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A price is a scalar, there isn't much information it can convey -- in simplified economics like what we are discussing, it just tells you where the intersection of the demand and the supply curves is. Even if you are a producer and can manipulate the prices to observe the shifts in demand, all you can find out is the approximate shape of the demand curve. There is no information about the total wealth of your customers in the price for common goods.
An interesting paper, though it seems to suffer from a serious confusion between the map and the territory. I also wish it would show the fit of the distributions to the data and the errors. As it is, we have to peer at not-too-detailed graphs and I don't know if they are as convincing as the paper makes them out to be. In particular, to my eye the switching point between the two distributions in Fig. 2 isn't necessarily where the paper says it is.