In this paper, the authors develop a measure of the cost of inflation uncertainty where a risk premium can be interpreted as the amount of real consumption that a representative agent is willing to forgo in order to be guaranteed a perfectly anticipated path of inflation. This premium can be calculated based on the estimation of a utility function that takes into account portfolio adjustment costs with respect to money balances and bonds, subject to a budget constraint that includes the after-tax returns on savings. With Canadian and U.S. data, it is shown that economic agents' preferences are such that the uncertainty of unexpected inflation was not big enough to induce a large premium.