Other things equal, a reduction in price leads to a lower quantity supplied.
But other things equal, price never changes. Price always changes because other things are not equal.
This tweet caught my eye:
This is an example of what I call “reasoning from a price change”. Don’t do it!
Most advocates of increased housing construction are proposing measures that would shift the supply curve to the right, resulting in both lower prices and higher output.
Reasoning from a price change is a very common mistake. You see Fed officials doing this when they speculate that higher bond yields might slow the economy. Not if the higher bond yields reflect higher demand for credit.