Often, when talking about the distribution of measurable human attributes, people refer to the bell curve, which is to say to a Gaussian distribution, more commonly known as a normal distribution.

One immediate difficulty is that the Gaussian distribution extends symmetrically without lower limit to measurements with positive probability, whereas the natural measures of most of the attributes that will interest us have lower limits of possibility (typically at or above zero). For example, no one has negative weight or negative height. Simply truncating the lower bound of a Gaussian distribution usually doesn't make a great deal of sense, because few people will even be near the lower bound, rather than a fair number at it or just barely above it.

Instead, the distribution will more typically look something like this:

Mind you that measures can always be transformed, and a measure that has a lower bound of b can be transformed into a measure without lower bound simply by the device of subtracting the bound and then taking a logarithm: measure₁(x) = log_e[measure₀(x) - b] Some set of transformations can surely be used to arrive at one with a distribution that is well approximated by a Gaussian distribution. But, for the most part, I'd rather use natural or familiar measures than manipulate the data to arrive at a Gaussian distribution, especially as one otherwise typically needs to invert the transformations at the end of the analysis, to make sense of things.

In the near future, I plan to post an entry about misreading the consequences of different variances in different human populations. What I have to say could all be expressed in terms of Gaussian distributions, but I don't want to do so, nor did I want that future entry to begin with a discussion such as that here.

The immoderate political left began speaking and writing of late[-stage] capitalism with the end of the First World War.

The idea has been that the industrialized world has entered the final stage of something called capitalism, with a revolutionary change to some form of socialism just around the corner…

…for more than a century now.

(Actually what we've seen is a slow, grinding transformation away from the use of genuine markets to an administrated order, which in more recent years has threatened to become a neo-feudalism. The transformation began well before the First World War, as technocratic thinking began displacing liberalism.)

A recent comment by Zenicurean notes, implicitly, that economic pædagogy often uses a widget as a hypothetical economic good.

I most frequently use the veeblefetzer (borrowed from Harvey Kurtzman) when I want a good about which the audience will know little or nothing, and the hot dog when I want a good that will seem familiar.

I like the hot dog as an example in part because it has a long tradition in economic education while being fairly absurd as an artifact.

I also like it because it is easy to explain the idea of a shift in the demand curve using the hot dog. First, I present my students with a set of prices, polling them as to how many hot dogs they would buy at each of these prices; that gives us an initial demand curve. Then I discuss some of the things that are permitted to go into hot dogs, and we repeat the process for the prices. (So far, the demand curve has always shifted inwards.)

But the main reason that I like to use hypothetical hot dogs is because I think back to a question on the economics GRE when I took it.[1] In the set-up for the question, a family was working-out its annual budget, and decided that they would spend $800 per year on hot dogs, regardless of the price of hot dogs.[2]

The question was of what sort of demand elasticity were here displayed. Elasticity is a measure of sensitivity or responsiveness, with a general form of

or of (Whether there's a negative sign and whether an instantaneous form is used is based on what's convenient and practicable.) In the case of demand elasticity, the y is quantity demanded, and the x is unit price. One might think that demand responsiveness could be measured more simply by slope (Δy/Δx or dy/dx), but elasticity has a useful property. When elasticity is less than 1 in absolute value, responsiveness is sufficiently weak that expenditures (the product of quantity demanded and unit price) increase as price is increased; whereäs if elasticity is greater than 1, responsiveness is sufficiently strong that expenditures shrink as price is increased. The seller gets less revenue by increasing prices in the second case, where the curve is said to be elastic (sensitive); the seller gets more revenue by increasing prices in the first case, where the curve is said to be inelastic (insensitive).

If the elasticity is exactly 1 (in absolute value) then quantity demanded drops or rises to exactly off-set any price change; expenditures are constant as price changes. This is called unit elasticity. (BTW, a demand curve that is everywhere unit elastic will be a hyperbola.)

On the GRE, I was supposed to identify the demand curve of the family in the question as unit elastic, and so I did. But, because I'm not autistic, I was also greatly amused by this example. Imagine a family that is conscientious enough to budget, but they eat hot dogs. Imagine a family that budgets, but budgets such that if a hot dog costs $1600 then they will try to buy half a hot dog, and if a hot dog costs a penny then they will buy eighty thousand g_dd_mn'd hot dogs!

I laughed when I read this question. And, because I made multiple passes through the test, I glanced at that question repeatedly, laughing each time. I was the only person in room laughing. (The room had people taking different subject GREs, and I may have been the only one taking the economics test.)

When I use hot dogs as an example, it's mostly just in fond memory of that hypothetical family, crazy for hot dogs.

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[1] This tale may seem somewhat familiar to those who read my now long-since-purged LJ.

[2] The amount may have been $600 per year, or perhaps $400 per year; it has been quite some time since I took that test, and I don't remember. But, mutatis mutandis, my remarks hold.

To address a small issue in the history of economic thought, I wanted to consult a copy of the first edition of The Theory of Games and Economic Behavior, by John von Neumann and Oskar Morgenstern. I didn't find it reliably quoted on-line, nor did I find it listed in the on-line library catalogue for USD nor in that for UCSD. So I thought that perhaps I'd buy a copy.

I consulted the Used and Out-of-Print listings of AddAll, and quickly concluded that, no, perhaps I won't buy a copy. The lowest price that I found was four thousand, nine hundred and fifty-nine dollars, and twenty-nine cents.

I'm not sure who would pay that much, but the next lowest seller wants seven thousand, five hundred and ninety-one dollars, and ninety-three cents.

Another remarkable thing is the range of prices being asked for just that next seller. Through Biblio.com and through Biblio.co.uk, the price would be that $7591.93. From that same seller, but through Find-a-Book (listed by AddAll as ilabdatabase.com), the price would be $7614.96. And through AbeBooks (whom I encourage you to avoid in any case), the book would be $7867.54, still from that same seller. There's a $275.61 range here, determined by which intermediate service one uses.

Now, even as I was writing this entry, some of these prices were changing; that's because the seller is based in London, and the exchange rate has been in flux. And that suggests that part of the price range may be explained by different methods being used to calculate a rate of exchange. $275.61 may not seem a trivial sum, but it's only about 3.63% of $7591.93.

Addendum (2019:09/30): This morning I returned to the aforementioned small issue in the history of economic thought, and discovered that in the time since I posted this entry Google Books came to provide what they call a snippet view of a scan of the first edition, which view was enough to answer my question. I wish that I'd had that answer when writing my paper on indecision; but at least I have it as I write my paper synthesizing a theory of decision-making in which preörderings both for preferences and for probabilities may be incomplete.