Bank balance sheet free response question | APⓇ Macroeconomics | Khan Academy

The following is the balance sheet of First Superior Bank.

So let's see, on the asset side, it has 200 of reserves and 1800 of loans. So its total assets are 2,000, and then that should be the same as its liabilities and equity. We see here that it has two thousand dollars in demand deposits; that's a liability because people can come to the bank and say, "Hey, I want that money." These are checkable deposits. They could even try to withdraw that money.

Since all of that two thousand dollars is on the liability side, there is no equity right over here. These two should sum up to two thousand dollars, the same as you have on your asset side.

Assume that the required reserve ratio is 10%. And just as a review, that's the percent of deposits that the bank needs to keep as reserves. We can see that it's at that reserve ratio right now; it has 2,000 in deposits, and so it needs to keep ten percent as reserves. Ten percent of two thousand dollars is two hundred dollars, so it's at its minimum reserves already.

Part A says: What is the dollar value of new loans that First Superior Bank can make? Explain. Pause this video and see if you can figure that out yourself.

Well, as I just mentioned, this bank is already at its minimum reserves; it's already loaned out as much as it could. If you get two thousand dollars in deposits and you have a ten percent reserve ratio, that means you can loan out ninety percent of that two thousand dollars, and it has already loaned out ninety percent of the two thousand dollars.

So what is the dollar value of new loans that First Superior Bank can make? Well, it's zero dollars. Zero dollars because it's already at minimum reserves.

Alright, let's do part B. Mr. Smith deposits 100 of cash in a demand deposit account in First Superior Bank. Calculate the maximum amount of new loans that First Superior Bank can now make. So pause this video again and see if you can figure that out.

Well, there's a couple of ways you could think about it. Before Mr. Smith makes that deposit, we already saw in part A that First Superior Bank can't make any new loans. And so now, if it gets a hundred dollars of cash in a demand deposit account, because the reserve ratio is 10%, the bank needs to keep 10 of that deposit as reserves, and it can loan out the other ninety percent.

So you could just say, "Well, I could loan out ninety percent of that new deposit," and so it'd be ninety percent times one hundred dollars, which is equal to ninety dollars of new loans.

Another way that you could think about it is after Mr. Smith's deposit, the demand deposits right over here go to 2,100. This increase in liabilities is offset by an increase in assets; it just got a hundred dollars of cash. So the reserves go from two hundred dollars to three hundred dollars.

Now, at this point, First Superior Bank is clearly above its minimum reserve requirements. 300 over 2,100 is more than 10%, so it can loan out some money.

How much can it loan out? Well, it has to keep 10 percent of this 2,100 as reserves, so it needs to keep 210 right over here. And so that other 90 it could loan out, and so this could be 1,890. Thus, it can make 90 in new loans as a result of Mr. Smith's 100 cash deposit.

Calculate the maximum change over time in each of the following in the banking system. So part one is loans. What’s the maximum change over time in the banking system of loans? Pause this video and try to figure it out.

Well, as we just said, Mr. Smith, by depositing one hundred dollars, First Superior Bank can make ninety dollars of loans. So that would be ninety dollars of new loans. But then whoever they loan that money to, they could then deposit that in a bank, and then that bank could loan out 90% of that.

So then it would be zero plus 0.9 times 90. Now, this bank that got 0.9 times 90 dollars, which is 81 dollars, it can then loan out 90% of that. So it's going to be plus 0.9 times this, so 0.9 squared times 90. You just keep going like this, and then this gives us essentially the equation for the multiplier, which you might have memorized.

This is just going to be equal to 90 times 1 over 1 minus you could say this 0.9 or you could say this is the same thing as 90 times 1 over the reserve ratio which is 0.1, and 1 over 0.1 is 10, so this is going to be equal to 900 dollars.

Now, what is going to be the maximum change over time in demand deposits? Pause this video again and try to figure that out.

When Mr. Smith first deposits that hundred dollars in cash at First Superior Bank, that creates a hundred dollar increased demand deposit here on First Superior Bank's balance sheet. So let me just write it this way, so you have 100, but then we already said that First Superior Bank could loan out as much as 90 of that.

And whoever they loan that to, they could put all of that into a bank as a demand deposit. So that's going to be plus 0.9 times 100, and then that bank could then loan out 0.9 times this, and then whoever gets that loan could deposit into the bank, creating a demand deposit.

So plus 0.9 squared times 100, and it keeps going on and on and on. You could just view this as this is going to be equal to 100 times 1 over 1 minus 0.9, which is the same thing as 100 times 1 over the reserve ratio.

And so this is just going to be 100 times 10, which is going to be 1,000.

Part D: As a result of Mr. Smith's 100 cash deposit, calculate the maximum change over time in the money supply. So pause this video again and try to think about it.

So you might be tempted to say, "Hey, maybe that's just going to be the same thing as the total maximum change in demand deposits." But we have to be very careful that the first hundred dollars already existed as cash in the money supply.

The maximum change is everything else; it's this part right over here. Mr. Smith deposits 100 in cash; that's not new money. But then the bank can loan out ninety percent of that, so that's ninety dollars in new money that someone could use to then deposit in another bank.

And so that other bank could then loan out ninety percent of that ninety, and we've seen this drill before. That was the exact same calculation for part one right over here. This is just going to be equal to 90 times one over the reserve ratio, which is equal to 900 dollars.

Part E: Provide one reason why the actual change in money supply can be smaller than the maximum change you identified in part D. Pause this video and see if you can figure that out.

Well, there are actually two good reasons why the actual change in money supply might be smaller than what we just calculated. One reason is if banks decide to keep more than the minimum reserves.

So banks might keep more than minimum reserves. You could imagine even though by law, according to this world, they have to keep a reserve ratio of 10 percent, if on average, the banks decide to keep a reserve ratio of 20 percent, then every time they would loan out 80 of whatever they get in deposits, and so you would have a lower number here.

There's another world where the people who get the loans don't deposit all of that into the banking system. So if you wanted a second reason, we've already answered their question—we've given one reason—but a second reason is people might not deposit all of their funds in the banking system.

So I will leave you there.