This paper analyzes the optimal inflation tax in economies with structural imperfections in labor, commodity, and currency markets. The Friedman rule is a classic result in economics that claims that the optimal monetary policy is to set a zero nominal interest rate. This Ramsey equilibrium is robust in a wide range of environments without imperfections in input, output, or financial markets. In many developing countries, however, a large fraction of activity takes place in the “informal” sector. Roughly speaking, the informal sector is the untaxed and unregulated market sometimes referred to as the underground economy. We obtain three results. First, we show that when structural imperfections such as an informal sector exist, the optimal inflation tax is positive. Second, we show that structural imperfections introduce an important asymmetry in the welfare cost function. Third, we provide quantitative results.