So, the correct answer is for Economist A.
The concept that you are looking for is that of a money multiplier. If we take out the other factors and just focus on the money multiplier and assume no taxes and that all money ends up in banks this is pretty simple. So, Fred gets the 20,000 from the Federal Reserve in exchange for Treasury bonds. Fred will now go and deposit this in the bank. Now, the bank has the 20,000. They will take that 20,000 and have keep part of it as the minimum reserve requirement of 8%. So the bank will keep 1,600 and have 18,400 in excess reserves. The bank will then want to make loans with that 18,400 dollars. The bank makes the loan to someone else, say Jill. Jill now has the 18,400, Jill is going to spend that money and that money will eventually end up in the bank account of someone else. Again, this 18,400 goes to the banking system where it must keep 1,472 and is allowed to loan out the rest. This loan is spent, comes into a bank in the form of deposits, is loaned out again, comes back in the form of deposits and so on and there you have the money multiplier. So, you can see that the Federal Reserve can influence the size of the money supply more than the initial 20,000 and in this case with this hypothetical situation would increase the size of the money supply by 250,000. Now, in real life the multiplier would not be so big, but the point of the problem is to understand that the growth of the money supply will be more than the inital increase because of this multiplier. The overall effect of the money multiplier can be formulated as so...
Increase in money supply = Initial Value * (1/reserve requirement)
$250,000 = $20,000 * (1/.08)
