Saturday, July 20, 2013

The information transfer model and the equation of exchange

This is a quick post about the equation of exchange as viewed in the information transfer framework. The equation of exchange is: $$ M V = P Y $$ where $M$ is the money supply, $V$ is the velocity of money, $P$ is the price level and $Y$ is real value of aggregate transactions. In the information transfer model, we take $M = Q^s$ and $P Y = Q^d$, so that $$ Q^s V = Q^d $$ or, suggestively, $$ V = \frac{Q^d}{Q^s} $$ If we compare to the relationship in the information transfer model (Equation 4) $$ P = \frac{1}{\kappa}\frac{Q^d}{Q^s} $$ we can identify $$ V = \kappa P = \left( \frac{Q^d_{ref}}{Q^s_{ref}} \right) \left( \frac{Q^s}{Q^s_{ref}} \right)^{1/\kappa -1} $$ Note that the "Cambridge $k$" is $k = 1/V = 1/(\kappa P)$. In this sense, one could view the information transfer model as a model for the velocity of money.

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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.