Back in 1964 Kenneth Arrow showed that, in theory, competitive markets could produce optimal allocations as long as there were state-contingent securities which allowed people to trade risks and so insure against them. The problem is, he said, that:

Many of the economic institutions which would be needed to carry out the competitive allocation in the case of uncertainty are in fact lacking.

Almost thirty years later, Robert Shiller showed that this remained the case. "The insurance industry has not devised policies that insure against many...causes of fluctuations in incomes" he wrote in Macro Markets in 1993.

He proposed creating GDP-linked securities which people who were optimistic about economic growth could buy whilst those worried about recession could go short. This would allow ordinary people to buy (via insurance companies (pdf)) insurance against recession. In the same spirit, he showed, securities could be created whose prices were linked to the incomes of specific occupations. These would serve a signalling function, showing young people which jobs to enter and which avoid, and an insurance role, allowing people to hedge the risk of a decline in demand for their skills. And, he added, we could also have house price futures. Young people who fear not being able to get on the "housing ladder" could buy these as insurance against rising prices, whilst people worried about falling prices (such as Buy-to-Let landlords or those planning on downsizing) could go short.

In ways such as these, financial markets could help people spread risk better.

But almost sixty years after Arrow and thirty after Shiller, such markets still don't exist or do so in still-rudimentary form. Judged by the standard of Arrow's ideal of complete state-contingent markets, we've seen astoundingly little useful financial innovation during my long lifetime. And this is not to mention the other failures of the financial system such as its tendency to generate crises; to commit crime; to mis-sell useless products; and (in the UK at least) fail to finance industry: for every pound that UK banks have lent to non-property SMEs, they have lent £11 in residential mortgages.

What we have seen in recent years, though, is a lot of innovation of dubious utility such as non-fungible tokens, special purpose acquisition companies, initial coin offerings, platforms to facilitate the mug's game that is day-trading, and Mintme's plan for people to issue tokens in themselves. And then there is the fact that it is not obvious what (lawful) need is fulfilled by cryptocurrencies.

Why, then, do we have so little useful innovation and so much useless?

It's because of a collective action problem. Imagine we had a thriving market in, say, house price futures. Who'd gain? The main beneficiaries would be ordinary people who could trade away their house price risks. Those who devised the securities, however, would get only origination fees, which should in principle be bid down as other firms entered the market.

And markets don't spring up from nothing. In his excellent An Engine Not a Camera Donald MacKenzie describes how Leo Melamed, head of the CME, encouraged growth of stock index futures, one of the few examples of useful financial innovation. A market, said Melamed, "is more than a bright idea. It takes planning, calculation, arm-twisting and tenacity to get a market up and going. Even when it's chugging along, it has to be cranked and pushed." In other words, it requires somebody to solve a collective action problem. Markets must be liquid but liquidity is a collective good: it requires many traders to come together.

Financial innovation, therefore, suffers from the problem described by William Nordhaus - that producers of new innovations capture only a "minuscule fraction" of their social gains. Which means that innovation is under-provided by the market.

What's not under-provided, however, are forms of innovation in which innovators can extract big rewards. And these come from being able to, in Keynes' words, "pass the bad, or depreciating, half-crown to the other fellow."

What we have here, then, is a simple failure of capitalism - the fact that the pursuit of private profit prevents the fulfilment of genuine social need. Mariana Mazzucato's point that the state can be a source of innovation applies especially to finance. State ownership of financial institutions might be necessary to solve the collective action problem that blocks useful innovation. One could imagine state-owned banks originating GDP or occupation-based securities which the government then gives to everybody as part of people's QE. When I say state ownership, I mean ownership that forces banks to become providers of public service (and not just in the context of improving financial innovation) rather than the botched nationalizations of 2008 that left the monkeys in charge of the zoo.

You might think this is a Marxian demand. In this context, though, it's not. There's a tradition in Marx (which I'm not wholly comfortable with) which sees markets as irrational, alienating and sources of chaos and unfreedom. Advocating more financial markets is therefore unMarxist. What it is, though, is bog-standard orthodox economics. If we really want to achieve the fundamental theorem of general equilibrium economics in which free markets are Pareto-optimal, we need more complete markets - and this requires state ownership and control of banks.

Which gives us a delightful paradox - that in a sense, conventional economics is more radical than Marxism.