Robert Samuelson fails first grade math

Even philosophy major Matthew Yglesias is offended by the mathematical failings of Robert Samuelson, who writes that "If you move to a home 25 percent larger and then increase energy efficiency 25 percent, you don't save energy." But as Yglesias points out, 1.25*.75=.9375, which is less than 1. Ouch.

PS Yglesias later noted that "irrespective of mathematical quibbling, Samuelson's gotten the physics of home energy use wrong. Energy usage should grow proportionately to the surface area of your house, not to its volume."

Comments

[ERF]

Hello Brenden Nyhan.

A hypothetical: If you install more efficient light bulbs (in your new 25% bigger house) which let you run 125 bulbs for the same total wattage as 100 of the old style bulbs, is it incorrect to say you have you achieved a 25 percent efficiency improvement?

If it is not imcorrect, then you and Yglesias have a retraction and and apology to write.

The point is the phrase "a 25% improvement" does not have to mean only what you two say it does, even in first grade math.

[Howard]

I agree with ERF (at least in part).

Samuelson is simply saying that if efficiency improves but usage increases to an equal degree (in terms of total absolute consumption) then there is no reduction in net usage.

But I don't think he's owed an apology. The piece was poorly written (or poorly edited). The entire article is filled with contradictory arguments.

It's good to show there are costs or limitations associated with a certain plan or program, but he has a tendency to denounce the same things he advocates.

Here is just one example. He is favor of less reliance on foreign oil but in his discussion of ethanol (which serves to meet that goal) he omits that point and notes that it doesn't reduce net consumption. Correct, it's an alternative fuel.

He says its use increases corn prices. Correct, but it probably lessens fuel-cost inflation.

He says it moves capital flows (profits) from one area to another (oil suppliers and refiners to ethanol suppliers and refiners). Sure. It's a different product. And is that a bad thing? Is having capital moving to our Mid-West region worse than having it move to Mid-East Gulf Region?

He says it doesn't reduce emissions. Correct, it's an alternative fuel, not necessarily a "cleaner fuel".

OK, ethanol is not a magic bullet, but it's a step toward energy independence.

It's a frustrating read because, like ethanol, every plan is presented as being both "too much" and "not enough" at the same time.

[Marie]

A hypothetical: If you install more efficient light bulbs (in your new 25% bigger house) which let you run 125 bulbs for the same total wattage as 100 of the old style bulbs, is it incorrect to say you have you achieved a 25 percent efficiency improvement?

Well, yes ERF, it is incorrect.
Let's say that S is the size of your old house and S' the size of your new house. We have:
S'=S*1.25
Let's say that P is the total wattage of the light bulbs in your old house. P' is the wattage in your new house. The total wattage is the same in both houses, therefore:
P'=P
The efficiency is defined by the total wattage divided by the size of the house. The efficiency of the new house is:
P'/S'=P/S'=P/(S*1.25)=(P/S)*0.8
You've actually decreased the efficiency of your place by 20%.
So, in short, keep the old house, get the new light bulbs.

[Howard]

Marie -

Your math shows that the increase in lights between the old house and the new house is equal to 20 % of the ending number of lights.

The fact that there was an increase in actual lights (where the old number of lights was 80% of the level of new number) really says nothing about energy efficiency, as the term is used in economics or in the original article.

Efficiency here looks at out-put (heat, light, transportation, etc.,) for a certain fixed level of energy input.

You are more addressing issues related to consumption, which is clearly the driving factor in energy use, but is generally considered separately from efficiency.

----

As to the original math question, Yglesias is correct and Samuelson was wrong in the way he made his statement (he should not have said one percentage increase will offset another equal percentage decrease).

ERF re-phrased Samuelson using a valid mathematical statement (although it wasn’t really what Samuelson had said - it was an improved version).

But ERF's restatement seems pretty clearly to be what Samuelson had intended to say from the start.

[ERF]

Hello again,

Commenter Howard understands my earlier point, but I think he put it better.

What Samuelson is clearly trying to say is that if you build a new, bigger house which you make energy efficient enough so the new house's total energy use is the same as your old house's, you won't save energy.

Samuelson said it in a way that, while not incorrect, could be intentionally misunderstood by those looking to nit-pick.

When I said Nyhan / Yglesias owed Samuelson an apology, I meant the apology was due only because Samuelson's little statement was not incorrect as they claimed. As for their beefs on the rest of his piece, hey, this is the internet; criticism is what it's all about. No apology required for expressing a differing opinion.

My opinion is that over the last 30+ years we have been ridiculously ineffective in moving our country toward energy independence. Both political parties have failed in this clearly needed area.