Well, I don't know if anything in economics is provable per se, but Europe (more specifically the UK) is going through this debate right now. The EU is a giant free trade zone. How valuable is that? People who do business all think it's essential, but people are who are just employees aren't so sure. Let the debate commence.
Whatever the reason, they still boosted domestic production and economic growth.
That may have been true in the USA (hard to say given the lack of in-depth statistics back then and difficulty of knowing the impacts of such things even today) but it probably wasn't the case abroad. Sure, the USA didn't care one whit back then about the impact of tariffs on British or European manufacturers, nor did they care much if Americans couldn't afford superior foreign-made products for a while. They valued economic independence more, and given their situation that was understandable.
But putting military concerns to one side, free trade theory is correct. Those tariffs made the world as a whole economically worse off. If governments could be trusted not to use their economies as weapons of war, it'd be better for everyone if tariffs were reduced and removed, because it makes people wealthier in the long run and that's why every so often countries and trading blocs try to engage in free trade treaties.
Of course the problem is, governments do so love using economics as a weapon
Banning loss leaders (a.k.a. market dumping) seems like an inherently attractive fix to improve free markets, but it's fraught with difficulty.
The most obvious problem is R&D costs. I do market research and decide that people would be willing to pay $100 for a widget. But said widget does not yet exist, so I spend a million dollars to develop it, and then start selling it for $100 a pop. I calculate it will take several years to break even but that's OK, because I'm a businessman who thinks long term and we like those sorts of people don't we?
I think you can see where this is going - the business runs at a loss for several years, to build the market and spread out the development costs. Eventually I can reduce the price of my widget because I paid off the R&D costs. But until then I'm still in the red.
Amazon is no different. If they make no profit, it's because they choose to charge low prices, build the market and develop new products all at the same time, instead of cashing out. Though actually I think you're distorting history by saying they "muscled their way into the market". Amazon was one of the first online stores. There was no market to muscle in to, nobody else was doing what they were doing. Bezos pretty much created a new market from scratch.
And sometimes it is, despite the supposed inefficiencies. That's what the French government thinks, and there are similar opinions in other European countries.
If governments could reflect the diversity of opinions in their population perfectly ever time, the world would be a simpler place.
In practice they tend to reflect the opinions of a very specific group of people - politicians (closely followed by bureaucrats) who are e.g. typically older and wealthier than the average man on the street.
There's an interesting article by an author on the topic, called "Don’t Support Your Local Bookseller: Buying books on Amazon is better for authors, better for the economy, and better for you". Worth reading, at least.
If it isn't better, why would you do it?
Small online book shop - you didn't hear about them so
Read this article about a commercial dispute between Amazon and a large publisher (Hachette). It was on the Colbert Report, a US news comedy show. The hosts book was caught up in this dispute and so he told people to go buy his book and others at Powell's Books, which I can only describe as a small (relative to Amazon) online book store.
The price of homes has become wildly disconnected from the cost of land thanks to their use as speculative asset, but even if that were not the case in most places you can build upwards way more than people do. And populations are stabilising or even falling in developed parts of the world. Only immigration keeps it from entering full-on collapse. So if our messed up financial system gets fixed and people stop using houses as piggy banks I see no reason why the cost of homes must go up forever.
If you want many participants in a market, most of them will be small. That is why small shops are worthy of protection.
You can't have it both ways. If you think markets can only support five competitors, simply shrinking the market doesn't radically change things, as by definition local bookstores only compete in a small local market with a small selection of books. If you want a book that isn't in the bestsellers list, then in your local town there's probably only one or two book shops that stock it at best and most likely none.
You also want to have employment in your country be fairly even, and not have some areas with high demand and low supply and some with low demand and many unemployed, which is why local shops are worthy of protection.
You could apply this sort of argument to anything but it'd still be based on a false premise: while it'd be nice to have geographically distributed demand for labour, in practice this has not been true since the invention of cities. Why should people in cities have to suffer so someone in the countryside can be given a useless make-work job and be told they're helping preserve the nations culture? This is how the CAP got started, a program so massively unfair it is routinely used as ammunition by Euro-skeptics in Britain and elsewhere.
What's more once you decide that lots of people deserve to be protected from changing times, what happens if everyone decides that the e-book is to reading what the automobile is to riding horses? Do we keep all these little local booksellers employed even though nobody goes into their shop anymore, just because it's always been that way? I hope not but that's exactly the kind of thing France excels at.
The Jurassic period. O2 in atmosphere was 130% modern levels
And all of the species that were dominant during the Triassic period did really well throughout the Jurassic...
The geek as cultural imperialist.
What has no value for me has no value for you.
Except I didn't say that. Go back and read what I wrote again before being so condescending. I said that I personally didn't see any inherent reason why bookshops are special and need protection, not that nobody else should value them. If you value local bookshops, there's a simple non-legal fix: go buy books there.
But obviously most French people are like me, otherwise France wouldn't have felt any need to pass such a law. French people would have rejected buying books on Amazon and the local players would have felt little impact. There would have been no problem to solve. So far from being a "cultural imperialist geek" I'm just pointing out the bleedingly obvious - regardless of what some columnist in the New York Times might think apparently most French people don't care much about their local bookshop culture, at least, not enough to pass up cheap and convenient book sales online. And that's fine.
As someone who has lived for a time in Europe (various times in France, Germany, and Italy), I can firmly state that I'd take their small food markets and shops over the U.S. any day
Sure, and you can do that by shopping there.
But Europe went through this process too. In the UK lots of people wailed about how Tesco and other big supermarkets were killing off the small local shops (implicitly assumed to be good). In fact, when pushed, many people would admit that the small local grocers often weren't really that great, that variety was non-existent and quality highly variable. Supermarkets crushed the little local shops because they were better and all the nostalgia in the world couldn't change that fundamental reality. And this isn't something restricted to the USA. Supermarkets did the same thing everywhere. It was just a better model.
BTW I don't buy it that America doesn't have small local food shops. At least when I've been in California there have often been open air markets with local produce. They aren't a scalable way for an entire population to get their food, of course.
And that's better than ordering it online, how?
Doesn't have to be from Amazon, could be from a small online book store.
No? I keep reading about how the economic recovery is creating lots of part time jobs.
What you're saying is that those jobs don't pay the same as a full time job. No, obviously not, but if the things around people keep getting cheaper then it doesn't matter: they can still end up objectively more wealthy. For instance, let's say 20 years from now everyone buys books cheap via e-readers and nobody has to own a car or parking spot anymore, because all the cars drive themselves and turn up on demand. People in such a world would have objectively better lives than ours - they'd be able to read any book they desired whilst on a long journey, get drunk if they wanted to when they were there, and get back home again, all for less than what they spend today and with more convenience. If they worked part time, they'd still earn less than a full time person would in that future world, but they'd still be better off than a full time worker in today's world who doesn't have those great things even though they have full employment.
Big internet sites make the economy more efficient. But the problem is an efficient economy doesn't need workers. And if there are no workers, there's no one to purchase the goods.
"Workers" can find something else to do, possibly newer and more interesting kinds of work, or possibly less work on a four day week, etc.
Look, humanity is stuck on this rock, we aren't going anywhere unless someone figures out how to do the impossible and fly around the galaxy faster than light. So our society needs an eventual end goal, and it seems widely agreed that this end goal should be that we all live lives of leisure and can do/go/explore/build whatever the hell we like, whenever we like it. Obviously along the way that means we'll end up doing less and less work until hardly anyone is doing any real work at all and it's all done by robots a la the world of Manna which was discussed here on Slashdot not that long ago.
So if books get delivered by radio to a device with a battery that lasts for a month and gives me access to the whole world's library for a pittance, how is that not a giant step towards the kind of utopia I described above? Small local bookshops staffed by smart shop assistant girls with cute French accents are great until you realise they don't have the book you want and you had to haul your ass into town in order to discover this fact (assuming the shop was even open by the time you got there). It's not something I would trade progress for.
Many French People in rural France loathe the Parisiennes. When a car with a Paris Department number plate comes to my Village the locals suddenly become sullen and un-coopoerative towards the visitors. When the car leaves, life returns to normal. Even to a 'Les Rostbiff' like me they are far friendlier that they are to anyone from Paris.
The same is true in reverse too. I picked up quite a thick rural Normandy accent when I speak French and discovered that everyone in Paris is a lot more polite to me if I speak French with an English accent...
 Cultural equivalents: For brits, think Devonshire farmer, for americans think deep south.