Dmitry Chernikov’s Blog

Why People Walk on Stairs and Sometimes Stand on Escalators

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:

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 similarly 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.

Note that, 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.

This entry was posted on Wednesday, August 8th, 2007 at 5:50 pm and is filed under Economics. You can follow any responses to this entry through the RSS 2.0 feed. You can leave a response, or trackback from your own site.