The study of monetary economics encompasses a broad range of directions, and this research aims to address several different areas of monetary economics through empirical and theoretical work. The first essay uses annual data from twenty-seven countries to determine whether unexpected inflation has an effect on unexpected output, as suggested by the Lucas Supply Function. Additional specifications are added to show that Lucas' base model is incomplete. Once money level equations were included, the results suggest money affects output through prices, as well as through other means. The second essay seeks to find stable predictors of the money demand function. The money demand function has been unstable since the 1970s, and this study focuses on the definition of money stock and adding measures of risk as solutions in stabilizing money demand. The results show that replacing the traditional measure of money stock (M2) with Money Zero Maturity, in addition to adding market risk and inflation risk to the specification for money demand, stabilizes the money demand function significantly. In this case, we have discovered a money demand function that is stable both in the short run and the long run, according to the LWZ criterion. The third essay attempts to verify Carl Menger's theory on the emergence of money through the observation of an online gaming economy. The results show that, while most of the observations were identical to Menger's theories, one interesting difference has emerged due to modern day technology and communication tools. Menger suggested that the creation of currency was due to trade being extremely unproductive under the "Double Coincidence of Wants," but our observations show that a barter system can coexist with a currency due to technology making search costs almost negligible.