Thursday, May 30, 2013

Economics as a counting problem

A quick note: The information transfer model is basically a counting problem: you have a long measuring stick that changes by some amount and you are determining the effect of that change on another long measuring stick.
Looking at an instantaneous snapshot of the economy, an individual has a set of allocations of current credit + cash to various goods and services over time. A car payment continues for the next couple years while a chair is a one-time expense. An individual's allocation (not showing the unused quantity) is then very much like an integer partition (a Ferrers diagram):
The interesting thing is that as the number of elements goes to infinity, the instantaneous allocation of every business, individual, etc looks more and more defined/tractable as an ensemble:
... and you could imagine a statistical mechanics (or information theory) approach would capture much of the phenomena.

2 comments:

  1. I've never understood the F&B notation and distinctions here:

    q is a generic process variable, they say, on (-inf,inf).

    |Delta_q| is an absolute value of the "considered natural process?" Why not just |q| instead? What's the capital Delta for? It's a difference from some starting point on (-inf,inf) potentially other than 0?

    |delta_q| makes sense to me (with the lower case delta).

    ReplyDelete
    Replies
    1. We are measuring q from a system reference in many physical processes. For economics, we don't need this since there is an absolute reference of zero and we have positive supply and demand quantities.

      Delete

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