Yes, of course Mariana Mazzucato is wrong, why do you ask?

Mariana Mazzucato is on a mission to persuade us all that as government provides all the lovely new technology and shiny shiny gadgetry we so enjoy then therefore we should all be coughing up a fee to said government for said shiny tech. There's a number of problems with this idea: one being the boring detail that government hasn't in fact been the source of all of that lovely research into tech:

I don't know about the CADC, but Tim Jackson's excellent book "Inside Intel" is very clear that the 4004 was a joint Intel-Busicom innovation, DARPA wasn't anywhere to be seen, TI's TMS 1000 was similarly an internal evolutionary development targeted at a range of industry products.

Looking at a preview of Mazzucato's book via Amazon, it seems that her claims about state money being behind the microprocessor are because the US government funded the SEMATECH semiconductor technology consortium with $100 million per year. Note that SEMATECH was founded in 1986 by which point we already had the early 68000 microprocessors, and the first ARM designs (from the UK!) appeared in 1985. Both of these were recognisable predecessors of the various CPUs that have appeared in the iPhone - indeed up to the late iPhone 4 models they used an ARM design.

However, there's two logical errors with her claim which are much more important than the technical details of what she's claiming.

The first is that she doesn't seem to understand the economics of government spending on research very well. There's certain things that the markets, entirely unadorned, don't do very well. While much too much of this is made in general it's at least arguable that the provision of the public good of basic research is one of these things. And given that one of the reasons we have government in the first place is to provide those things, like public goods, that markets don't deal with well then her argument falls into something of a trap. For she's arguing that government should get a slice of the returns (through ownership of patents, of shares in companies that use government funded research) from the provision of that research.

But why? The very idea of government doing this work is that without government intervention we'll not get this public good. We pay our taxes, government provides the public good and we're done. There's nothing extra that should be done about it: assuming that government has done the research, the research is indeed valuable, we've now got here an example of government doing what it has already been paid to do. Hurrah, celebrations and bring out the marching bands etc. There is no logic at all to the idea that government should get two bites of the same cherry.

The second logical problem is that she's arguing that (and this is the real point of her work) the EU research budgets should end up owning a chunk of whatever it is that turns up of value from EU funded research. There must be commercial arrangements for Brussels to recoup some of the profits from the use of the results. And her clinching argument is that Darpa, the US military research budget, produces huge value from the research that it funds. Therefore we should do as they do.

The problem with this is that Darpa deliberately doesn't try to retain an ownership interest in technology derived from research that it funds. On the grounds that it just wants to produce the public goods of the results of that research and when it's done that its job is done. And it's also a great deal easier and more productive to give scientists grants to do research than it is to have arguments with them over ownership, in advance of any actual findings, of whatever the results might be.

That is, we're being advised to a) do as Darpa and b) not do as Darpa in the same sentence.

It's nonsense sadly, but influential nonsense.