There seems to be a huge leap in paragraph two. Stiglitz writes "if markets were as efficient in transmitting information as the free marketeers claimed, no one would have any incentive to gather and process it." The implications of this observation have a degree of inevitability which I work though below.

Suppose you want to make money on the stock market. If you could work out the true value of the companies listed there you could manage a portfolio by buying underpriced stock and selling it later. Perhaps you hire a team of PhD economists to do the valuations for you. Suppose their valuations are accurate and you make money on your trading. Your friends will be envious at first. If however it turns out the money you make trading fails to cover the cost of running your research team, you will end up having to sell your yacht and your friends will laugh at you.

What is the relationship between research costs and prediction accuracy? We might at first guess 1/x. However, if we had spent a million dollars to get a 10% accurate prediction, do we really think that a second million would get us to 5% accuracy? The biggest issue is that stock values depend on the future and the future is usually exponentially sensitive to initial conditions. Perhaps the accuracy with which our research determines initial conditions is inversely proportional to the cost, but that still leaves an exponential divergence.A reasonable first guess is that if we want an accuracy of x% the research will cost exp(1/x).

Meanwhile we need to take a stab at the function form of the profit from trading. Perhaps it is proportional to the difference between the true price and the market price, but that ignores the question of how long we have to wait before we can sell and realise our gains. The dynamics of the market are at issue. The traditional saying is "markets can stay irrational longer than you can stay solvent.". Well, yes, but the more prices are out of wack, the faster the pressure for a correction builds up. Dynamics is difficult. Let's just guess that the profits from trading on difference btween true price and market price have a form something like x tanh x.

Putting these together and equating marginal chances leads to what I call the "dead zone" theory of markets. Market prices are wrong and bumble about in a dead zone around the true price. Reasonable functional forms give quite firm edges to the dead zone.

An interesting follow question asks for the probability distribution of the true price in the dead zone. Perhaps there is a strong central tendency, but what might produce it? Perhaps the distribution is uniform across the dead zone? Or maybe psychological factors push the dead zone so that the true price is at one end or the other. (If only we knew which!) However I want to get back to Stiglitz' book review.

The reasoning that Stiglitz adumbrates leads to the notion of a dead zone of some definite size. Three responses are the pessimistic, the "markets fail, use markets" of Bryan Caplan and Stiglitz's maneouvre.

A pessimist could follow up with a critique of modern society that claims it is out of control and heading for disaster. The pessimistic critique could insist that technological challenges and uncertainies make the future unmangeable and unplannable, and futher more market solutions will not help because the dead zone is huge; Adam Smith's invisible hand might as well not be there.

A free-market advocate need not be much embarrassed by even a large dead zone. How should production and exchange be organized? It is a choice between competing options and the difficulties that give rise to the dead zone seem to place heavy burdens on the alternative options.

Stiglitz treats the dead zone as huge, so large that "Adam Smith's hand was not in fact invisible: it wasn't there." I don't know why. The dead zone clearly has to exist, but that sheds no light on whether it is large or small.

I'm not managing to make much sense of economic discussions. Does efficient-market-theory" really deny the existance of the dead zone? Do the opponents of efficient-market-theory really believe that because the dead zone exists it is necessarily huge?