If the same number of people are chasing the same number of apartments but making more money, the natural conclusion is that the price of the apartments will go

If the same number of people are chasing the same number of apartments but making more money, the natural conclusion is that the price of the apartments will go up. If the same number of people are chasing _more_ apartments, the price of the apartments will go down (ignoring induced demand, but I think this is minor for NYC/SF). You can't just legislate a higher wage because in the long run rents will stabilize at a higher level to compensate and all you've done is make landlords richer and fuck over every small business in the city. You need to actually have more supply.