Sorry about the lack of posts lately -- I've been busy with with work and on travel. I also discussed actual research money for the model through a (somewhat non-traditional for economics) funding agency and put the idea in front of two professional economists. Understandably, skepticism all around (I have an upcoming post on one of those interactions).
I am also working on a post that started out as a start towards fully incorporating the idea of expectations (as a source of information loss) in response to a piece by Nick Rowe, but Nick has another interesting one that I haven't fully digested yet. Still writing there.
So here's a quick post. Awhile back I did a post on the minimum wage; I used a least informative prior with the non-ideal information transfer to say that the observed price is somewhere in the lower triangle of a supply and demand diagram (see link at the beginning of this sentence for details) -- I don't know where. If we take each position in that lower triangle to be equally probable, then you can show that the centroid appears below the ideal price but at the same quantity supplied/demanded as the ideal equilibrium.
What happens to this point under shifts of the supply and demand curves? Well, it turns out, the non-ideal price follows along a non-ideal supply (or demand) curve that is parallel to the ideal curve. Here's a graph; the purple points represent the starting point and the point after the shift while the dashed purple curve represents the locus of points for different shifts: