This paper presents a general equilibrium model of money demand where the velocity of money changes in response to endogenous fluctuations in the interest rate. The parameter space can be divided into two subsets: one where velocity is constant and equal to one as in cash- in-advance models, and another one where velocity fluctuates as in Baumol (1952). Despite its simplicity, in terms of paramaters to calibrate, the model performs surprisingly well. In particular, it approximates the variability of money velocity observed in the U.S. for the post-war period. The model is then used to analyze the welfare costs of inflation under uncertainty. This application calculates the errors derived from computing the costs of inflation with deterministic models. It turns out that the size of this difference is small, at least for the levels of uncertainty estimated for the U.S. economy.