This is silly.
Markets are a solution to a coordination problem. They are not a channel of communication.
Prices may have a 'signalling' function if 'dis-coordination' games exist- i.e. there are arbitrageurs.
However, for this to happen there has to be a noise generator.
If not, no information or preference aggregation occurs because it would represent a waste of resources.
Noise is a 'bad' for Information theory. It is vital for Market signalling.
Smith is a physicist. He wrote a blogpost on 'Evonomics' which begs for money to fund worthless shite like Smith's on the grounds that it is trying 'to make the world a better place'. It solves a coordination problem for stupid people who want to give away their money and stupid pedants who need to get paid to pose as saviours of humanity.
Smith says- 'Let’s start with a set of people who want blueberries (demand) and a supply of blueberries. These represent complex multidimensional distributions based on all the factors that go into wanting blueberries (a blueberry superfood fad, advertising, individual preferences) and all the factors that go into having blueberries (weather, productivity of blueberry farms, investment).
Why is Smith is starting off with a situation where there is perfect inter-subjective information available to his auditors through some ubiquitous error free communication channel? Shannon's insights are useless here. Information Theory has no purchase.
Perhaps he believes that there is a God who creates a distinct Universe at every moment. Furthermore, this God is under his control. So he says to this God- 'Start by creating a set of people with such and such preferences and endowments'. God may reply 'such people can't be the product of evolution. Under Natural Selection, there can be no unique 'complex, multidimensional' mathematical representation for what you ask. What you get is Red Queen races on Fitness landscapes. Indeed, it is nonsense to say 'people want blueberries'. They don't. Natural Selection endowed them with plasticity in this respect which is why they didn't go extinct. Please don't be so stupid. You begin with a premise which wholly vitiates the argument you are trying to make.'
Smith isn't really making an argument. He's just displaying stupidity and ignorance because that's how we can make the world a better place- right?
Stable prices mean a balance of crop failures and crop booms (supply), population declines and population booms (demand), speculation and risk-aversion (demand) — the distribution of demand for blueberries is equal to the distribution of the supply of blueberries. Nonsense! Stable prices means prices are stable. If we assume everybody has perfect information- i.e. an ubiquitous error free information channel is instantaneously available to everybody without any cost cognitive or otherwise, then, assuming convexity, no hedging, homogeniety, gross substitutability, etc, etc, then Smith wouldn't necessarily be telling stupid lies. However, there would also be no need for a market or prices or Information Theory or Physics or Mathematics. Everybody would be a Leibnizian monad continually reflecting on the perfection of an Occasionalist God.
Prices represent information about the differences (or changes) in the distributions. And differences in distributions mean differences in information. Nope. Prices don't represent anything unless we make a bunch of assumptions which make Information Theory redundant. The truth is, the price vector is just an abstraction. All that matters is that bilateral transactions proceed. Everything else follows very quickly because evolution has hardwired us in a particular way. Thus overall we get a Hannan consistent result featuring arbitrage and evolutionary channelisation of diversity. This may look a Liebnizian outcome to pedants or polemicists, but it isn't. It is regret minimising.
In the remainder of his post, Smith appeals to the following two notions. Both fatally vitiate his argument
1) The principle of maximum entropy- this justifies Samuelson type Economics even in the absence of ergodicity. But if Samuelson type Econ is permissible, Muth Rationality must be even better. Hence, Information theory has no purchase because we always have a better discriminator than that of a
2) A Generative Adversarial Network. The joke here is that availability cascade based shite like Smith's gets past its own peer review process. Why? Because it is 'second order', not alethic. It seeks to make the world a better place not by actually doing so but by asking for money to continue being a fucking parasite on rational discourse.