In this paper we argue that inventory models are probably not useful models of household money demand because the majority of households does not hold any interest bearing assets. The relevant decision for most people is not the fraction of assets to be held in interest bearing form, but whether to hold any of such assets at all. The implications of this realization are interesting and important. We find that (a) the elasticity of money demand is very small when the interest rate is small, (b) the probability that a household holds any amount of interest bearing assets is positively related to the level of financial assets, and (c) the cost of adopting financial technologies is positively related to age and negatively related to the level of education. Unlike the traditional methods of money demand estimation, our methodology allows for the estimation of the interest--elasticity at low values of the nominal interest rate. The finding that the elasticity is very small for interest rates below 5 percent suggests that the welfare costs of inflation are small. At interest rates of 6 percent, the elasticity is close to 0.5. We find that roughly one half of this elasticity can be attributed to the Baumol--Tobin or intensive margin and half of it can be attributed to the new adopters or extensive margin. The intensive margin is less important at lower interest rates and more important at higher interest rates.