system
Given the following post, respond as if you're commenting on Reddit:
human
Could higher interest rates cause higher inflation?

I understand that raising interest rates to decrease the rate of money supply increase (and therefore demand) aims to reduce inflation. 

But could this also cause inflation?

Higher interest rates are also a negative supply shock not just demand. If business loan repayments go up, they will need to take in more cash to pay them. If homeowners mortgage payments go up, they will need a higher wage to pay this. 

If this is a greater force than the reduced demand (say because people deplete their savings) could inflation be made worse?

Would it not be more worthwhile to raise interest rates on new lending only?
gpt
No, it doesn't work like that.

> If business loan repayments go up, they will need to take in more cash to pay them.

That increase in costs gives the business no pricing power to increase prices. Many businesses have little to no debt and no reason to raise prices. They will not raise prices because *other* businesses have debts. The businesses with debts must accept the market price.

Businesses that already have pricing power will already be taking advantage of it. They will already have raised prices as high as they possibly can without reducing profits.

> If homeowners mortgage payments go up, they will need a higher wage to pay this. 

This is the same as the situation for businesses.  The homeowner's labour does not become more valuable because of the extra debt they must pay. There is not reason for businesses to pay more.