A convergent cobweb reflects a situation when price and quantity fluctuate in the long run due to expectations but eventually converge to the equilibrium price. A divergent cobweb on the other hand reflects a situation when price and quantity fluctuate due to expectations but instead of approaching equilibrium they constantly move further and further away from it. We observe the phenomenon of a cobweb in perfect competition when the assumption of perfect foresight is relaxed.
A convergent cobweb is observed when demand is more elastic than supply whereas a divergent one is observed when demand is more inelastic than supply. A convergent cobweb is illustrated in the following diagram.
In the above cobweb we see that demand is relatively more elastic than supply as a result when we assume that a producer has misinterpreted equilibrium quantity to be Q1 as opposed to Q2 he gets price P2 instead of P1 that he expected. Since producers estimate how much they should produce according to the price they get for their product in the previous year the next year the producer will respond by producing quantity Q2 and then again when he sees that he gets price P3 he switches to a lower quantity until eventually the quantity he produces and the price he gets are Q*-P*. However, this only happens when demand is relatively more elastic supply because responses to price changes are faster and adaptations in quantity supplied can’t be that great. If supply is more elastic than demand we get a divergent cobweb as seen in the diagram below.
In the above diagram where demand is relatively more inelastic than supply we observe a divergent cobweb as illustrated by the dashed red lines in the above graph. The producer initially miscalculates equilibrium quantity to be Q1 as opposed to Q* and as a result gets a price P2 as opposed to price P1 for which he is willing to sell his product. In the next production season he thus produces quantity Q2 assuming equilibrium price is P2, which however doesn’t yield a response in terms of demand that was large enough to consume the excess supply generated and as a result the cobweb keeps moving further and further away from the equilibrium.
This is observed because when consumers are sensitive to price changes the quantity demanded will still change even for small variations in output. At the same time given that supply is relatively inelastic quantity can’t change by large margins so producers are forced to push their production towards the equilibrium point. On the other hand when supply is more elastic than demand producers have the capability to increase production according to expectations and producers are relatively insensitive to price changes so even at rather large increases in price they won’t reduce consumption by as much as they would had they been sensitive to price changes.