Wednesday, April 18, 2007


Here's an update to my previous post, explaining some of the things I left out.
I assume that Hockett used the formula for the Average Total Cost to create the graphs in the original graph. I used the formula found at

Average Total Cost = Fixed Costs/Quantity + Variable Costs

In the case of the ceramic mug, that would be AC = 14/Quantity + 0.18 since each mug costs 14 mj to make and 0.18 mj to clean after each use. Here are the other formulas I used to recreate the graph:

Foam: AC = .2 (There are no variable costs, and a new foam cup is used every time)
Paper: AC = .55 (See foam.)
Glass: AC = 5.5/Quantity + 0.18
Plastic: AC = 6.3/Quantity + 0.18

To find the area under the curve for, I used an Excel plug in from down to "PK Functions for Microsoft Excel".

You can use the area under the curve numbers to calculate just how many mjs you would save by using ceramic, glass, or plastic instead of foam or paper.

Using a ceramic mug twice a day for about 2 years will save 1,639 MJ over using foam cups. That's a savings of 8,195 foam cups (1639/.2)! Still, your better bet is the plastic coffee mug which saves you 13,112 MJ over those 2 years--65,560 foam cups!

See Peter's correction in the comments!


Peter said...

I don't understand how you're getting to your conclusions.

Using a ceramic cup twice a day for two years uses this energy:

14 MJ + (0.18 MJ * 2 * 2 * 365) = 276.8 MJ

Using foam cups consumes:

0.2 MJ * 2 * 2 * 365 = 292 MJ.

The difference is equivalent to 76 foam cups.

liberal elite said...

Doh! You're right. I was calculating the area under the curve. That's a running total of all the average costs. But I should have just been looking at the final points for both curves.
I knew I was going to make a mistake. Thanks!

liberal elite said...

I realize now what confused me. The area under the curve is the total energy cost for the foam cup because it's a flat line. The final point is the upper right-hand corner of a rectangle, whose area gives you the total energy used:
Total Cost = .2 * Quantity.
However, the area under the Ceramic curve is not the same as the total energy cost since the Average Total Cost changes with the number of uses.
Total Cost = 14 + .18 * Quantity.
Again the final point on the Total Average Cost curve is the upper right-hand corner of a rectangle whose area is the total energy cost.

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