Bhattacharya, Joydeep; Guzman, Mark G.; Smith, Bruce D.

Canadian Journal of Economics Vol. 31 no. 3 (August 1998): 596-623.

Does monetizing a deficit result in a higher or a lower rate of inflation than does bond financing the same deficit? Sargent and Wallace (1981) produced conditions under which bond finance leads to a higher rate of inflation than deficit monetization ("unpleasant monetarist arithmetic''). However, it has been argued that unpleasant arithmetic is unlikely to obtain in practice, as it requires a number of conditions to hold that are rarely satisfied empirically. We develop a model essentially identical to that of Sargent and Wallace, and modify it to allow for a simple type of financial intermediation that they exogenously precluded. In the presence of reserve requirements, unpleasant arithmetic arises even when the real rate of growth exceeds the real return on bonds. Moreover, under a very mild restriction on the interest elasticity of savings, there exists a unique equilibrium to which unpleasant arithmetic results necessarily apply. No "Laffer curve'' considerations arise. We also discuss various tensions that arise between determinacy and efficiency of monetary equilibria.