One of the original directions I took on this blog was to look at stochastic paths bounded by the information equilibrium supply and demand curves ... a direction that turned out to be not very fruitful. Despite that, I thought I'd revisit it in light of two years of improving understanding.
I think the first time I used the "maximum entropy" point in the area under the supply and demand curves was here. Let's assume that is our starting point and look at a stochastic path bounded by the supply and demand curves. I assumed the log scale of prices represented the uniform density of states (and a lower bound). It looks something like this (left is log price, log p, and right is price, p):
Here is the resulting price path vs time (yellow, in the presence of inflation, and blue, the "real" price):
The bounds are shown as the solid lines and the maximum entropy price is shown by the dashed lines. Here is the distribution of price changes (in the "real" price):
Anyway, I'm not really breaking much ground here. This just shows that it's possible for price movements to look like a normal random walk, thus the information equilibrium view doesn't have to be inconsistent with the efficient markets hypothesis. However, sometimes the boundaries have an impact and you can get biases towards prices falling and staying low for awhile: