The paper functionally describes the income velocity of money by including the cost of a key substitute to money: exchange credit. Financial innovation causes the cost of credit to fall, the quantity of money demanded to fall, and the velocity to rise, all without shifting the money demand function. The paper derives a general equilibrium money demand function, specifies a parametric equation of the income velocity of money from the model, and finds cointegration between the relevant variables in an expanded velocity equation which also produces consistent dynamics. It explains U.S. post-war long-run velocity through only the substitution effects from the relative cost of exchange by money versus credit. It explains short run dynamics with the same substitution effect. In addition, evidence suggests that an income effect helps explain the dynamics as predicted by an application of the permanent income hypothesis.