Quantitative Easing and its impact in the US economy

Essay Question A
Quantitative easing has not increased the rate of inflation with the main reason being that banks have held on to the newly created money supply as excess reserves. Traditionally, when the Federal Reserve engages in bond buying or mortgage-backed securities purchasing it usually promotes growth in the money supply. Prior to 2008, banks were required to keep a certain reserve percentage of checkable deposits, around 10%, and any excess over this amount would not make any interest, with the cost of holding on to these excess reserves being the opportunity cost of the interest the excess reserves could have generated if lent out, so banks had no reason to hold on to excess reserves. After 2008, however, the Federal Reserve began to pay interest on these excess reserves, and with the massive influx of money supply generated because of the QE program the Fed launched in the same year, banks began to hold most this new money supply, over $4 trillion now, as excess reserves, over 81.5%. When looking at the money supply formula, M = m*MB, when expanding the money multiplier we have (1+c)/(r+c+e) with e being excess reserve ratio, E/D, as part of the denominator. As banks hold on to more and more of this new money supply as excess reserves, the excess reserve ratio increases which in turn increases the denominator in the money multiplier. A higher denominator leads to a smaller money multiplier, and even though there has been an increase in the monetary base, an increase in excess reserves leads to small money multiplier meaning that there has been little money expansion. This shows that excess reserves is negatively related to money supply. This explains why Quantitative easing has not increased the rate of inflation, because banks have held on to the newly created money supply as excess reserves, effectively halting monetary expansion. Since little money has entered the economy, inflation rates have been proportionally low and it is why QE has had little impact on GDP.