In a free market supply and demand determines?

The brilliant thing is that no-one has that job. The buyers determine the demand, without colluding, and the sellers determine the supply. If they get it right, demand equals supply.

If demand exceeds supply, people have to queue up. People at the back might shout out that they will play a higher price, so they jump the queue and that drives the price goes up.

If supply exceeds demand, some sellers might shout out that they will sell more cheaply than the rest, and that drives the price down.