David R. Henderson  

The Marginal Cost of Perfection

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In my Executive MBA class, I use The Economic Way of Thinking by the late Paul Heyne, Peter Boettke, and David Prychitko. In a recent problem set, I used a question from the chapter on externalities. The authors have a graph with $ cost per car per year on the vertical axis and percentage reduction in emissions on the horizontal axis. The curve is exponential. Here's the question I asked:

Why does the curve rise slowly at first and then rise more steeply as the percentage reduction in emissions gets closer to 100%? Is this a peculiar characteristic of automobile exhaust-control systems or is it a more general relationship? Explain.

One of my students, a Navy doctor, gave this answer. [She gave me permission to use it.]

Perfection is unattainable. The more you work at reducing emissions there is diminishing marginal productivity. The closer you get to perfection the harder it gets to attain it and this costs more money. This is a general relationship--for example in screening for cervical cancer at Naval Hospital Camp Pendleton. 1 year ago we had 6300 patients who needed to be screened. We added special clinics on the weekends three times a year, called the patients and sent letters. We have successfully brought this number down to 182 people needing to be screened. Although we have fewer patients to be screened, more hours are being spent concentrating on trying to get those people in than it took to get the other 6000. The closer we get to the >90% screened, the harder it is to get those last 182 patients in. My recommendation has been to change the screening goal as we are wasting valuable to time and money on people who obviously do not want to help us prevent them getting cervical cancer. Unfortunately, BUMED [The Navy Bureau of Medicine and Surgery] sees it differently.


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COMMENTS (19 to date)
Gorgasal writes:

I have heard this (trying to get from 98% to 99% perfection, expending inordinate amounts of resources) being referred to as "polishing one's asymptotes" (Asymptotenpoliererei in German, with a clear derogatory undertone)...

Mark Brady writes:

"My recommendation has been to change the screening goal as we are wasting valuable to time and money on people who obviously do not want to help us prevent them getting cervical cancer."

Rather condescending, eh?

Bill Nichols writes:

There is a more or less generalizable relation that one sees in Pareto type distributions (the so-called 80/20 rule).

As you approach perfection, 100%, imagine that the next factor of 2 in performance (e.g. 98% to 99% say) costs the same as the previous halving(96% to 98%). The return (1%) is only half the previous return (2%). Repeat a few times and very quickly, the next improvement yields a microscopic return.To try this out, multiply the number 2 by itself ten times and see what you get! This diminishing return applies to getting a perfect vacuum, obtaining absolute zero, HEPS air filters, vehicle emissions, or vacuuming your carpet. There is less return because for each increment there is less remaining to be removed, but costs are proportional to the ratio, not the absolute.

But it's worse. In practice, this is an overly optimistic scenario because it usually takes more than twice the cost for the factor of 2 improvement.

Engineers recognize the maxim, "Perfection is the enemy of the good enough!"

RPLong writes:

I agree with all of the above, but would add that in some cases, achieving a new level of perfection at significant expense is an act of entrepreneurial investment/discovery.

In some cases, there may be significant return on investment for achieving a new level of perfection. (But of course I have to bring in exogenous factors to demonstrate...)

Rick Hull writes:

Mark,

I think the doctor was pandering to BUMED's paternalistic stance with the tone employed. Tongue-in-cheek, if you will.

David R. Henderson writes:

@Mark Brady,
I couldn’t detect the condescension that you perceive. I think the tone was more of frustration.

Silas Barta writes:

Interesting anecdote. That said, I don't think thing that having zero net vehicle emissions is impossible, as we would expect of "perfection".

Also, I have to say that one setence grates on me. This:

"The more you work at reducing emissions there is diminishing marginal productivity."

should be

"The more you work at reducing emissions, the lower the marginal productivity of efforts to do so."

or

"Work at reducing emissions runs into diminishing marginal productivity."

or even

"The more you work at reducing emissions, the more marginal productivity diminishes."

if you want to make a claim about increasing rats of change. As it stands, she shifts from one of the above to another halfway through.

joeftansey writes:

Totally disagree. This behavior is specific, not general. There is no a priori reason why a certain property would become more difficult to obtain as you move towards greater concentrations.

For example, the largest cost may be simple fitting a filter on cars. Improving this filter once you already have it may or may not be more expensive than the initial cost of having it.

A more physical example is fire. It has a large initial cost, but then the reaction snowballs and eventually becomes self sustaining (zero cost).

Its just that we don't readily see examples of this in industry, because if you ever got a "fire" type reaction, companies would have carried it out to its maximal benefit to the consumer. No company is going to say "yeah it costs $1000 to produce the product, and only $0.01 to make it a little better, so that we can make a perfect product for $1005, but we stopped at $1003 for no reason".

They probably exist, but they're likely to be rare for this reason.

I also reject the idea that you can always improve on a product or outcome. Anything with fractal behavior is going to have an irreducible residual error associated with it. If you think this is obscure, just consider that a significant number of our genes exhibit fractal behavior. The weather acts like this too.

So it doesn't make sense to even draw the graph out past a certain point. Extrapolating past where you have actual data is like walking off a cliff.

David R. Henderson writes:

@joeftansey,
The question was not whether this kind of pattern is general; the question was whether it’s “more general.” It is, as her example showed.

joeftansey writes:

Its not general if it depends on the specifics of each individual case. Just because you have n-many examples of a phenomena doesn't mean it can't be particular. The phenomena is emerging from within the production process itself, not running up against a general problem in human endeavors.

Put differently, your framing of the question is basically just asking whether or not we can change the x-axis of the graph while maintaining plausibility. But you can do this with virtually any graph. Does this mean all phenomena are general?

RPLong writes:

joeftansey,

First, you say that diminishing process productivity is not a general phenomenon.

Second, you say that not every product or outcome can be improved upon.

Doesn't your second statement imply the first statement?

joeftansey writes:

n>1 does not imply general phenomenon. You might get that curve because the technological requirements become more complex, because of spatial constraints, because of regulations, etc. Difficulty or inability in improvement depends on that product's specific production process. Whether or not you get this exponential curve depends on the specific (read: not general) things going on in production.

Bryan Willman writes:

It's a very common phenomenon.

The medical example cited is a classic - what about the people who refuse that treatment?
Anytime anybody says "everybody will want this" I always know they are either confused or being sloppy with the word "everybody".

As for techology issues like air pollution control on cars, at what point does the environmental burden of the electric generation, more complicated factories, more materials to be processed for the car, etc. outweigh the reduction in burden from the car itself?

Oh, and the "double the price for only a little gain" is rampant at any particular technology level in the computing industry. Of course, in 18 months you'll likely get double the gain for the same price.

SkippyMaximus writes:

This exponential cost is the same reason why the program "No Child Left Behind" should be called "The Money Pit".

The cost of "not leaving behind" those last few percentages of children would theoretically bankrupt the education budget.

If we accepted this proposition, that the last percentages have exponential costs, is it fair to the rest of society to ensure "no one is left behind"? Is it fair to bankrupt a society to meet an unrealistic obligation? If so, this presents lots of questions to lots of issues that face our country.

Should Social Security cover everyone, if covering the last few percentages of people has an exponential cost?

Should Medicare cover all elderly, if covering the last few percentages of people has an exponential cost?

Should countering every possible terrorist plot against the U.S. be executed, if countering the last few percentages of terrorists has an exponential cost?

Maybe it's a flawed assumption, as joeftansey infers. But what if it's not? Now that's worth discussing.

Mark Brady writes:

@ Rick Hull

Perhaps your charitable interpretation is correct, although that's not how I read it.

In any event, it's a widespread attitude among the medical profession, particularly among government doctors. Like all government employees, their attitude is "We're the government, and we're here to help" with the unstated follow-on "and if you know what's good for you, you'd better like it."

It's worth pointing out that there are good reasons to refuse screening for cervical cancer. For a few, go to the National Cancer Institute's statement on the risks of cervical cancer screening.

Bill Nichols writes:

@joeftansey :
If you don't like the term general, how about broad class?

...There is no a priori reason why a certain property would become more difficult to obtain as you move towards greater concentrations."

For example, the largest cost may be simple fitting a filter on cars. Improving this filter once you already have it may or may not be more expensive than the initial cost of having it.

Auto emissions (and fuel consumption!) are perfect examples of diminishing returns. Zero emission is hard, as is burning ALL the fuel. We have a catalytic converter specifically to deal with the incomplete burn. Even a forest fire won't take every iota of potential fuel before petering out.

The central limit theorem for normal and log-normal distributions applies to very broad classes of phenomena. Most processes have some intrinsic variation resulting from limits of tooling, variation in the inputs, inconsistency in the use, or Brownian motion. They also usually run into constraints of scale. Where multiple factors apply the effects can be additive or multiplicative. The specifics will vary, and there may some exceptions, but if you want to make betting odds, your Baysian prior better not be 50%.


Jay writes:

The first 90% of a job takes the first 90% of the time.

The last 10% of a job takes the other 90% of the time

Jonathan Guthrie writes:

joeftansey, while the tendency may not be universal, there is a reason that most people know what the term "diminishing returns" means. I'm actually surprised that it took a number of comments before that term appeared because that is the first thing I thought of when reading the article.

In fact, there's also a reason why the article has two concrete examples of the phenomenon and you have to make up a hypothetical counterexample. It's really dang common in the real world.

The fact is that while initial steps for doing anything are often easy, once you do the easy things, you're left with more difficult things. To riff off your "add a filter" example, okay you've added a filter and done all the easy things, now what? Well, you could use a better filter, but you already used the best filter you know how to make, so you need to learn to do better, and that requires research and time and effort. This isn't time and effort you needed to spend with the first step, so the second step is harder.

Maybe you've managed to achieve a perfect filter, so now you have to figure out why the system works better with the filter so that you can replace it with something else. You may have to invent new theories to explain the phenomena that you observe where before you could use a heuristic approach. All that requires far more effort than what you did initially. Invention tends to follow a pattern of slow innovation in the beginning, while people figure things out, then rapid invention while people use an improved understanding to expand the immature technology, and then slower innovation at the end while the number of easy things decreases.

joeftansey writes:

@Bill,

"If you don't like the term general, how about broad class?"

What I don't like is that the question implies that there's the same "thing" going on whenever you have an exponential curve. But as I pointed out above, there's no reason to expect the curve to have that particular shape over any other shape, and multiple things can cause the curve to be exponential like that.

The "right answer" is supposedly derived from observing that N>1, which sounds (and is) too good to be true.

"Auto emissions (and fuel consumption!) are perfect examples of diminishing returns. Zero emission is hard, as is burning ALL the fuel."

Actually you could achieve zero emissions by just not driving. So the cost for "perfection" in emissions is just whatever the opportunity cost of not-driving is.

But even if you don't buy that, if you agree that driving must cause *some* emissions, costs can't be said to increase exponentially because there simply is no cost associated beyond a certain point on the curve.

"The central limit theorem for normal and log-normal distributions applies to very broad classes of phenomena."

And the central limit theorem (of what property...?) doesn't matter because it doesn't say anything about whether the largest marginal costs occur at the start of the curve or at the end. Observing that there might be different factors of production pulling in different directions just gets us to ask "whats the net?". It doesn't imply an exponential curve.

Consider an apocalyptic future where steel and oil are very scarce resources. Building a car PERIOD might be very costly, but fitting it with supercomputers and an efficient engine may add very little relative cost to the car.


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