Cobweb model

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The Cobweb model or Cobweb theory explains why prices in certain markets are subject to periodic fluctuation. It is an economic model of cyclical supply and demand in which there is a lag between response of producers to a change of price. It is sometimes called the hog-cycle, a reference to the fluctuation of American pig prices in the 1930s. The cobweb model was identified by the Hungarian economist, Nicholas Kaldor.

1 Examples
2 Criticisms of model
3 Human Experimental Data
4 References
5 See also

[edit] Examples

Farming is a good example, as there is a lag between planting and harvesting. The classic example is that of the market for agricultural goods, such as the market for strawberries. As a result of good weather, the strawberry crop is very good and strawberry farmers go to market with many strawberries. This unusually high supply, equivalent to a rightward shift in the market's supply curve, results in low prices. Therefore, the following year, farmers will reduce their production of strawberries in favor of other goods. When they go to market, the supply will then be low, equivalent to a leftward shift in the supply curve, resulting in high prices. Thus, the following year, farmers will increase their production of strawberries and then find that when they go to market, prices are low. This process is also known as the spite effect or also the pork cycle.

Another example is illustrated in the diagram to the right. (note the unusually labeled axis, generally Supply/Demand curves are shows as Price [Y-axis] vs. Quantity [X-axis]) Equilibrium is at the intersection of supply and demand, where Q satisfies supply and demand at price P. If there is then a poor harvest (using the farming example) in period 1 (1 on the diagram), supply falls to Q₁, and prices rise to P₂, corresponding to point 2 on the diagram. Producers then start new production influenced by this high price, and in the next period (3) supply Q₂. Prices must now fall to P₃ (point 4 on diagram) to sell all output. The process repeats itself, until it eventually converges at Q₀, where the system is stable.

A cobweb model can, simplified, have these three outcomes:

If the price elasticity of demand is less than the price elasticity of supply, the fluctuations would increase in magnitude per cycle, so a plot of the equilibria in for each cycle would look like an outward spiral (divergent). This is referred to as an unstable cobweb model.
Alternatively, if the price elasticity of demand is more than the mean price elasticity of supply, fluctuations decrease in magnitude per cycle, so a plot of the equilibria in for each cycle would look like an inward spiral (convergent). This is referred to as a stable cobweb model.
Fluctuations may also remain of constant magnitude, so a plot of the equilibria would produce a simple quadrangle. Such a result would be given from a unit elastic price elasticity of both supply and demand.

In either of the first two scenarios, the combination of the spiral and the supply and demand curves often looks like a cobweb, hence the name of the theory.

[edit] Criticisms of model

One criticism of this model is its assumption that producers are extremely shortsighted; they are fundamentally unable to judge market conditions or learn from their pricing mistakes that result in surplus/shortfall cycles. This assumption is seen to be unrealistic.

[edit] Human Experimental Data

In 1989, Wellford conducted twelve experimental sessions each conducted with five participants over thirty periods simulating the stable and unstable case. Her results show that the unstable case did not result in the divergent behavior we see with cobweb expectations but rather the participants converged within the area of the rational expectations equilibrium. The price path variance of the unstable case was however greater than the stable case, which was statistically tested by Wellford.

[edit] References

J Arifovic, 'Genetic Algorithm Learning and the Cobweb Model ', Journal of Economic Dynamics and Control, vol. 18, Issue 1, (January 1994), 3-28.
N Kaldor, 'A Classificatory Note on the Determination of Equilibrium', Review of Economic Studies, vol I (February, 1934), 122-36.
M Nerlove, 'Adaptive Expectations and Cobweb Phenomena', Quarterly Journal of Economics, vol. lxxii (1958), 227-40.
CP Wellford, 'A Laboratory Analysis of Price Dynamics and Expectations in the Cobweb Model', Discussion Paper 89-15 (University of Arizona, Tucson, AZ).