A working paper exploring the idea that information equilibrium between an information source and an information destination is a general principle for understanding the micro- and macroeconomic allocation problem. [Here] is a first draft.

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.

...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.

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")?

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?

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.

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

ReplyDelete...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.

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

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

DeletePerhaps 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")?

ReplyDeleteTodd, those are great questions.

DeleteThe continuous analog of number of X and unit of X.

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

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?

DeleteWith 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.

DeleteBut 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.

I should say demand for a single widget.

DeleteOr demand event.