Final answer:
To increase the money supply by $100 million, the Fed would need to purchase $58.82 million in bonds in July 2008 and $111.11 million in bonds by January 2009, due to a declining money multiplier from 1.7 to 0.9.
Step-by-step explanation:
During the Great Recession, the Federal Reserve (Fed) engaged in open-market purchases to increase the money supply. Given the money multiplier's decline from 1.7 in July 2008 to 0.9 by January 2009, the required open-market purchases would differ significantly between these two periods to increase the money supply by $100 million. If the money multiplier is the quantity of money the banking system can generate from each $1 of bank reserves, we can calculate the necessary purchase as:
July 2008 Calculation:
Money Multiplier (MM) = 1.7
Desired Increase in Money Supply = $100 million
Required Increase in Bank Reserves = Desired Increase / MM
Required Increase = $100 million / 1.7 = $58.82 million (rounding to two decimal places).
January 2009 Calculation:
Money Multiplier (MM) = 0.9
Required Increase in Bank Reserves = $100 million / 0.9 = $111.11 million (rounded to two decimal places).
This analysis indicates a dramatic change in the efficiency of monetary policy measures from July 2008 to January 2009. In July 2008, the Fed needed to purchase $58.82 million in bonds to increase the money supply by $100 million. By January 2009, they would need to purchase $111.11 million in bonds to achieve the same increase in the money supply, highlighting the impact of a lower money multiplier during economic recessions.