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.