# Why does central banks lowering interest rate incentivize more borrowing?

I'm a layman trying to understand how the US monetary system works. I'm particularly interested in how the Federal Reserve can create inflation without printing new dollars and putting them in M1. My problem is that I don't get how the Federal Reserve can create inflation through lowering interest rates.

It's pretty intuitive on paper: when interest rates are lower people tend to demand more credit. Borrowing increases the M1 money supply. So we get inflation. I don't have trouble understanding that.

It's the other side of the trade that I don't understand. Why would a bank lend money at very low interest rates if that would create enough inflation that they'd be losing purchasing power? Maybe they do more than lending and it fits into a bigger picture that does make sense. But I can't find a good explanation of this.

Is there anyone that could explain/clarify this to me? I'm not an economist and the answers I find online are rather vague and complex for people like me in my opinion.

Thank you very much in advance, Joshua

• if they don't, someone else will? And what else would they do with that money? Would they like to have some income, by lending their money out, or no money, by not lending it out? If central bank rates are negative it's even worse, the bank has to pay money for the privilege of not lending it out. Apr 15 at 13:14
• I'd expect banks to at a certain point lend the money at an interest rate equal to what they expect the inflation rate will be taking into account how much they and their competitors are lending. But given how much we are fearing unprecedented inflation I'd expect your average 30-year US mortgage rate not to be trending down for half a century. Or when it does, I wouldn't expect bank stocks to be mostly up. Apr 15 at 13:42
• The central bank is still printing that money regardless, and you can't stop them. Do you want to earn some interest from it or should it all go to your competitors? Apr 15 at 14:35
• The Federal Reserve doesn't literally print money. The money it injects into the economy eventually leaves it by various means as I understand it (please enlighten me on how it wouldn't if I am wrong). And if you are losing money in real terms in the business of lending, why not just close your bank and go do something else that outpaces inflation, like a business in any other sector would do? Apr 17 at 0:03
• the central bank is increasing numbers in their database, which gives their clients the right to ask for money to be printed for them. And you are asking why all the banks don't just shut down...? Apr 17 at 8:58

Banks lend because it is profitable for them to lend out money. Banks do become less profitable in low interest environment, but they are still empirically able to maintain profitability, although there is evidence that goes hand in hand with some increase in risk taking (e.g. see Bikker & Vervliet 2018). Consequently, the direct answer to your question is that banks expand their lending because it is still profitable for them to do so.

Additionally, if central banks would be really determined they could expand money supply by open market operations (e.g. purchase of government bonds) and various other channels, so if a determined central bank would want to expand money supply it can do that whatever the private banks are doing.

Furthermore, inflation does not necessary means that the bank will become worse off. If there is 2% inflation in an economy but bank's profits increase by 5% during the same period then a bank is still better off in real terms.

Lastly, there is not necessarily 1:1 correspondence between increase in money supply and inflation. For example, even in a simple money market equilibrium model (which determines price level - increase of which is inflation) given by equation of exchange (See Mankiw Macroeconomics pp 87) as:

$$MV=PY$$

Where $$M$$ is the money supply, $$V$$ velocity of money, $$P$$ price level and $$Y$$ output.

Solving for price level and log-linearizing we get:

$$\ln P = \ln M + \ln V - \ln Y$$

Consequently, ceteris paribus, if $$M$$ increases by $$1\%$$ and $$Y$$ increases also by $$1\%$$ then the net effect on price level will be zero (and consequently inflation will also be zero). Even in this simple model you will only get inflation if $$\ln M + \ln V - \ln Y > 0$$ so when bank increase money supply it won't necessarily result in an equivalent inflation. Furthermore, in more complex models inflation depends on other factors such as people expectations meaning the relationship is not necessarily even proportional, but discussing this in depth would be beyond scope of this answer.

• Thanks for your very clear and elaborate answer! I know the Federal Reserve has several tools to create inflation. But I'm mainly interested in the use of lower rates to increase lending to consumers and thus inflation. A Google search shows that average US 30-year mortgages have interest rates of about 3.17% now. At that figure, when you discount the annual cash flows to the bank it would need about a 3.1% or lower US inflation rate to profit in real terms. Apr 15 at 20:26
• So would you say that this signifies that banks are confident inflation will be lower than 3.1% in the US or is this interest rate figure mostly created by the Federal Reserve by lowering rates while US inflation might in fact go above 3.1%? Sorry if this is a stupid question. I am not an economist. Apr 15 at 20:27
• @JoshuaSchroijen but that back of the envelope calculation is not completely accurate 1. the reason why lower central bank rate results in lower rate for customers is that banks can borrow money at that central bank rate and they earn money on intermediation margin. That intermediation margin will always be positive since banks will set their rates slightly higher. 2. The profit of a bank depends not just on interest rates but on quantity of loans as well. Generally profit function of a company is given by PQ-CQ where for bank P is interest rate (price they charge)
– 1muflon1
Apr 16 at 11:16
• Q is quantity of loans they give out. Next c for a bank would be the cost of getting those funds - as long as (p-c)>0 bank will be profitable and if bank earns positive profit per loan then the higher Q they they provide the profit gets higher even more. For example, suppose that originally interest rate was 6% bank could get money at 2% at 6% interest rate demand for loans was 100 and there is zero inflation. That means that profit of the bank would be 4€ (0.04*100). Now let us suppose central bank lowers its rate by 2% and so do private banks so now private bank interest rate is 4% and CB 0%
– 1muflon1
Apr 16 at 11:23
• Let’s suppose that causes 5% inflation rate but at lower interest demand for loans expands from 100 to 10000. Now the profit for the bank is (0.04-0.00)*10000, which is 400. Now let’s adjust that 400 for that 5% inflation 5% inflation means new CPI is 105 so real value of that 400 is 400/1.05 is approximately 381€ so despite high inflation in this case profits in real terms grown by over 9000%! The point is banks will only lend money if it’s profitable but low interest rates do not mean banks cannot earn profit. What matters is intermediation margin and then quantity of output
– 1muflon1
Apr 16 at 11:30