tag:blogger.com,1999:blog-6837159629100463303.post2986110735467007343..comments2022-11-10T00:45:32.228-08:00Comments on Information Transfer Economics: Apples, bananas and the information transfer model of supply and demandJason Smithhttp://www.blogger.com/profile/12680061127040420047noreply@blogger.comBlogger9125tag:blogger.com,1999:blog-6837159629100463303.post-81407947135325058312016-01-17T13:40:41.452-08:002016-01-17T13:40:41.452-08:00Jason, I can see why Michael was confused. You pre...Jason, I can see why Michael was confused. You present n_d as the number of apples sold: "...we've sold nd apples..."<br /><br />Thus, in the post, when you introduce n_s without further explanation, it's natural to assume that the number of apples sold = the number of apples purchased, and n_s seems like it must fit this bill.<br /><br />Now it's clear enough (I think) that the number of potential apple buyers (d) is going to be different than the estimate of the size of this number of buyers (s) by the sellers (as you present it in the text), but it's not at all clear whether s will be less than or greater than d.<br /><br />Perhaps if you explained exactly what n_s is when you introduced it the concept would be more clear.<br /><br />It's be interesting to see you present this (live) to some skeptics, with limited math skills.<br /><br />I'm wondering if it would make sense to introduce the concept of apple pies here, each requiring x apples per pie.<br /><br />Also, the introduction of B and S might be confusing.<br /><br />"If we take the smallest unit of bananas to be dB"<br /><br />I think a lot of people might jump to dB = 1 banana at that point, making B = n_b. Same for S and n_s. I know you say they get "infinitesimal" later to define the exchange rate, which makes sense, but where does that leave B and S?<br /><br />I read this post when you first made it, and I was confused by some of this, but I pressed on anyway. I know I can go to your draft paper and I can refer to Fielitz and Borchardt. I love that gas law analogy... it always helps me, but the way you presented it above would leave me scratching my head I think. First off, it's not clear that D is analogous to the right hand side, and that V is analogous to S, and that p is analogous to P. <br /><br />Imagine we shrunk the degrees of freedom down from 10^23 in a gas system, to such a low number that it was clear that sometimes<br /><br />Iq > Iu<br /><br />I.e. "large deviations from the ideal" (Iq = Iu) What would that look like?Tom Brownhttps://www.blogger.com/profile/17654184190478330946noreply@blogger.comtag:blogger.com,1999:blog-6837159629100463303.post-91363259980946822832015-10-21T22:34:25.881-07:002015-10-21T22:34:25.881-07:00Sorry about the long delay in getting back to your...Sorry about the long delay in getting back to your comment (I remember I was travelling Jun 20th, so that's probably why I missed this).<br /><br />n_d is the number of demand units<br />n_s is the number of widgets<br /><br />These are basically proportional to each other (via the information transfer index).<br /><br />And yes, in information equilibrium, these are equal (up to the IT index). However, information equilibrium only holds in large systems (and then only in the case when the market is functioning). Sometimes<br /><br />n_d > k n_s<br /><br />Which is the case of non-ideal information transfer.<br /><br />You can think of these variables in the same way you think of variables measuring an ideal gas. The ideal gas law says that<br /><br />p V = n R T<br /><br />However, that is only in thermodynamic equilibrium (ideal info transfer) and in the limit of a large number of molecules. Only then can we say p = 〈p〉and the fluctuations around the average (measured by the variance) are small. Economic systems (10^6 - 10^9) don't have as many degrees of freedom as thermodynamic systems (10^23), so you'll see larger deviations from ideal in the former.Jason Smithhttps://www.blogger.com/profile/12680061127040420047noreply@blogger.comtag:blogger.com,1999:blog-6837159629100463303.post-85604012698702358802015-06-20T06:45:29.566-07:002015-06-20T06:45:29.566-07:00You lost me at inequality (2). What is "n_s&q...You lost me at inequality (2). What is "n_s" supposed to represent? Up to that point, it seemed that n_d was the amount acutally sold into a market of size d. But if s is, as you say, the sellers estimate of market size, then its corresponding amount sold will not be an acutally realized, observable quantity.<br /><br />If I take it that the realized sales should be on both sides of (2), so that the two n_ are the same, then the inequality holds if and only if the seller has underestimated the size of the market. That's about half the time, but you seem to be treating this as true in general.Michael Margolishttps://www.blogger.com/profile/00454854828001494319noreply@blogger.comtag:blogger.com,1999:blog-6837159629100463303.post-25453650444526869722015-01-24T16:02:14.725-08:002015-01-24T16:02:14.725-08:00Is this directed at me (the author)? Because that ...Is this directed at me (the author)? Because that is not what the math above says. One out of one apple conveys no information (log 1 = 0) and one out of a million conveys 6 log 10 ~ 20 bits.Jason Smithhttps://www.blogger.com/profile/12680061127040420047noreply@blogger.comtag:blogger.com,1999:blog-6837159629100463303.post-38854287754583256192015-01-24T12:41:11.527-08:002015-01-24T12:41:11.527-08:00I stopped reading at the second sentence, as soon ...I stopped reading at the second sentence, as soon as it became clear the guy thought there was the same amount of information in one apple out of one being sold at the end of the story and one apple out of a million being sold at the beginning.<br /> <br />Why would a guy post something that's obviously senseless?<br /> <br />-dlj.DavidLJhttps://www.blogger.com/profile/04477517602668340521noreply@blogger.comtag:blogger.com,1999:blog-6837159629100463303.post-77229202192678790932014-04-12T10:40:21.409-07:002014-04-12T10:40:21.409-07:00I used ID numbers because it is an intuitive expla...I used ID numbers because it is an intuitive explanation of why the amount of information is proportional to $\log d$. In information theory, all that matters is that in principle you could assign ID numbers (people are distinguishable -- a case where this fails is in quantum systems and you get corrections of order $N \log N$ where $N$ is the number of indistinguishable particles, see the Sackur-Tetrode equation for example).<br /><br />The underlying idea is that each of the $d$ states are equally probable so that all the probabilities in the Shannon information are equal ($p = 1/d$), therefore:<br /><br />$$<br />I = - \sum_{i}^{d} p_{i} \log p_{i} = - \sum_{i}^{d} (1/d) \log (1/d)<br />$$<br /><br />$$<br />I = \log d \sum_{i}^{d} (1/d) = \log d<br />$$<br /><br />Imagine flipping a coin five times. After the first flip, you get heads (H, versus tails T) and you learn that the sequence is H????. After the second, you get heads and you learn that the sequence is HH???. After the second flip, you've eliminated all of the sequences that started with TT, so you eliminated 8 possible sequences (you gained information). <br /><br />Now the real world probably doesn't have equal probability of all states, so the "ID number" argument is an approximation. However, it's one that seems to work pretty well for macroeconomics because the system is really large (that's why the assumption of maximum entropy, the principle of indifference or the ergodic hypothesis work for statistical mechanics ... I believe it is the information theory formulation of the efficient markets hypothesis).Jason Smithhttps://www.blogger.com/profile/12680061127040420047noreply@blogger.comtag:blogger.com,1999:blog-6837159629100463303.post-51724657260078679892014-04-12T07:34:15.087-07:002014-04-12T07:34:15.087-07:00In a real market the guys trading bananas for appl...In a real market the guys trading bananas for apples don't use ID numbers. Yet real markets work. Can you explain the information transfer that is going on without using ID numbers?Vincent Catehttps://www.blogger.com/profile/06502618776820144289noreply@blogger.comtag:blogger.com,1999:blog-6837159629100463303.post-83121323496427696512014-03-14T10:25:25.592-07:002014-03-14T10:25:25.592-07:00Thanks! I will fix the typo :)Thanks! I will fix the typo :)Jason Smithhttps://www.blogger.com/profile/12680061127040420047noreply@blogger.comtag:blogger.com,1999:blog-6837159629100463303.post-11130904904199006152014-03-14T09:35:37.643-07:002014-03-14T09:35:37.643-07:00Nice explanation. I really like the idea of money ...Nice explanation. I really like the idea of money as a medium of information transfer.<br /><br />Just a quick note:<br />"If we assumed the market for apples is about the same size as the market for apples"<br />I get an impression that you've mixed bananas with apples in the middle.<br />Anonymousnoreply@blogger.com