To explore the argument of how difficult to plan accurately the agricultural output, the cobweb theorem is used. At equilibrium, we expect that the market clears. That is, quantity demanded is equal to quantity supplied. However, due to unforeseen bottlenecks or catastrophes, there is always a divergence between actual output and planned output.

The cobweb model postulates a situation in which there is an immediate response to a change in price on the demand side but a delayed response on the supply side. Producers plans are fulfilled after a time lag: supply coming on to the market in period t will always be a result of a decision made in previous period t - 1. This is very common in the agricultural sector. The farmers' decision about how much they will plant will depend on the existing price but the output will be received in the next season

D_t = f(P_t) demand in the current period t is a function of the current price P_t.

S_t = f(P_t _ ) current supply depends on the price of the previous period.

Dj, = S_t = Q_t is the market clearing equation.

If the demand and supply curves have slopes of opposite signs, the time path of the market price oscillates producing a cobweb-like path pattern

Damped (convergent) cobweb - stable equilibrium

This is when the absolute value of the slope of the supply curve is greater than the absolute value of the slope of the demand curve. The demand is more responsive to the price changes than supply. The price elasticity of demand is greater than the price elasticity of supply. In other words the demand curve is more elastic than the price curve.

In this case, we have smaller price fluctuations leading to the equilibrium position and hence we have the damped cobweb (Figure 2.26).

Convergent (damped) cobweb.

Suppose that we start off with the supply which is not planned and the market is not in equilibrium. Supply in period 1 is OQ-, and producers can sell this quantity at price OP-j. If now producers base their prices for period 2 on the expectations that price OP-| will continue, they will plan to supply the larger amount OQ₂ in period 2. Producers offer more if the price is high.

But producers find that they can only sell OQ₂ at a lower price OP₂. If their supply for period 3 is based on price OP₂, the producers would only supply OQ₃ in period 3 - but the price would rise to OP₃. The process will continue till an equilibrium price is achieved when S_t = D_t.