Talk:Hotelling's law

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"It would be more socially beneficial if the shops separated themselves and moved to one third of the way along the street at different ends". Why a third? Would a quarter be even better? --Henrygb 18:38, 8 Mar 2005 (UTC)

because that is overall closest to as many places as possible, well that is the reasoning, you would have to ask a mathematician for the exact optimal distance. Bluemoose 19:47, 8 Mar 2005 (UTC)

I am a mathematician and I think a quarter would be better. Anyone give me a good reason why not?--Henrygb 23:58, 8 Mar 2005 (UTC)

It seems to me that 1/4 would be better as well. That should minimize the distance any person would need to walk to reach a store. Assuming someone is coming from either end, they only need to walk 1/4 of the length of the street to reach a shop, and so would someone in the middle of the street. If they were located 1/3 apart, people on the ends would have to walk farther, even though people in the middle would have a shorter distance. This case could possibly be a better solution if the density of people is significantly greater in the center of the street, but assuming uniform probabilities of starting location, 1/4 would be better. KristinLee 01:19, 9 May 2006 (UTC)

[edit] Multiple shops

As I remember it from my economics degree, Hotelling's law only applies to two shops: there is no equilibrium for n of shops>2. Can someone who knows more about this confirm and add? Chris Martin 23:36, 16 May 2006 (UTC)

Well for 3 I tried and couldnt find any stable formations, but with four there seems to be at least one equilibrium point (for a 20 long row of houses, place the four shops at the 5th, 6th, 15th and 16th spots and they all have 4 customers each, and no position can be moved to that gets more than 4 customers). As a guess if the number of customers is divisible by the number of shops, and their is an even number of shops you can have an equilibrium (whether in practise the equilibrium can be achieved by individual maximisation efforts by each shop is open to question without playing with it more, but that depends a lot of your assumptions about when and how each shop moves). -- 86.128.253.74 15:06, 11 October 2006 (UTC)

[edit] Hotelling effect?

Somebody started an article called the Hotelling Effect. They created said article, then disambiguated a link 3 months later, now it's been a year and a half with no other edits. After linking Harold Hotelling, I discovered the Law article. If no one objects, I'll merge in the substance of the other article into an extra illustrative application. Xaxafrad 14:35, 27 July 2006 (UTC)

Okay, I WAS going to add this in:

<block>Alternately, assume two snack vendors are peddling on a beach of length X (running from 0 to X), one is at .25X and one is at .75X -- they each have access to .5X and will get half the consumers on the beach who want snacks (assuming people walk to the nearest carts, prices, selection and service are the same, etc.). When the first vendor moves to .33X he still gets everyone from 0 - .33X coming to him, but now gets half the people from .33X - .75X, stealing business from the second guy, who promptly moves to .66X to make up for it. Eventually they end up at .49X and .51X (or both at .50X if you want), glaring at each other, each still getting 50% of the business, any intermediate gains lost. The people at the far ends of the beach suffer as a result. However, this leaves open the possibility that a third and fourth entrepreneur may capitalize on the convience-seeking of the beach-goers at both ends. If the original vendors had taken an economics class, they might have foreseen this outcome and stayed where they were.

John Hopkins Magazines, April 1997 </block>

but it's a might not be encyclopedic quality. Second opinions? Xaxafrad 15:01, 27 July 2006 (UTC)

I don't think this extra example adds anything considering how much it would need to be cleaned up, if people want an extra example for clarity it would be as useful to create one from scratch I think. -- 86.128.253.74 14:45, 11 October 2006 (UTC)

[edit] "perfect location for two ice cream vendors on the beach" theory

There is an economic theory abut where two ice cream vendors who sell an identical product end up on a beach (right in the middle). There's a Wikipedia article about it and I wanted to link to it as it is the same idea just in economics - but I can't find it. But it exists because i know I read it. If you can think of it, please add it, thanks a lot.--Soylentyellow 22:45, 23 May 2007 (UTC)