This paper develops an analytically tractable Bewley model of money demand to shed light on some important questions in monetary theory, such as the welfare cost of inflation. It is shown that when money is a vital form of liquidity to meet uncertain consumption needs, the welfare costs of inflation can be extremely large. With log utility and parameter values that best match both the aggregate money demand curve suggested by Lucas (2000) and the variance of household consumption, agents in our model are willing to reduce consumption by 3% 4% to avoid 10% annual inflation. The astonishingly large welfare costs of inflation arise because inflation increases consumption risk by eroding the buffer-stock-insurance value of money, thus hindering consumption smoothing at the household level. Such an inflation-induced increase in consumption risk at the micro level cannot be captured by representative-agent models or the Bailey triangle. Although the development of financial intermediation can mitigate the problem, with realistic credit limits the welfare loss of moderate inflation still remains several times larger than estimations based on the Bailey triangle. Our findings provide a strong justification for adopting a low inflation target by central banks, especially in developing countries where money is the major form of household financial wealth.