The rent will adjust to what the highest willing renter will pay. If I think Sidi's flat is worth $1/month but you are willing to pay $10, guess what Sidi will charge?
Put another way, Sidi will come between you and your profit, and make the most amount of money he can get away with. I want to be like Sidi when I grow up, we all should :)
This gets a little more interesting when you consider the cost of production: here, the cost will move upwards until it exactly matches the revenue from the most expensive unit of production, so that unit operates at break-even. Everyone else therefore makes outsized profits equal to the delta between their own cost and the market price. This is the "scarcity rent" that power production companies in the US love so much: Power price is designed to afford the most expensive gas plants to break-even, so cheaper variable, base power sources (hydro, wind, even nuclear) will make outsized profits. Every producer then does a race of the bottom to create cheaepr units of production, thereby slowly decreasing the highest marginal cost of production, and therefore the price to us consumers.