Wednesday, March 23, 2016

Some information transfer model basics

I do this kind of thing from time to time to make sure I have everything straight in my own head. There's no reason not to share it with you.






10 comments:

  1. Good... I'm always curious what goes on inside the sausage factory. ;)

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    1. ...someday you might be able to scrawl "dD/dS = kD/S" on a check and be confident it'll never be cashed. I'd still contribute to your 401k though, just in case.

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    2. I admire Jason's courage! Most of the time random scribblings of what is in people's heads would not be so productive.

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    3. I'm not sure I'd use that equation in that way because I didn't derive it -- it's Fielitz and Borchardt's.

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  2. Perhaps a dumb question so that I can understand- what is the practical meaning of "amount of D" and "element of D" (and reciprocally, "amount of S" and "element of S")?

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    1. Todd, those are great questions.

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    2. The continuous analog of number of X and unit of X.

      Sum of unit of X up to number of X equals X. Integral of differential element of D up to D equals D.

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    3. Once again just so I understand the relevance to economics and supply and demand (calculus was a LOOONG time ago for me)- demand for widget (Dw) would be the number of widgets that people want to buy at a given price, and dDw would be how much that changes as a function of time, or supply? Usually the derivative is a function of time (dDw/dt), but it is not clear to me that this is the case- is it dDw/dSw?

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    4. With the Leibnitz notation (I.e. dy/dx) you can treat the dy and dx like they are dividend and divisor. It's frequently said it's an abuse of notation, but in most ordinary circumstances it's fine.

      But really, dx is a differential element (an infinitesimal quantity).

      And there's no "usually" for derivatives. You can take them with respect to time, space, other functions... all kinds of stuff.

      In this case you can think of dD as a single widget. But there are so many widgets that dD is infinitely small.

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    5. I should say demand for a single widget.

      Or demand event.

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Also, try to avoid the use of dollar signs as they interfere with my setup of mathjax. I left it set up that way because I think this is funny for an economics blog. You can use € or £ instead.