Question

Please show all work for part C

The Money Multiplier. For this question e denotes the ratio of currency to deposits, p denotes the ratio of required reserves to deposits, and e denotes the ratio of excess reserves to deposits S (a) (3 points) Express the money multiplier m in terms of c, p, and e (b) (4 points) Suppose that: = 0.5 (1) C (2) 0.1 = (3) 0.02 e = Find the value of the money multiplier m. If the Fed's objective were to have a money supply equal to $1 trillion, then how large would the monetary base need to be? (c) (3 points) Now suppose that the ratio of currency to deposits e rises to 0.75. Assuming e and premain constant, by how much would the Fed have to change the monetary base in order to keep the money supply comstant and equal to $1 trillion? Will the Fed need to conduct an open market purchase or sale? Answer: (a) The money multiplier 1 +c m= c+p+e (b) m 2.41935. MB = S413.33 billion - (c) The Fed would have to increase the monetary base by $83.81 billion to keep the money supply constant at $1 trillion. The Fed would need to conduct an open market purchase

Answer 1

New currency deposit rate (c ) =0.75
p =0.10    e =0.02
Money Multiplier(m) =1+c / c+p+e
m =1 + 0.75 /0.75+0.10+0.02
m =1.75 / 0.87 =2.0114942
Money base required for $1 trillion as per new money multiplier =$1 trillion / 2.0114942 =0.49714287021 trillion
or $497.1428 billion
Now the money Base is $413.33 billion. So it has to conduct an open market purchase
of $83.8128 billion($497.1428 billion - $413.33 billion) to keep the supply at $1 trillion