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Is the Bank of Canada making things worse?
(www.cbc.ca)
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People don't have to buy anything. But they are buying mortgages, and the rising cost of mortgages is what is causing high inflation. If the mortgage vendors dropped their prices, inflation would be within the target range.
And because mortgages are debt, it's a funny situation as debt shrinks with inflation. The higher the inflation, the more compelling debt becomes β hence why rates rise to try and scare people away.
But with interest costs being the driver inflation this time around, we're entering an interesting feedback loop. The higher the interest rates go, the higher the inflation goes, the more compelling taking on debt becomes, the higher inflation goes, the higher the interest rates go, ...
https://www.bankofcanada.ca/core-functions/monetary-policy/
I am just going to leave this here, and if you don't trust BoC, maybe check other literature that explains how central bank, over night rate, etc works to control the market. Cause you seems to have a misunderstanding on how this work if my apple business example above don't work for you.
Your apple business example is fine, and if apples were driving inflation then higher interest rates would quash things pretty quickly. But we're in a situation where it is interest costs themselves which are driving inflation. I'm not sure that has ever happened before. Certainly not in any recent memory.
As before, debt becomes more appealing when inflation is high. If we, for argument's sake, had 100% inflation YoY, a $100,000 loan today will have a principal balance of just $50,000 (constant dollars) next year. That is one hell of a steal! As such, demand for loans increases with inflation, and the cost of acquiring loans (interest) begins to rise to find equilibrium β basic supply and demand.
The trouble we're in is that each time the rates go higher, so too does the cost of borrowing, which in turn sees inflation go higher with borrowing costs being the thing causing inflation this time, which makes debt more appealing and able to burden higher rates β later, rinse, repeat.