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The Fisher effect says that highter inflation rate leads to a higher nominal rate.

I found an interesting explanation about the interest rates:

Lower interest rates translate to more money available for borrowing, making consumers spend more. The more consumers spend, the more the economy grows, resulting in a surge in demand for commodities, while there’s no change in supply. An increase in demand which can’t be met by supply results in inflation. Higher interest rates make people cautious and encourage them to save more and borrow less. As a result, the amount of money circulating in the market reduces. Less money, of course, would mean that consumers find it more difficult to buy goods and services. The demand is less than the supply, the hike in prices stabilise, and sometimes, prices even come down. So when we have inflation, this could mean that the money supply has increased. So when the money supply has increased and we have an inflation, according to the fisher effect there has to be a higher nominal rate. In the above explanation, they say that lower interest rates translato to more money available.

I can't understand now, does it lead to higher or lower interest rate?

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The issue is that in the macroeconomy a lot of things happen at the same time and many effects go both ways. When we talk about certain effects, we often make the "ceteris paribus" assumption, which means "all else being equal". This is to isolate each effect from all the other things going on. What you observe in equilibrium is then the interplay of all effects. Furthermore, it is important to distinguish the timing of effects, as they do not all occur simulataneously and instantaneously.

So, the fisher effect you describe says that higher inflation leads to higher interest rates.

The passage you cited says that lower interest rates can lead to higher inflation. However, this effect often takes some time to occur.

Both these things are true. They describe different directions of effects. Of course, it follows that lower interest rates lead to higher inflation, which then increases the interest rate later on. Where the whole process of back and forth effects stops, is the equilibrium.

This shows the importance of knowing what is driving the effects, because whether the "ceteris paribus" assumption applies to a certain effect depends on what is causing it. It is important to distinguish whether we are analyzing an "exogenous" shock that increased inflation or that reduced interest rates, in order to distinguish which effects are second round. Depending on what started the chain of events in the macroeconomy, you may expect different things to happen.

The effects can also depend on whether we look at the economy in the short run or the long run. Some effects (like an increase in inflation) take longer to occur than others.

The nominal interest rate is equal to the real interest rate plus inflation: $i = r + \pi $. Here $i$ is the nominal rate, $r$ is the real rate and $\pi$ is the inflation rate. If you lend money, there is a certain "real" return that you expect, which is $r$. However, if there is inflation, then the face value of the money you receive when you get paid back is less than what you lent, due to inflation, so you adjust for that as well. That's why inflation increases interest rates.

If you lower the interest rate, then as you describe in your question, the inflation rate may increase over time.

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