Cobwebs can be used to solve a pair of simultaneous equations but they are notorious for the problems associated with them. In the preceding blog I estimated the intersection point by using a formula for computing where two straight lines will cross.
In the figure below the two lines were fitted using least squares to obtain the coefficients for the linear equations. The values a and a' above are the points where the lines intersect the y-axis with b and b' being the slopes of the lines. The distance of the intersection point from the origin is x.
A simple explanation of the formula is the distance of the intersection point from the origin is the separation of the lines there, Δa, divided by their rate of approach, Δb. As one gets closer to the intersection point the data becomes relatively more linear but eventually one sees more and more relative error in the estimate as one zooms in.
Supplemental (Mar 15): The equilibrium price is a topic discussed in Economics. See the Wikipedia articles on Economic equilibrium and Bayesian game. One can explain the divergent cobwebs as due to the incomplete information that results from basing estimates on past history in a changing market. It's an example of a flaw in the use of Bayes' theorem where current statistics differ from those of the past. Basically what works here doesn't always work there and the situation spirals out of control.
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