General economic activity effects the velocity of money which effects inflation. If capital—for businesses or individuals—is more expensive, some of people's plans for spending will be shelved, that reduces activity and velocity.

See "Monetary transmission mechanism"

* https://en.wikipedia.org/wiki/Monetary_transmission_mechanis...

* https://www.ecb.europa.eu/mopo/intro/transmission/html/index...

* https://www.rba.gov.au/education/resources/explainers/the-tr...

* https://www.pragcap.com/monetary-policy-transmission-mechani...

Of course inflation is caused by things other than demand (e.g., supply: energy prices, food prices (thanks Russia!)).