Wednesday, November 30, 2011

7.4 - Supply & Demand Equilibrium via Price

If we assume that the growth in Supply and Demand is defined by Price, whereas the decline of Supply is determined by Demand and the decline in Demand is determined by Supply directly, we come up with a model that produces some strange dynamics. Try to figure out what causes this strange dynamics. What are the other possible trajectories that may be generated? Is there an equilibrium? 

It seems that delays cause the wonky behavior. Notice that as demand rises, price rises but lag behind. And as price starts to rise, supply is still falling. It looks like the slope of supply is driven by the inflection of price. That is, when the second derivative of the price function is negative, supply falls, whether price is increasing or decreasing. But I think that in the market, as price falls, regardless of its second derivative, supply would also fall.

By removing the direct informational link between supply and demand; that is, with price as their only intermediary, the behavior generated is similar to that of the predator-prey system from the chapter before last. There's no equilibrium here, because there's no mechanism for supply or demand to fall we just get continuous growth.

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