This paper examines the implications of ex ante skill heterogeneity for long run inflation. We develop a dynamic general equilibrium model in which there are two types of labor (skilled and unskilled), two types of capital (human and physical), and money is introduced via a cash in advance constraint on consumption purchases. Skill heterogeneity is characterized in terms of (i) a parameter governing the ease with which the two types of labor can be substituted for each other in production; and (ii) the "productivity" of human capital in the production of skill. The model includes the accumulation of human capital which in turn creates skill heterogeneity among workers through an efficiency wage mechanism. Numerical experiments indicate that there is a range of parameter estimates in which the Friedman Rule may not be optimal. Furthermore, our quantitative experiments also indicate that there is a range of parameter values in which a greater degree of skill heterogeneity may be associated with a greater preference for inflation. Empirically, we also find that the inflation and heterogeneity correlation is positive.