Someone linked to my blog at reddit, and someone else in response linked to an interesting take by John Bryant [pdf] on using the ideal gas equation of state as the quantity theory of money. Bryant's equation is (brackets in the original):

*P V = [N k] T*

Where

*P*is the GDP deflator,*V*is the output volume (which I think is RGDP =*Y*),*N*is the money stock (he uses M4) and*T*is velocity (it'd be velocity of M4; he calls it the index of trading value). That is to say, he exactly reproduces the quantity theory of money equation of exchange:*P Y = M V*

since

*M*is M4 and*V*is the velocity of M4:*V = PY/M*. Bryant then uses various thermodynamic relationships to look at changes in*P, V, N*and*T*.*P = k M^(k - 1)*

Where the relationship between money and the price level is analogous to an isentropic (adiabatic) expansion

*log P - γ log V =*constant. The analog of the ideal gas equation of state would be [1]*P M = k N*

or in terms of the symbols of the equation of exchange

*P M = k P Y*

Or in terms of Bryant's symbols:

*P [N k] = P V T*

Bryant later gets a changing elastic index (adiabatic index, related to the information transfer index), but as yet, I haven't fully digested it.

Overall, it is a different take, but may include some interesting insights.

**Footnotes:**

[1] If you want to make this look more like the equation of exchange, you would write it as:

*P M = k N*

*P N^(1/k) = k M^k-1 M*

*N^(1/k) = M*

*(PY)^(1/k) = M*

I've set a bunch of constants equal to 1 in the entire above presentation.

That's majromax (not majormax, as you might think) who left the link. He leaves a lot of comments at Nick Rowe's blog, and sometimes other places as well.

ReplyDeleteCheers, Tom. I thought it seemed familiar ...

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