Web Diagrams

What you are looking at is sometimes called a web diagram, which in this incarnation illustrates the "Law" of supply and demand. The interpretation is as follows: the falling line represents the price-demand curve, describing how many items of a product will be demanded by the public at various prices and the rising line represents how many items producers are willing to supply at a given price. For both lines the number of items is along the x-axis while price is along the y-axis.

Now what does the intersection of the two lines represent? At this point every item produced is sold and is called the equilibrium position. Now, imagine yourself in an industry such as hog farming (not my example, though the present situation in B.C. makes it topical). It takes a few months to respond to any increase or decrease in demand (i.e. what the consumers demand) by which time the market may have changed. Suppose somehow things are perturbed from equilibrium and demand falls. With a fall in demand price rises, and with a rise in prices the hog farmers decide to increase supply. So far we have the upper horizontal line. Now, when the hogs come to market, the supply exceeds what will be demanded at the old price. Guess what happens to the price? It falls until demand matches what is available i.e. until the vertical line farthest to the right runs into the price-demand curve. Now farmers find the price too low, so they cut back on the supply. When the hogs come to market we are where the lowest horizontal line intersects the price-supply curve. However, now with the given supply, consumers are willing to pay more. This gives the vertical line on the far left. As you can see, this intersects the price-demand curve a bit to the left of the original starting point. Going through the cycle several times you see that each iteration brings you closer to the equilibrium point.

What has been happening in the B.C. hog farming industry is that the high price of hogs and the growing Asian market brought many more suppliers to hog farming. When the Asian market collapsed, the oversupply of hogs drove the price given to hog farmers down. Since the lower price was not passed on the consumers, this did not result in an increase in demand. You can imagine what this means for pig farmers!

Now for some real math. For the two curves chosen if the system is perturbed from equilibrium as time passes (and assuming no further perturbations) the system will approach equilibrium again. Is it possible to choose two curves where this never happens? Is it possible to find two curves where "small" perturbations return to equilibrium but large ones do not? Is it possible to get even more interesting behaviour, say where small perturbations do not return to equilibrium but instead approach some "cyclic" state?

The answer to all of these is "yes". The original system as well as the third are called stable, the second and fourth are called unstable, and the cycle is the last case is called a homoclinic orbit. From a mathematical point of view what we are looking at are iterative maps, or discrete dynamical systems. While the ones we have shown do not display any really wild behaviour such things can behave chaotically.