You're thinking about the problem from the wrong perspective. Higher prices do encourage people to sell more (in this case their labor). But a price floor excludes a whole category of people (the young, unskilled, or transient) from the market. Its this category of people that would now be eligible to compete in the labor market
Labour supply is the amount of workers willing to work at a given wage. Demand for labour is the amount of workers wanted at a certain wage. If someone's excluded from the market at a certain wage, it means there isn't demand for their labour at that price.
> Labour supply is the amount of workers willing to work at a given wage. Demand for labour is the amount of workers wanted at a certain wage. If someone's excluded from the market at a certain wage, it means there isn't demand for their labour at that price.
If the person is excluded from the market, how does that show lack of demand for their labour at a certain wage? The person isn't even a market participant at that point.
If someone is willing to work for $5, they will be willing to work for $15 [0]. The fact that they don't work is at all when the wage floor is $15 is because no one is willing to hire them at that price. Hence, it is a demand side issue.
The supply/demand curve here is a bit tricky, becauce, given a minimum wage of $15, the demand for labor at $14.99 is actually less than the demand for labor at $15, because employers are generally not willing to break the law over $0.01/hr
The very word excluded implies that the person excluded wants to be included, otherwise we'd simply say they're outside the labour force or non-participants.