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Source link: http://archive.mises.org/6993/why-people-walk-on-stairs-and-sometimes-stand-on-escalators/

Why People Walk on Stairs and Sometimes Stand on Escalators

August 15, 2007 by

Here is the problem, according to Steven Landsburg:

Taking a step has a certain cost, in terms of energy expended. That cost is the same whether you’re on the stairs or on the escalator. And taking a step has a certain benefit — it gets you one foot closer to where you’re going. That benefit is the same whether you’re on the stairs or on the escalator. If the costs are the same in each place and the benefits are the same in each place, then the decision to step or not to step should be the same in each place.

In other words, a step either is or is not worth the effort, and whatever calculation tells you to walk (or not) on the escalator should tell you to do exactly the same thing on the stairs.

Landsburg’s solution is that

before you can weigh costs against benefits, you’ve got to measure the benefits correctly. And in this case, “getting one foot closer to where you’re going” is the wrong way to measure benefit. Who cares how close you are to where you’re going? What matters is how long it takes to get there. Benefits should be measured in time, not distance. And a step on the stairs saves you more time than a step on the escalator because — well, because if you stand still on the stairs, you’ll never get anywhere. So walking on the stairs makes sense even when walking on the escalator doesn’t.

It is easy enough to understand why people walk on stairs yet joyride on escalators all the way:

Benefits of Walking Costs of Walking
Escalator 30 seconds ≅ ¢33 gained Physical exertion
Stairs Got to destination ≅ $100 gained Physical exertion

Clearly, the total profit/loss of walking on stairs differs from the profit/loss of walking on an escalator, assuming as I do that the benefits of each action in terms of money are reasonably determined. But why do people make the marginal steps? Here is what Rothbard has to say about it:

For example, it is erroneous to argue as follows: Eggs are the good in question. It is possible that a man needs four eggs to bake a cake. In that case, the second egg may be used for a less urgent use than the first egg, and the third egg for a less urgent use than the second. However, since the fourth egg allows a cake to be produced that would not otherwise be available, the marginal utility of the fourth egg is greater than that of the third egg.

This argument neglects the fact that a “good” is not the physical material, but any material whatever of which the units will constitute an equally serviceable supply. Since the fourth egg is not equally serviceable and interchangeable with the first egg, the two eggs are not units of the same supply, and therefore the law of marginal utility does not apply to this case at all. To treat eggs in this case as homogeneous units of one good, it would be necessary to consider each set of four eggs as a unit. (Man, Economy, and State, 73ff)

Another example. Suppose it costs $1 to buy a candy bar. I start giving you pennies, one after another. First you have 1 penny, then 2, …, then 99. No matter how many you have so far, you can’t get what you want. Whether you have 1 penny or 99 doesn’t make a difference. But now I give you the 100th penny, and suddenly you have the means to obtain the candy bar. It’s no longer merely more of the same — the situation is qualitatively different. Does it mean that the 100th penny has more utility than any other penny or even the first 99 pennies? Rothbard would probably argue that the 100 pennies constitute one marginal unit. But out pops Landsburg and asks our Austrian school hero why it was in his interest to get penny #46, say. Landsburg explains that it was because that penny reduced the number of pennies still needed to buy the candy bar by 1. And that (he says) is its utility.

Even more simply, suppose that in order to make some product P you need 25X + 3Y + 8Z; these factors are perfectly specific; and you can’t sell them. If you obtain 15X or even 25X, 3Y, and 7Z, is there a benefit to you? On the one hand, in the latter case now you only need somehow to procure 1Z to make the product. (Suppose you are making the factors by hand; you’ve worked for several days, and now you only need to spend 1 more hour to manufacture the remaining 1Z.) On the other hand, the factors are still useless. In a way, the making of the factors will be shown to have been useful only after P is built. If you change your mind and decide to abandon the project at the last minute, then your 25X, 3Y, and 7Z will sit there doing precisely nothing. So, an Austrian economist could reasonably proclaim {25X, 3Y, 8Z} to be the marginal unit.

Lastly, it is true that the journey of a thousand miles begins with a single step. But even if you have completed 99.9% of the journey, the final mile is just as important as the 999 miles you have already traveled. Again, the 1,000 miles would be the marginal unit, because only when you’ve reached your destination does all your effort pay off.

The marginal unit in Landsburg’s example then is the whole staircase/escalator. And the reason why it makes sense to walk on stairs and sometimes to stand on an escalator is simply that in the former case the benefits ($100) may outweigh the costs, while in the latter case, the costs may outweigh the benefits (¢33), the costs being the same in both situations. (Don’t misunderstand, the profit of getting to your destination on the escalator is $100 as opposed to not getting to your destination, if you do not walk; and the same profit on the stairs is ($100 – the cost of physical exertion), assuming that you walk as fast as the escalator moves. So, it is good to have an escalator.) In addition, walking on stairs is essential to reaching your end, while walking on an escalator is not. Our author concludes that

Every producer knows that workers should spend less time with inferior machinery. Compared to an escalator, a staircase is an inferior machine, so the “workers” — that is, the people who use the stairs — should try to minimize their time there. The way to limit your time on a staircase is to keep walking until you get to the end.

But in saying that he implicitly acknowledges that it is surmounting the whole staircase that is the goal, and therefore the whole staircase is the marginal unit.

Finally, Landsburg writes that “The same argument proves, incidentally, that even if you choose to walk on the escalator, you should always walk even faster on the stairs.” On his own terms, clearly it does not so prove, because the faster you walk, the greater, presumably, the cost of walking per step. On our terms, the psychic profit of walking on an escalator can be compared with the psychic profit of not walking on the escalator (and doing something else instead), and similar for stairs, but it makes no sense to compare the profit of walking on an escalator with the profit of walking on stairs: it is not a choice with which one can meaningfully be presented.

A final objection. Why do we seemingly arbitrarily set the marginal unit to the whole staircase, rather than, say, to half the staircase, or to a single step, or to the staircase + the distance to wherever you may still be going after you have climbed our stairs? The answer is that we are dealing with ends and means. Climbing the staircase is the end, attaining which, we assume, will give one a certain amount of satisfaction, while claiming half the staircase or a single step will not. Here each step is merely a means to the end, and its value is wholly derivative from the end. If we had set making a single step as the end sought, then each step would indeed be the marginal unit. If we had set staircase + some further distance to be the goal one is trying to reach, then that entire thing would be the marginal unit.

To go with Rothbard’s example again, we are not confusing the cake as the marginal unit (1 cake, 2 cakes, …) with the 4 eggs as the marginal unit (4 eggs, 8 eggs, …). Both can be such in various circumstances, and if the eggs are essential to baking the cake, the two are all but interchangeable.

{ 11 comments }

Don Lloyd August 15, 2007 at 4:23 pm

Dimtry,

I have traveled on actual escalators, and sometimes I walk and sometimes I just go along for the ride.

In my judgement, your ends are too comprehensive to be the determining factor.

Let’s assume that you are on an escalator and that you have a wireless remote control that controls the speed of the escalator with a three digit display setting of 0 to 999 steps per second. Assume that there is no subjective cost for setting any of the 1000 choices. Unless you decide to set the speed to 999 steps per second, you cannot claim that low travel time is your ultimate end.

In practice, your rate of climb on an escalator may be either too fast or too slow for subjective comfort. With the remote control, you just set the speed which feels closest to just right. Without the remote control, you have the choice of adding a physical climbing rate to the escalator rate, but not without an exertion cost.

For simplicity, assume that a normal stair climbing rate is one step per second. Assume that the inherent rate of climb of the escalator is also one step per second and you have no remote control.

Your choice is whether to add a climbing rate of one step per second to the escalator rate of one step per second to get a total rate of two steps per second.

This is a simple demonstration of the law of diminishing marginal utility. Adding one speed unit to an existing one speed unit is less valuable than adding the same unit to the starting zero rate of the stairs or a stopped escalator.

Regards, Don

Dmitry Chernikov August 15, 2007 at 9:29 pm

So, in your opinion, the marginal unit is not the distance or time saved with each step, but speed. This is an interesting solution. The first unit of speed is used to satisfy the most urgent desire, which I presume is getting to your destination; while the second unit is used to satisfy the second most urgent desire (or third, after, say, riding and reading a newspaper) which is saving 30 seconds.

Jim August 15, 2007 at 10:34 pm

Wouldnt’ you say that the marginal unit is simple a set of stairs? On my way to my office, I walk up a set of stairs, 50 to be exact. Yet,I only consider the set of stairs as the marginal unit.

If I needed a hammer to pound a nail, I would even consider the individual fibers of wood that make up the handle. I want a hammer: the marginal unit.

One can also introduce a concept similar to sunk costs: If I am to breakdown each step as a separate means, once I have taken a step it is history and no longer a point of action. So, I never compare the 99th step to the 98th step once I have taken the 98th step. That step is a, so to speak, sunk cost.

Therefore, if you were to impede my progress at the (say) 100th step of 100 steps, my value of that step in this instance would be the full value of what I obtain by taking it, less costs associate with the step (alternative costs included).

So, it may appear that the 100th is valued higher than the 99th step. But, the 99th step has been taken and is no longer subject to action. My preference rank reshuffle at each step taken.

Don Lloyd August 15, 2007 at 11:48 pm

Dmitry,

So, in your opinion, the marginal unit is not the distance or time saved with each step, but speed. This is an interesting solution. The first unit of speed is used to satisfy the most urgent desire, which I presume is getting to your destination; while the second unit is used to satisfy the second most urgent desire (or third, after, say, riding and reading a newspaper) which is saving 30 seconds.

Not really.

The purpose of eating is prevent starvation. But the consideration of this end is of little relevance in deciding whether to take a second helping of potatoes at the dinner table.

Regards, Don

Person August 16, 2007 at 8:17 am

Dmitry_Chernikov: Good post. I think you summarized well one of the problems I had with Murphy’s and Landsburg’s analysis of the issue. Their determination of the marginal unit was questionable, but I had a hard time spelling out why precisely.

For another example, you could consider it a “mystery” why people mow their lawns (walk) when they *haven’t* hired someone to do it regularly (stairs), but not when they *have* hired someone to do it regularly (escalator).

Bill Barnett August 16, 2007 at 12:46 pm

The only reason that the “problem” arose was because Landsburg et al. framed the issue incorrectly from the beginning. The answer to their question: “If people stand still on escalators, then why don’t they stand still on stairs?” does not depend, as they thought it did, on a correct application of marginal analysis. Rather, the answer depended on a correct application of the concept of opportunity cost.
The alternative to standing still on an escalator is to walk on the escalator. The alternative to not walking on stairs is to walk on stairs. Assuming, as seems reasonable, that if one walks on an escalator one walks in the direction that the escalator is moving, and arrives at the destination sooner rather than later, in which case one will walk if the time saved is more valuable than the effort saved by not walking. In either case he gets where he is going, which, it is natural and reasonable to assume, is the primary objective. That is, the alternatives to be considered are: 1) standing still on the escalator and getting to one’s destination in an elapsed time of x seconds; or, 2) exerting the necessary effort in the form of walking on the escalator and getting to one’s destination in less than x seconds. In contradistinction, if one does not walk on the stairs he does not arrive at his destination, assuming that was the purpose of his being on the stairs in the first place. However, if one walks on the stairs he will arrive at his destination. That is, the alternatives to be considered are: 1) standing still on the stairs and never getting to one’s destination; or, 2) exerting the necessary effort in the form of walking on the stairs and getting to the destination.
Therefore, we see that people “always” walk on stairs, else they won’t arrive at their destinations, whereas people on an escalator always arrive at their destinations whether or not they walk. Consequently, an individual walks only if and when the effort put forth to arrive at the destination sooner has a value to him that is less than the value of the time saved.

Dmitry Chernikov August 16, 2007 at 2:47 pm

Murphy talked briefly about this puzzle in one of his lectures at Mises University, but I did not realize that he had his own solution to it. I quite like his neoclassical take on it, except for two small details: (1) k is a variable, so he should’ve said that the total number of steps is “n” = 10, not k = 10 (otherwise it’s a bit confusing); (2) it may be a good idea to stress a little more that the utility of being on the kth step of the stairs is k*10, because the utility of reaching the destination while being on the kth step of the stairs is k*10.

In the Austrian solution he says that “The answer of course is that a pool with X gallons of water in it is a different good to Joe than it is to Sally. For Sally, a pool filled halfway with water has the same value as a pool full of water, since the former is a means to the latter.” It seems to me that the pool filled halfway with water has no value at all, much less the same value as a fully filled pool. It is true that Sally’s pool will fill “by itself,” and so seemingly an empty pool and one which is full of water are equally serviceable, i.e., have the same utility: V,e(k) = 100 for every k. But by saying that Murphy harks back to his neoclassical solution which ignores time and uncertainty. Sally might choose to use buckets of water in addition to using the hose in order to save some time. Murphy realizes something so obvious, of course: “if Sally has guests coming over for a party, a pool filled halfway may not be the same as a full one. But this is true in the staircase example too; if someone is rushing to catch a plane, he might run up an escalator.”

A pool filled halfway can be called valuable only if it is certain that it will be fully filled in the future. In the case of such certainly, is it true, as Murphy says, that “a pool filled halfway with water has the same value as a pool full of water”? Or am I right in saying that “the pool filled halfway with water has no value at all”? Or is its value somewhere in between?

Mike August 20, 2007 at 1:37 pm

Leave it to economists at top universities to devote enormous amounts of time and effort to asking and answering a question that has no basis in the real world: If people stand still on escalators, then why don’t they stand still on stairs?

The simple answer is “They don’t so why bother explaining it.” People, of course, walk on escalators, stand on stairs, walk halfway up sets of stairs then go back down, walk the wrong way on escalators, choose to walk up stairs even when they are beside an escalator, and even spend significant portions of their lives taking steps on machines that don’t get them anywhere.

It’s no surprise that a nonsensical question begets a nonsensical answer. The folly is in trying to explain the “average man” who is a phantom, as Jim Fedako pointed out in his article “Forgotten at the Door”. I think the question asked implies “average man” and, thus, the answer has no significance as an explanation of why real human beings act in certain ways.

Dmitry, I think you are falling into a similar trap. You seem to want to assign value to the amount of water in the pool in terms of utils, which also have no basis in the real world. There is no objective value for a half full pool at all, only the subjective value of the owner.

You have missed the most important part of what Mr. Murphy said: “*For Sally*, a pool filled halfway with water has the same value as a pool full of water, since the former is a means to the latter.”

Sally’s valuation is only revealed through her actions, and the value she assigns to any end is just her ordinal ranking of that end amongst the various alternatives at that time. If Sally leaves the hose to fill the pool, as in the example, her actions tell us that she considers other things more valuable that saving time filling the pool.

You mistakenly try to insert “utils” into the Austrian example when Mr. Murphy left them out for a reason. Sally may indeed begin carrying buckets of water to the pool or she may shut off the hose and drain the water she has already put in. Her actions simply reveal the subjective and ever-changing nature of her value scale not her attempt to obtain an objective value by the most efficient means.

Mike

John Delano August 22, 2007 at 1:53 am

There’s nothing wrong with thinking about these things, Mike. It looks like you bothered to read it.

In reality, an escalator is often full of a crowd of standing people while the stairs are empty, and I can run up them in a fraction of the time I would be staring at the back of someone on the escalator ride.

Mike August 22, 2007 at 1:24 pm

John,

In reality some people, few as they may be, simply prefer stairs to elevators. I disagree that there is nothing wrong with thinking about economics in the way that Landsburg and his colleagues do. Ideas have consequences and they pass theirs on thousands of students each year. Students who have been taught that marginal analysis can be applied in this manner and that value can be measured any more than love go out into society with the idea that public policy is a great tool for improving economic efficiency. How much suffering has this caused in the world?

Mike

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