This paper applies previous theoretical and empirical results on inflation and demand for money to a study of inflationary finance and the welfare cost of inflation. The amount of revenue generated by a steady inflation is derived as a function of the inflation rate and some underlying parameters. Empirically, the revenue-maximizing rate is on the order of 140 percent per month with the corresponding revenue approximating 15 percent of national income. It is argued that hyper-inflations become unstable when the revenue-maximizing rate is exceeded. Because inflation leads to higher transaction costs (resulting from greater payment frequencies and reduced use of "money" as a payments medium), there is a net social cost attached to inflationary finance. The model implies that marginal collection costs of inflationary finance exceed 50 percent for all positive rates of inflation-hence, alternative means of raising revenue should be socially preferable. The analysis also provides estimates of the social gain from moving to the optimum quantity of money as 1-3 percent of income.(This abstract was borrowed from another version of this item.)