Question

The Fed, the U.S. central bank, has reportedly injected trillions of dollars into the economy since 2009. Can you tell where those dollars are? If not, why not? How can you use what you’ve learned from this course to explain the impact of the Fed’s actions? K

Answer 1

Consider the given problem here the “money supply = M” is given by the sum of “C=currency in circulation hold by people” and “D=deposit”, => M=C+D. Now, the “monetary base = B” is equal to “C” and “R=reserve hold by bank”, => B=C+R. Now, bank reserve a fraction of deposit, => “R=rr*D”, where “0 < rr < 1” and people hold a fraction of total deposit, => C=cc*D, “0 < cc < 1”.

So, M/B = (C+D)/(C+R) = (cc*D+D)/(cc*D+rr*D) = (cc+1)/(cc+rr) = m = money multiplier.

=> M = m*B, “m > 0”. Now, if “B=monetary base” increases implied the money supply increases.

Now, if the “Fed” inject trillions of dollar into the economy, => that will increase “B” that will increase the total money supply of an economy. Let’s see all the intermediate adjustments to increase the money supply.

So, 1^st as “Fed” inject trillions of dollar into the economy, => “B” increase in the form of increase in “C”. Now, people will decide how much to hold and how much to deposit, => “D” increases that will increase the “M”. Now, banks will hold some amount of “D” as reserve as lend the rest to people. Now, people further decide how much to hold and how much to deposit, => “D” further increases that will increase the “M”. Now, the same process will continue until the lending will be “0”. So, here some portion of additional dollars are hold by normal people and rest of the part is kept by bank as reserve.