## Thursday, April 25, 2013

### The previous post with more words and fewer equations

The idea behind the information transfer model is that what is called "demand" in economics is essentially a source of information that is being transmitted to the "supply", a receiver, and the thing measuring the information transfer is what we call the "price".

Choosing constant information sources (i.e. keeping demand constant) or constant information destinations (i.e. a fixed quantity supplied) allows you to trace out supply and demand curves and the movement of those curves (allowing the information source and destination to vary) recovers the Marshall model. We can see diminishing marginal utility in the downward sloping demand curves; this comes from the definition of the "detector" measuring the price having supply in the denominator which follows from the identification of the demand as the information source.

Note that since Fielitz and Borchardt originally described physical processes with this information transfer model, we can make an analogy between economics and thermodynamics, specifically ideal gasses:
• Price is analogous to the pressure of an ideal gas
• Demand is analogous to the work done by an ideal gas (and is related to temperature and energy content)
• Supply is analogous to the volume of an ideal gas

The equation relating the price, supply and demand is analogous to the ideal gas law. One point to make here is that we haven't made any description of how the demand behaves over time, just how it behaves under small perturbations from "equilibrium" -- by which we mean a constant price defined by the intersection of a given supply and demand curve (with ideal information transfer). Humans will decide they don't want e.g. desktop PC's anymore (because of tablets or laptops or whatever reason) and the demand will drop. The economy (and population) grow. Economists frequently use supply and demand diagrams to describe models or specific shocks and this information transfer framework recovers that logic. In the future, I would like to see where else we can take model. In the next post, I will show how you could get (downward) sticky prices from this model by looking at non-ideal information transfer.

PS If we use the linearized version of the supply and demand relationship near the equilibrium price, we can find the (short run) price elasticities from
$$Q^d =Q_{\text{ref}}^d +\frac{Q_0^d}{\kappa }-Q_{\text{ref}}^s P$$
$$Q^s = Q_{\text{ref}}^s-\kappa Q_0^s+\frac{Q_0^s{}^2\kappa ^2}{Q_{\text{ref}}^d}P$$
Such that
$$e^d = \frac{dQ^d/Q^d}{dP/P} =\frac{\kappa Q^d- Q^d_0 - \kappa Q_\text{ref}^d}{\kappa Q^d}$$
Expanding around
$$\Delta Q^d=Q^d-Q_{\text{ref}}^d$$
$$e^d \simeq - \frac{Q^d_0}{\kappa Q^d_\text{ref}} + O(\Delta Q^d)$$
And analogously

$$e^s \simeq \frac{\kappa Q^s_0}{Q^s_\text{ref}} + O(\Delta Q^s)$$

From which we can measure $\kappa$.

(Note, I said fewer equations.)