Cobweb Theorem

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Cobweb model (know as Hog Cycle) is a dynamic analysis which provides an explanation for certain types of cyclical behaviours due to regular fluctuation in price and output.


This model, as most other economic models, is based on some assumptions. It assumes that prices are determined by current prices i.e. farmers expect that the future price will be the same as the present ones. This is known as the ‘Naïve Expectation’. This assumption is considered to be unrealistic since prices might fluctuate due to unplanned variations, which might effect output such as weather and disease. The model also assumes that there is a one period time lag in production response. In Cobweb model a cycle duration is assumed to be multiplied by a production lag. However, in reality this is too short, therefore we observe cycles, which are 4 multiplied by production lag.


There are three types of cobweb cyclical process continuous, converging and diverging cobwebs. Figure (1) shows a continuous cobweb, which is also, known as a stable cycle. In a continuous cobweb, supply (S) and demand (D) curves both have linear function i.e. straight lines and have the same slopes but they are in the opposite directions. This means that the elasticity of demand and supply are equal, but has different signs. This is also a very special case according to Cobweb Theorem.


S


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Price Price


P1


Rising Falling


Pe Price Price





P


D


Q1 Qe Q Quantity 1 Time


(a) (b)


Figure (1)


Pigs production can be described using this type of cycle. Looking at Figure (1)a, we can start from the equilibrium point (where supply and demand curves crosses). At this point the price of pigs is Pe and quantity (supplied = demanded) is Qe. Lets assume that there is a shortage in the supply of pigs due to some diseases i.e. quantity supplied will fall to Q1. At this point demand is higher than supply and this will push the price to P1. In the next period, this rise in price will attract producers to plan a larger production in pigs i.e. quantity supplied will increase to Q. However this high price P1 will decrease demand and therefore the price will fall down to P. In the following period, producers plan to reduce their pig production to Q1, which will rise prices to P1 and the cycle starts all over again. The relation between price and time (periods) is shown in Figure (1)b.


Figure () shows pigs inventory in the US in the period from 1 �000. This illustrates Continuous Cobwebs.


(Source http//www.caf.wvu.edu/resm/courses/are1/1ch10.ppt)


Figure ()


As seen in Figure (), the S curve is steeper than the D curve i.e. elasticity of demand is less than the elasticity of supply. This creates a cycle described as the ‘Converging Cobweb’ were the cycles become smaller and smaller and they converge on the equilibrium point. Cereals usually have this type of cycles.


The third cobweb cyclical process is called ‘Diverging Cobweb’ which is the case of cattle, shown in Figure (4). In this type of cycle the slope of the demand curve is steeper than the supply curve. In this case the elasticity of demand is greater than the elasticity of supply and therefore the cycles become larger and larger.


Figure (5), which shows cattle figures in the US since 1867, support this since it shows that cattle has a Diverging Cobweb cycle.


(Source http//www.caf.wvu.edu/resm/courses/are1/1ch10.ppt)


Figure (5)


Although there are three types of Cobweb cycles, continuous cobwebs are more acceptable even though Cobweb Model assumes that this is a special case. We can give many reasons why continuous cobwebs are more realistic. One reason is that in reality, the supply curve is not linear but it is a non-linear curve, which is relatively flat around the equilibrium point as shown in Figure (6). This gives us a Diverging Cobweb around the equilibrium since elasticity of demand is less than the elasticity of supply and a Converging Cobweb at lower prices.


In conclusion, Cobweb Theorem gives a valuable explanation of how prices cycles can arise and persist over long periods of time. Farmers tend to react as if the prices they observe today are the best indicator of the prices they will experience next year, and often fail to consider the effect which their and their neighbour’s production changes will have on prices then.


Cobweb Theorem suggests that Continuos Cobwebs are special cases but in realtity this is not the case and we can drive both Diverging Cobwebs and Converging Cobwebs around it.


Colman, D. and Young T., 18, Principles of Agricultural Economics, Cambridge University Press


Hallett, Graham, 181, The Economics of Agricultural Policy, nd Edition, Basil Blackwell


Hill, B. and Ingersent, k. 177, An Economic Analysis of Agriculture, Heimann London


Ritson, C., 180, Agricultural Economics Principles and Policy, Granada London


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