PTP #15
From Landsburg, again
Some people stand on escalators; some people walk. Some people do a little standing and a little walking—and of those latter people it is almost always in that order: stand first, walk toward the end. Why is that? Why do people walk in the second half of their escalator trips?
Or an adjacent question, as Landsburg puts it: why do people stand still on escalators but not on stairs?
If I may editorialize: I posed the question to a friend, and she rightly pointed out that “it would be crazy” to walk the first half and stand the second half of an escalator trip. Think about doing it yourself! Philip Wicksteed uses the line from Goethe as an epigraph to The Common Sense of Political Economy (his translation): We are all doing it; very few of us understand what we are doing.
Reminder: you could check the source right away for the answer, but you are only cheating yourself…
Source: ‘Steven E. Landsburg, “Ups and Downs,” The Big Questions, December 19, 2018. (video).
I don't think Landsburg is correct, or that there should be any prediction about which half of the escalator people take their rest on: Imagine 6 people going up a 30 m escalator or flight of stairs, everyone walks at 10 m per min and the escalator also moves at 10 m per min. Person 1 walks up the stairs, person 2 waits 1 min and then goes up the stairs, person 3 walks up the escalator, person 4 rests for 1 min on the escalator and then walks up the escalator, person 5 rests for the first half (15 m) of the escalator and walks up the rest of the way (15 m), and person 6 walks up the first (15 m) and rests for the second half (15 m). The time cost to the journey for the 1 min rest is 1 min for stairs but only 0.5 min for the 1 min rest on the escalator, and there is no difference in journey time for person 5 and 6 even though person 5 rested in the first half and person 6 rested in the second half.
The answer to Landsburg's question should be that the time cost of resting while going up the escalator is because you are moving while you are resting. To be more precise, the time cost is determined by the speed of the escalator relative to your stair climbing speed. So you could ask the question: are you more likely to walk up a slow escalator or a fast escalator? The answer is that you are more likely to walk up the slow escalator (and rest on the fast escalator) because the time cost of rest is higher on the slow escalator. Imagine 2 900 m escalators, 1 that goes 10 m per min and one that goes 90 m per min, and a person who climbs at 10 m per min. If you rest all the way up both it takes 90 min on the slow one and 10 min on the second. If you walk up both, it takes 45 min on the slow and 9 min on the second. Walking up the slow one cuts the journey cost in half but walking up the fast one only saves 1 min (only reduces by 10%). Also, if you have each person rest 1 min and then walk the rest of the way, the journeys now take 45.5 min and 9.1 minutes, so the 1 min rest costs 0. 5 min and 0.1 min respectively on the overall time it takes to go up the escalator. A staircase is just an infinitely slow staircase, so you are least likely to rest on a set of stairs (assuming no tiring) and most likely to rest on the worlds fastest escalator