How much does supply and demand affect prostitution?

Supply and demand is one of the key concepts I learned in the economics class I once took. Assuming there were no significant outside factors (like subsidies), the cost and ease of production would affect the supply of the product, and the demand for the product would affect the price and the quantity produced. Yet, when I look at the situation in the Red Light District and talk to the women there, it feels like something has gone horribly wrong with the economics here. These are the details for someone working in Amsterdam (i.e. the math):


The costs are: 
- Room is 100-150 euros per day (more in the evening); paid in cash.
- Housing is likely 1500 euros per month, as you're not eligible for any rent-controller housing and rent prices in Amsterdam are extremely high. It could possibly be cheaper, but then you're living outside of Amsterdam and paying extra travelling costs.
- Per customer, you give out about 5 euros on supplies
- Health/insurance costs: 200+ euros per month (being self-employed, these costs are higher than average);
- No vacation or sick leave because of the loss of income and the high risk of losing your window;
- Taxes are relatively high, especially since it is, for tax reasons, financially better for the person renting you the room to give you as few receipts for the room as possible, and so you can't declare your rent half the time. Complain, and you run the risk of losing your room to the next woman/pimp looking for a room. 
- Emotional and physical costs, as well as potential theft and abuse.

Thus, simply in order to make ends meet, you need to earn about 200 euros per day. If you charge 50 euros per customer (the standard rate), that means 4 customers in a 10 hour workday; 5 customers if you work the night-shift when the rooms are more expensive. For every person that pays more or every extra customer, that's extra income. But that also assumes every women is using the standard rate. But if you're only getting 3 customers per day at 50 euros, then it makes sense to lower the rate to 40 so that you get 4 or even 5. The cost per customer to the woman is low enough, that the appeal of lowering the rate is pretty high - the appeal only increases if there's a pimp threatening to beat you if you don't make several hundred euros extra per shift. But if everyone starts lowering, then everyone starts making less, and woman lower even further to 30 euros or by doing unsafe things. That means a lot of customers simply to make ends meet, let alone earn extra for food, smokes, pimp, money for home, savings and so on.

Many of the women work 7 days a week, 10 hours a day: crappy hours and a lousy job where you are often treated poorly and seen negatively. Because of that, you would expect that supply of women wanting the job would decrease - and less windows would be rented and the rent would have to go down because of the lack of demand. But there are an endless supply of women, new women arriving constantly. And this is where the economics has gone horribly wrong. There have been too many stories of easy money, too many others pushing women into the business, too many women believing they have no skills, too many countries where poverty is so high that even this bad is better than there.And those who are working in these conditions - barely making ends meet, let alone earning a decent wage - do not leave, even though every economic principle says they should. Is not any other job better? But most stay, as there are no other jobs, little hope of something better, and also, I believe, because the world of prostitution has a (spiritually) dark side that is stronger than the economic rules of supply and demand.