The purpose of the seastead is to provide the people living on it with the freedom to form a new autonomous government. It isn't because people are running out of space on land. And while there is still plenty of space on land, every single square inch of it is already owned by another nation.
Many countries are willing to sell some uninhabited islands as property that, while theoretically are administered to by the government, are practically independent. These have the benefits of not requiring engineering that we don't currently have, or at least that we don't have without enormous wads of cash.
You could also go the Sealand route if the opportunity passes, which fits in more with the autonomy.
Remember, the seastead would be privately funded.
What would be privately funding this? What company or individual would have any reason to go for this? People with money don't tend to have gotten there by shelling out billions so that random people can 'form a new autonomous government... unless you include banana republic sorts of governments, but I don't think that's what you were intending. Anyway, for the costs that this thing could incur, it'd still be cheaper to just blow away some third-world nation if they were already lacking that morality.
And while a preexisting government could potentially give money to a group of people to help them get the seastead started, I would highly discourage that. Starting off in debt would be a bad start.
Because these unknown 'private donors' would surely have no strings attached whatsoever to that huge amount of money, right?
If you're referring to the Nimitz-class carrier, than yes, it does cost between 4.5-6 billion dollars to build. Take into consideration though, that it was originally 675 million dollars to produce, but it received upgraded multirole systems, hull redesign and a transition to a wider variety of offensive and defensive roles. Not to mention they also last a considerably longer amount of time than the previous models.
Provided these seasteads were to be successful as you claim, how would you intend for them to be defended? Also, a very key statement at the last part. Durability is a big part of what they shelled out for, and it's arguably even more important on a city; I don't know about you, but having the city I live in collapsing into the ocean due to cheap construction would be a bit of a bummer. That aircraft carrier version with the lesser durability still costs the larger part of a billion to create, and that's without gluing a city to the whole thing.
As for the cost of the seastead itself... I posted a link somewhere in this thread that I'll have to find. It has more information on that.
Also posted a link to more information relating to this. I'll find it and edit my post.
Post when you do.
[TL;DR
The economy could focus on
hydroponics, fresh water production, energy production, ocean fishing/fishing hatcheries, resource extraction and manufacturing, etc.
Most of the sectors you've listed here require a good deal of space to function, and even more to have a hope of competing, let alone factoring in all the storage and such that they would have to do while waiting to ship off their products. On these sorts of things, space is an incredibly expensive resource; it requires much more cash to construct and much more to maintain, and there's more of an area for something to go wrong.
Though the guy has an interesting point about how they would have to be forced to work harder to survive, there comes to be a threshold where that just becomes stupid for a person to do, where the obvious advantages of the other side make up for any amount of effort one could possibly get in.
For example, let's seize on that hydroponic farming. With limited space (remember, it's extremely costly) and water resources (converting from salt water to fresh isn't that cheap), you can only grow so many crops. Once they mature, the boats that come by ship them across the ocean, where they will eventually arrive at a market. At this market, these crops are expected to compete with gigantic agricultural machines that pretty much don't have the similar restrictions on space (do you know how much land the better part of a billion dollars can get you in prime agricultural territory? Hint: It's more than an aircraft carrier's worth of space) and aren't always required to be shipped over the ocean. At best, food grown in seasteads would be a novelty; I can only foresee those hydroponic plants being used effectively to feed the people on the seastead.
