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This paper presents an econometric analysis of the demand for the monetary aggregate M1 for Mexico. Using cointegration techniques, we identify both a stable long-run relationship between M1 and its determinants, and a statistically sound single-equation error-correction model. Results are used to carry out the following simple applications: i) empirical determination of the value and stability of dual inflationary equilibria, given the observed seigniorage levels; ii) calculation of the seigniorage maximizing inflation rate, and iii) analysis of the potential relationship between a measure of excess money and inflation. Results indicate that the low inflation equilibrium is stable, and that the excess money indicator shows, in retrospective, some capacity in predicting inflationary pressures. [ABSTRACT FROM AUTHOR]