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A common interpretation is "Higher interest rates put less borrowing power in the hands of consumers and businesses. And when they spend less, firms are not selling everything and prices naturally falls." In the perspective of AS-AD model, this is caused by a downward shift of the demand curve.

However, I suppose it will cause a supply curve shift as well. Today, most production is funded by short-term borrowing and relied on people paying them for the goods and then pay back the loans. So when the interest rate goes up, the production costs go up, and hence causing a negative supply shock as well.

But reality seems to confirm the fact that higher interest rate lower inflation. Why is that? Is that because the supply shock is not as significant as the demand shock? If so, why is that?

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In the short run, why do higher interest rate lower inflation?

As you say:

"Higher interest rates put less borrowing power in the hands of consumers and businesses. And when they spend less, firms are not selling everything and prices naturally falls."

There's also the effect on the velocity of money and the money supply that less borrowing brings to provide further downward pressure on prices.

I also think your concerns about supply falling in the short term are unfounded. Firms are slow to adjust their production/supply due to greater borrowing costs. Instead, they will attempt to keep up production and clear their inventories by lowering prices in the hopes that the next season will show them a success and bail them out. Any such effect from interest rates would be a much longer-run effect.

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In the (very) short run, (VAR-)studies sometimes find a 'price puzzle': raising interest rates raises prices, instead of lowering them. This can be explained by the cost-channel of monetary transmission which is exactly what you described. It should be noted, however, that this puzzle does not always appear in all studies and that there may potentially be other explanations for the price puzzle. Caveat: falling prices when interest rates are raised, do not necesserily imply the absence of the cost channel, but can also indicate its subordination to other channels of monetary transmission. But there surely is a truth in your reasoning.

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We need to understand the state of economy. When prices are rising rapidly we might be in the classical range of economy that is when a positive output gap exists. In such a situation, prices will change according to the higher interest rates (the supply curve will be vertical) and there will be a strong impact of monetary contraction or expansion on the prices and not on quantity as such. And if we are somewhere in the middle where we can safely say that the supply is influenced by price positively. In short run some price adjustment will take place. Firms will not reduce their capacity so swiftly in short run but reduce price instead. But yes the supply can really shift under if this persists.

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The primary source of monetary inflation is when banks create deposits. Another way of putting this is that banks artificially create liquidity (money) when they mismatch short term low yield debt with long term high yielding assets (aka demand deposit reserves are lent out).

Maturity mismatching is the key source of inflation and is poorly regulated by the Fed. In fact is it encouraged, which is strange as it is inherently unstable and inflationary.

So why do higher interest rates lower inflation? Again, monetary inflation roughly equals the extent to which maturity mismatching takes place. Yield is roughly proportional to maturity...so in a siltation with high interest rates if you have long term debt than short term debt (relatively speaking). Put another way, it is tougher for a bank to engage in maturity mismatching when the price of short debt goes up.

This hinders a banks ability to create money and is why high interest rates reduce inflation.

Many attribute inflation to non-banking factors like private production and what not...but this is mostly not true. Most inflation or deflation comes from the private banking sector.

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