Macroeconomics as information transfer

Is it possible to do a simple extrapolation from the generic supply and demand model to an aggregate supply (AS) and aggregate demand (AD) model? We can identify the information source as the demand and the destination as the supply; we can identify the "price" (the information transfer detector) as the price level in the economy. With this dictionary, many of the previous results carry over: the normal heuristics for shifts in the supply and demand curves apply and we have sticky prices. We can draw the same economic "forces" (left, below) for systems out of equilibrium (here a downward shift in AD), and have what appears to be a downward sticky price level in the traditional economics view (right, below):

If we use "rational expectations" (as defined for this model where given non-ideal information transfer, the observed price is a lower bound on the AS curve, i.e. the black dot on the dashed line in the graphs above), then there is a tendency (on average) for the price level to drift upward until it approaches the center of the uncertain band:

A sample path and the average are shown in the figure above. A question: is this inflation? Is it the tendency for people to think observed prices represent a lower bound of the best estimate, and because it is a lower bound, this estimate will tend to drift upward? This is likely an irreducible part of inflation: for high levels of inflation, inflation is primarily a monetary phenomenon (as Milton Friedman said) and the quantity theory of money is a fairly good model. This drift would only be important/noticeable for low levels of inflation. If AD moves upward in this picture, the price level moves upward to follow:

In the figure above, we show the price level drifting upward with a rightward shift in the AD curve, and there is an increase in the price level (blue curves are with AD shift with average being the dashed curve, gray curves are as in graph above):

Interestingly, including the sticky prices (above), we obtain an AD/AS model that appears in the traditional economics view to have a sharp right angle (dashed red lines) at the current price level for shifts in the AD curve:

This recovers the modern view of the AD-AS model: if output falls below its equilibrium the price level doesn't fall due to sticky prices and instead resources are idled (unemployment, empty storefronts, auto assembly robots turned off) and output is reduced. Policies to boost AD will restore the original output level without producing significant inflation. However, policies to boost AD from the equilibrium point will only cause the price level to drift upward without any increase in output (inflation). Note that the classical view holds that the AS curve is purely vertical.