by the freezer goes into keeping the steak frozen, so the electricity cost "E" is given by:

E = 0.10 \$/kWh * 0.2 kW * 24 hr/day * 365 days/year * "t" yrs = \$175.2*t

Now, the cost for situation 1 (C1) is the original \$10 plus the electricity cost "E", and is given by:

C1 = \$10 + \$175.2*t

The cost for situation 2 (C2) is simply the cost of the replacement steak:

C2 = \$10*e[t*ln(2)/20]

Equating these two expressions, and solving for "t" using a numerical method (MS Excel Solver), we get "t" = 240.9 years. However, you asked:

Anyway, what is the point in the freezer you want to decide to eat the steak because it will soon cost more to keep it frozen than to replace it.

If you check the costs for any time less than 240.9 for "t", you find that the electrical cost is greater than the replacement cost. So the real answer is, eat the steak as soon as you buy it or it's going to cost you to keep it in the freezer.
3. XanthosNZ
Cancerous Bus Crash
14 Feb '06 22:48
Originally posted by PBE6
The details of the question were a bit unclear, so I'm going to assume you want to compare:

1) The cost of purchasing a steak at \$10, plus the cost of freezing said steak for some amount of time "t"; and

2) The cost of waiting until time "t" to buy the steak and not freezing it.

I'm also going to assume you wanted the cost of the steak to increase cont ...[text shortened]... s soon as you buy it or it's going to cost you to keep it in the freezer.
But if you kept the steak in the freezer longer than 240.9 years than you could sell the steak for more money than you have paid in electricity costs. The longer you keep it the more money you would make.
4. sonhouse
Fast and Curious
15 Feb '06 00:405 edits
Originally posted by PBE6
The details of the question were a bit unclear, so I'm going to assume you want to compare:

1) The cost of purchasing a steak at \$10, plus the cost of freezing said steak for some amount of time "t"; and

2) The cost of waiting until time "t" to buy the steak and not freezing it.

I'm also going to assume you wanted the cost of the steak to increase cont s soon as you buy it or it's going to cost you to keep it in the freezer.
I was looking for how long into the future the value of the steak
would be exceeded by the value of the electricity.
So if it costs \$175/ year for electricity, then dovide by 12 means it
costs 14 bucks and change per month. So after one month the
electricity is already 40 % more than the steak. So The gist is you
better eat it in the first week!
If you indeed saved the steak for 240 years, you better get more
than 42,010 bucks for it or you will only break even! (175\$/yr X 240 years = \$42,000)
So the gist of it is you wait more than a couple of weeks at that rate,
you are better off eating it and replacing it.
It makes the idea of long term frozen food storage look not so good,
financially. How good an idea is it to freeze food in the first place,
given that cost? You buy that steak for \$10, one week later its up to
\$13.30 or so, the electricity costs \$3.30 odd dollars per week.
So you better shop sales and eat it that night and not freeze it.
the idea being at least I would'nt have to go to the store so much,
but the store is only one mile away, 1/20th of a gallon or so, at \$3
per gallon, 0.15 to get there , 30 cents to make the round trip.
So you save a lot more not running a freezer and just buying new
bread when you need it. Interesting, eh?
Well, Xanth was wrong about the price, the steak would cost
just under \$41,000 so you would lose a thousand bucks on the deal.
2^12 (4096) * \$10= \$40,960 (12 doublings in price)
Thats not even taking into account the fact that inflation would
up the cost of electricity at about the same rate as the overall
inflation rate.
Looking at the added cost in terms of percent per day, its about
5 percent per DAY more to keep it frozen. Thats a price stiffer than
the frozen steak! Imagine if we could get that much interest at the
bank! Of course we are giving an example of a single steak, when
the average freezer could hold, say, 50 steaks, so 500 bucks worth
that goes up at the rate of one tenth of a percent per day.
So at the end of one year, the steaks now costs 675 bucks.
Still about 35 percent per year.
5. PBE6
Bananarama
15 Feb '06 02:41
Originally posted by sonhouse
I was looking for how long into the future the value of the steak
would be exceeded by the value of the electricity.
So if it costs \$175/ year for electricity, then dovide by 12 means it
costs 14 bucks and change per month. So after one month the
electricity is already 40 % more than the steak. So The gist is you
better eat it in the first week!
If ...[text shortened]... .
So at the end of one year, the steaks now costs 675 bucks.
Still about 35 percent per year.
This entire argument is flawed. There's no accounting for food spoilage, food quality, bulk savings, time or convenience, your travel costs and freezer use model are incomplete at best, your economic model would have us spending wheelbarrows full of cash on a chocolate bar, and on top of all that Bowmann was right - you are pretty verbose. I felt like I had ADD reading that gigantic paragraph.ðŸ™„

As a math problem it was a neat question, but it's not transferable to the real world without major tweaking. If you live beside a farm field, farmer's market or grocery store, then throw out your fridge by all means. The rest of us will keep ours.
6. XanthosNZ
Cancerous Bus Crash
15 Feb '06 02:42
Originally posted by sonhouse
Well, Xanth was wrong about the price, the steak would cost
just under \$41,000 so you would lose a thousand bucks on the deal.
2^12 (4096) * \$10= \$40,960 (12 doublings in price)
Actually if we assume that steak increases in price smoothly rather than stepwise (it doesn't sit at one price for 20 years and then instantly double it instead increases along a growth curve [the one PBE6 used]) then my answer is correct.

240.9 years is 12 doublings plus another small multiplier (the 0.9 of a year), as the price is very large by this point it accounts of nearly 1300 dollars.
7. 15 Feb '06 04:361 edit
Originally posted by XanthosNZ
Actually if we assume that steak increases in price smoothly rather than stepwise (it doesn't sit at one price for 20 years and then instantly double it instead increases along a growth curve [the one PBE6 used]) then my answer is correct.

240.9 years is 12 doublings plus another small multiplier (the 0.9 of a year), as the price is very large by this point it accounts of nearly 1300 dollars.
I don't know any steak supplier whose price is a smooth continuous curve. In the real world it will always be piecewise.

But this question certainly has no use in the real world....
8. sonhouse
Fast and Curious
15 Feb '06 12:541 edit
Originally posted by PBE6
This entire argument is flawed. There's no accounting for food spoilage, food quality, bulk savings, time or convenience, your travel costs and freezer use model are incomplete at best, your economic model would have us spending wheelbarrows full of cash on a chocolate bar, and on top of all that Bowmann was right - you are pretty verbose. I felt like I had A et or grocery store, then throw out your fridge by all means. The rest of us will keep ours.
Sorry about the long post, had thoughts one after another, and they
I guess the same could go for fridges but it points out the importance
of advancing the science of refrigeration. The best of the new freezers
actually take a lot less than 200 watts to run, better insulation, more
efficient heat pumps, etc. I hear numbers now like 50 watts, a small
which saved my butt on a job at Lucent, but thats another story.
9. 22 Feb '06 23:14
Originally posted by sonhouse
You have a freezer, it can store food indefinitely, great freezer.
It takes an average of 200 watts (0.2 Kw) to run.
Electricity costs 10 cents a KWH (US\$) Now you buy a steak for
10 bucks. The inflation rate is 5 percent per year, that means the
price doubles in 20 years, so twenty years from now, that same steak
will cost 20 bucks. So here is the pu ...[text shortened]... o decide
to eat the steak because it will soon cost more to keep it frozen than
to replace it.
"Ok", a question for you, why do you start a the title with "ok"? What are you agreeing with or is it superfolous?!
10. sonhouse
Fast and Curious
23 Feb '06 04:15
Originally posted by Silver Slayer
"Ok", a question for you, why do you start a the title with "ok"? What are you agreeing with or is it superfolous?!
Well I am not sure if its just Folous or as you say, SUPER folous. Its
a mystery. It can folous both I think.
11. 23 Feb '06 17:43
Also the question fails to address the compounding effect of inflation.
Inflation is not calculated at the original base year but the preceeding year which already has infaltion in it.

This results in the 5% inflation doubling the cost in 15.5 years, not 20.
12. XanthosNZ
Cancerous Bus Crash
23 Feb '06 18:36
Originally posted by Bishopcrw
Also the question fails to address the compounding effect of inflation.
Inflation is not calculated at the original base year but the preceeding year which already has infaltion in it.

This results in the 5% inflation doubling the cost in 15.5 years, not 20.
Sonhouse can't do math.
13. 23 Feb '06 20:52
Originally posted by XanthosNZ
Sonhouse can't do math.
I wouldn't say that,

But he does like his balloonsðŸ™‚
14. sonhouse
Fast and Curious
26 Feb '06 04:32
Originally posted by XanthosNZ
Sonhouse can't do math.