The answer is very simple: corruption.

Umbrella business owners are likely paying off the local government and/or organized crime to keep competitors off.

> The money must be going somewhere.

> with the appropriate kickbacks to the local politicians

It's down to supply and demand. You get a license from local govenrment, buy some nice furniture, hire some young people, and set up shop offering a nice looking product of beach access with food, drinks, service at your umbrella, for 75 euro. More if you want front row beach access. You do leave the required free space for the public to put down their own umbrella (or not!). If you're the only shop on that particular beach, and it's a nice beach, people will come, and to enough of them your product will look "sexier" than the public beach area. By paying for it, they solve a need of theirs (beach fun) and can also brag about paying for it on social media.

I don't know who you are but chances are they saw you as a guillible sucker. That price is completely unrepresentative for Greece. Two beds and an umbrella for a day range in the 5-10 euro a day and I'm vacationing in Greece since 15 years now so I know. If you know where to look you can find "free" beds and umbrella provided you consume something from the beach bar, starting with 2 euro for a coffee. I'd get like a 5 euro frappe and give 2 euro off record to the lady who hands the tickets and that's it. For a few hours it's enough given that I don't lay the whole day in one place.

Nope, that's just how much beds in Paros cost.