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Assume that the banking system has total reserves of $\$$100 billion. Assume also that required reserves are 10 percent of checking deposits and that banks hold no excess reserves and households hold no currency.
a. What is the money multiplier? What is the money supply?
b. If the Fed now raises required reserves to 20 percent of deposits, what are the change inreserves and the change in the money supply?
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Yi Chun Lin
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working with the monetary system, we're going to be using money multipliers and the money supply to understand how changes in required reserve ratios impact both of those things. So we're given is that the total reserves is $100 billion 10%. So for part A. here we'd like to know what the money multiplier is and what the money supply is With the understanding that the money multiplier can be calculated as one over R Reserve ratio. We can start to plug these values in. We know that our reserve ratio is equal to 10%. So let's just take one divided by 0.10, That gives us the money multiplier, which is equal to 10. Now if we wanted to know what the money supply is, all we need to do is take that money multiplier, which we just found to be 10 And multiply it by our total reserves, which we know is 100 billion. So if we multiply these together, what we get is a money supply that's equal to $1,000 billion. Now for part B, we're going to consider if the reserve ratio is now 20%. So how have the money multiplier? And money supply changed. So calculating the new money multiplier with the same formula of one over our reserve ratio, we have one over this new reserve ratio 0.20 because it's 20%. that gives us a new money multiplier which is equal to five and the money supply. We're gonna do the same thing as before. Take that Money multiplier five multiplied by your total reserves of 100 billion. And that gives us a new money supply which is equal to $500 billion. And what we can see here is that by raising that reserve ratio from 10 to 20%, we see that our money supply has dropped in half, so our decline here, we can calculate that is that 1000 billion dollars in our money supply that we had prior to the rays subtract from that, this new money supply of $500 billion. And we can see that we had a decline in our money supply Of $500 billion.
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