## Friday, May 10, 2013

### What is arbitrary here?

After the previous post, I decided to try and make a list of the unfounded assumptions or non-mathematical arguments made in the blog thus far.
• The identification of the price as the "detector" of an information transfer model of supply and demand is the fundamental assumption of the model. However, to get the basics of the theory right, the demand must be the information source and the supply the destination for the signs to work out right (i.e. having the model show that more demand given fixed supply causes prices to go up as well as reproducing diminishing marginal utility).
• We assumed the Hartley definition of information content (we could use Shannon/Renyi ... though Hartley is Renyi for $\alpha = 0$, and Shannon is Renyi for $\alpha = 1$). It implies all states are equally probable.
• That the "observed" price forms some kind of lower bound on the supply curve. This is, in a way, the "rational expectations" of this theory: if you know that the best you can do is ideal information transfer, you know you are below the "ideal" price. I don't know if the ideal price is something to which you'd want to peg your expectations, though. However, this assumption does not do as much work as it seems. You would get sticky prices for any starting point (assuming the forces in the next bullet) -- however if you start close to the lower bound, prices are typically sticky downward and if you are near the upper bound they are sticky upward. This also leads to an upward drift (if you start near the lower bound) downward drift (starting near the upper bound), ending when you reach the center. This means the assumption (again, assuming the forces in the next bullet) is not stable.
• That the observed price experiences no upward or downward force inside the uncertain region. I made an argument for this here. That is just an argument based on the idea that the demand curve is based on the information source and the supply curve is based on the information destination.
• You might think choosing a point near the center of the uncertain region would be stable -- however if you don't know the distance to the ideal supply curve, then you can't know where the center is. If you did know the distance to the ideal supply curve, then somehow the demand information gleaned from the ideal price is being transmitted to you (when we chose $I_{Q^s} < I_{Q^d}$).