Sorry for being a broken record, but the supply is not cut in half. The supply continues to increase every 10 minutes until it reaches 21 million. It is the production that is halved. It is a common misconception.
The distinction is important because the claim that "the supply is reduced" it is typically followed up with a statement along the lines of, "and a lower supply causes a higher price." The logic is erroneous because the supply is not reduced.
Inflation rate cuts half after a halving, each halving. New supply will be a half less than before a halving but there will be more bitcoins appear with each new block till 2140 after 20,999M bitcoins all mined from bitcoin blocks.
Bitcoin inflation rate and supply vs time.