Bombelli predates corporations on any large scale, so including his work seems strange in this context.

I don't know anything about interventionist causality, and Objectivism seems like a waste of time. The rest all seem to have produced worthwhile results.

But this is costless analysis! Of course if you buy lots of lottery tickets, and look only at the winners, then buying lottery tickets looks worthwhile. You have to consider the opportunity costs, not just of these research projects, but also of every other similarly situated research project. And you also have to do time-discounting. Bombelli discovering complex numbers in 1572 looks like a waste, when they weren't useful for 200 years or more.

Moreover, I don't know why "corporations" is the comparison. The comparison is the private sector generally. Huge amounts of scientific work are done, and continue to be done, by enthusiastic amateurs, and the charitable sector. I am not making the claim that in an ideal world all government academics should be fired (although I do think that would be a big improvement on the current situation). I merely claimed that, on the margin, we are hugely oversupplied with academics, and undersupplied with businessmen.

For basic research, the is number is larger- it was around three decades from Einstein's explanation of the photoelectric effect to the commercialization of cameras based on it.

Another problem with fundamental research -- from a commercial corporation's point of view -- is that its results may not be applicable at all to products in your target market. For example, you might start by researching the formation of clouds in the atmosphere, and end up with major breakthroughs in atomic theory. Those are interesting, to be sure, but how are you going to sell that ?

This is but one of the reasons why large corporations tend to stay away from fundamental research, unless they can write it off their taxes or something.

I don't think anyone has a good way of doing that.

You stated that academics aren't easily funded by the private sector because of an externality argument. I agreed that it is possible to argue that "basic research" or some such is underprovided by the market, because the private sector may not be able to capture all externalities, and that this is in some sense a market failure. However, I am saying that:

• No-one can say how by much the private sector is underproviding. Therefore even if the intervention were done by angels, it is as likely to make things worse as better.
• Government intervention will cost money, resulting in deadweight losses through tax.
• The creation of a powerful body of rent-seeking will cause academic research to be massively oversupplied
• Moreover "research" is not a fungible good; the money and resources will not necessarily go to the most useful areas, but to the most politically convenient ones
• The rent-seeking will also have deadweight costs (e.g. academics spending lots of time writing grant proposals, taxpayers having to organise to prevent themselves getting robbed blind)
• This will also incentivise rent-seeking elsewhere (if the academics are successful in asking for a subsidy, it encourages the farmers)
• The adoption of the subsidy discourages market participants from finding new ways to capture the externality.

So, even though there may be a textbook "market failure," there is no reason for any intervention. Dissolve the modern-day monasteries, and let academics prove their use, if they can. And indeed, I'm sure Alvin Roth would be just fine if we did.