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The cobweb theorem in Economics
Vinod Anand | 17 Feb 2012

This refers to the analysis of the question of whether, in a market in which the amount currently supplied depends on what the price was in some previous period, price will tend to converge to an equilibrium, or diverge from an equilibrium, if it is ever out of it.

THE ANALYSIS was first developed in the context of certain agricultural markets - it was for some time referred to as the 'hog cycle' phenomenon. Suppose farmers plant now an acreage of a particular crop, which, given climatic conditions and the absence of stocks, determines the amount of the crop which will be supplied after the harvest.

If the acreage devoted to the crop depends on the price at the time of sowing, then supply at a given time depends on the price one period earlier. In this case, if the market is ever out of equilibrium, there will be a series of fluctuations in prices, which may get smaller and smaller and eventually converge to an equilibrium, or larger and larger and never converge.

At time period 1, price will be at a particular level; farmers will plant accordingly, and in one period's time will put the resulting crop on the market. Suppose, however, that at that time demand is higher than it was previously, so that the available supply is insufficient to meet the demand at the old price, and price must rise to 'ration off' available supply among buyers. Then, at time period 2, farmers will plant a larger acreage of the crop than they did previously, because price is now higher, and so, in one period's time, a larger supply will be forthcoming on the market.

This supply will be more than that required to satisfy demand at the price which prevailed at period 2, and so price must fall to induce buyers to take up the extra supply. Less will therefore be sown at time period 3, and so less will be put on the market at time period 4, and so price must rise again. And so the process continues. The important question is: do the price changes become smaller each time, or larger each time? If the former, then the market will converge to equilibrium - eventually, the amount put on the market will be just equal to the amount buyers are prepared to take at the price which existed last period. If the latter, the price simply oscillates infinitely. It is possible to formulate in precise terms the conditions under which each occur, and in fact the analysis of these conditions was one of the earliest examples of dynamic analysis in economics.

The importance of the Cobweb Theorem is as one of the earliest and easiest examples of dynamic analysis, which raises in sharp but relatively simple form many of the basic problems of dynamic analysis. Also, despite its assumptions that individual producers act in an uncoordinated way (no longer true even of agricultural markets), form their expectations in a very naive way, by considering only one price, prevailing at the time of planting, and do not learn as their expectations are continually proved wrong, the analysis does shed light on the reasons for price fluctuations in certain markets. It obtains its name, the 'cobweb' theorem, because if the movements of prices and quantities are plotted on a conventional supply and demand diagram, the pattern of lines looks much like a cobweb.