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