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Cobweb theorem
 

 

An 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 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. 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 !arger acreage of the crop than they did previously, because price is now higher, so that one period later a larger supply will be forthcoining on the market. This supply will be more than that required to satisfy demand at the price which prevailed at period 2, and price must fall jo induce buyers to take up the extra supply. Less will therefore be sown at time period 3, less will therefore be put on the market af time period 4, and price must rise again. 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, and eventually the amount put on the marker will be just equal to the amount buyers are prepared to take at the price which existed last period. If the latter, the price fluctµations become steadily larger. It is possible to formulate in precise terms the conditions under which each occurs. 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 assiunptions that individual producers act in an uricoordinated way (no longer true even of agricultural markets), form their expectations in a very naive way (by considering only one price - that prevailing ai 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 is called 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.

Reference: The Penguin Dictionary of Economics, 3rd edt.