Cob-Web model 11-3-15.pptx

Micro economics

1. COB WEB MODEL Cob web theorem is the simplest model of economic dynamics when equilibrium is reached over time between demand and supply and price is investigated. Producers supply function shows how producers adjust their output to changes in price. At higher price they respond to produce more and vice-versa. But this adjustment in production in response to changes in price does not occur instantaneously but takes a good deal of time. Thus there is a time lag between a change in price and appropriate adjustments in supply response to it.

2. The time gap between decisions to change in the quantity supplied in response to a given price and its actually being supplied is known as supply lag. The supply lag is often found in case of agricultural commodities . The supply lag often result in Cyclical movements or oscillations in price and quantity over time. The dynamic analysis of stability investigates whether these oscillations converge to equilibrium values or move away from them.

3. Cob Web model: For instance, we consider for sugarcane, where the supply of sugarcane is lagged function of price. In order to keep our analysis simple we assume that there is a one year lag in the response of quantity supplied of sugarcane to a given market price of it thus: 1. S=f(Pt-1) The demand function there is no time lag that is the quantity demanded of this year depends on price of this year thus: 2. D=f(Pt)

4. It is used to explain the dynamics of demand, supply and price over long period of time. The cob-web model (or Theorem) analyses the movements of prices and outputs when supply is wholly determined by prices in the previous period . As prices moves up and down in cycles, quantities produced and also seem to move up and down in a counter-cyclical manner (e.g. prices of perishable commodities like vegetables ). In order to find out the conditions for converging, diverging or constant cycles: one has to look at the slope of the demand curve and then of the supply curve. 

5. Assumption The cob-web Model is based on the following assumption : The current year’s (t) supply depends on the last year’s ( t-1 ) decisions regarding output level . Hence current output is influenced by last year’s price. i.e. P ( t-1 ) The current period or year is divided into sub-periods of a week or fortnight. The parameters determining the supply function have constant values over a series of periods. Current demand ( Dt ) for the commodity is a function of current price (Pt). The price expected to rule I the current period is the actual price in the last year. The commodity under consideration is perishable and can be stored only for one year. Both supply and demand function are linear .i.e. both are straight line curves which increases or decreases at a constant proportion

6. The Cob-web Model : There are two types of Cob-web Models: 1. Convergent 2. Divergent 3. Continuous (1) Convergent Cob-web Under this model the supply is a function of previous year i.e. S= f ( t-1 ) (‘t’ is the current period and‘ t-1 ’ is a previous period) and on the other hand the demand is the function of price i.e. D t =f (P). The equality between the quantity supplied and quantity demand is called as Market equilibrium. i.e. S t =D t . Equilibrium can be established only through a series of adjustment if current supply is in response to the price during the last year. But this adjustment will take place over a several consecutive periods.

7. For e.g. suppose we take the example of sugarcane growers who is producing one crop in a year. The sugarcane growers will grow this year on the assumption that the price of sugarcane this year will be equal to price in the last year. The market demand and supply curves for onions are represented by DD and SS curves respectively in diagram .

8. Suppose the price in the last year was OP 1  and Producers decide the equilibrium output OQ 1  this year. Now suppose there is crop failure due to natural calamities which decrease the output OQ 2  which is less than OQ 1  (i.e. equilibrium output). Lack of supply will increase the price to OP 2  in the current period. In the next period, the onion growers will produce OQ 3  quantity in response to the higher price OP 2 .But this is more than the equilibrium quantity OQ1 which is the actual need of the market. The excess supply will lower the price to OP 3 . This will encourage the producer to change the producer plan, where they will reduce the supply to OQ4 in the third period. But this quantity is less than the equilibrium quantity OQ 1 . This will lead to again rise in price to OP 4 , which in turn will encourage the producers to produceOQ 1  quantity.

9. The equilibrium will be established at point g where DD and SS curves intersect. This series of adjustments from point a,b,c,d,and e to f is traced out as a cobweb pattern which converge towards the point of market equilibrium g. This is also called as the dynamic equilibrium with lagged adjustment . .

10. ( 2) Divergent Cob-Web The divergent cob-web is unstable cobweb when price and quantity changes move away from the equilibrium posting. This can be explained with the help of following diagram ,

11. We will start with the initial equilibrium price is OP 1  and equilibrium quantity OQ 1 . Now suppose there is a temporary disturbance that causes output to fall to OQ 2 . Due to lack of supply the price will rise to OP 2 . The increase in price will in turn raise the output to OQ 3  which is more than the equilibrium output OQ 1 . The increase in supply will lead to fall in price to OP 3 . This fall in price will increase the demand and there will be excess demandOQ 2  than supply. The excess demand will shoot up the price to OP 4 . This shows that the price will be still away from the equilibrium after the adjustment by the producers. This is called as Divergent cob-web.

12. 3 ) Continuous cob-web The cob-web models in this show the continuous changes in price and quantities.

13. Suppose we start with the price OP 1  as shown in the diagram. As the supply will be more due to high price in the market. On the other hand the demand will be less as compared to the supply OQ 2  and the demand will reduced to OQ2. The fall in demand will force the producer to decrease price to OP 2  in next period. But at this price OP 2  the demand will be OQ 2  which is more than the supply OQ1 which reduced. This way the prices and quantities will circulate constantly around the equilibrium.

14. POLICY IMPLICATIONS : The stability of equilibrium of a market has important implications for economic policy. If a competitive market is in stable equilibrium it implies that it can survive any external disturbances however large and drastic it may be . That is if any disturbance causes disequilibrium in the stable nature of market equilibrium ensures that certain forces will automatically come into play to bring it back into equilibrium. This is a very important conclusion because if market equilibrium is stable and automatic corrections of disequilibrium is possible, theoretically there is no need for government interfere in a free market equilibrium.

15. POLICY IMPLICATIONS : In case unstable market disequilibrium free competitive market could collapse under the pleasure of either high inflation or recession. In fact in the real world we witness un stable equilibrium in some commodity markets. Foreign exchange market and therefore, rely on self-correction by the market would not take place. Therefore, the government interference is necessary to achieve equilibrium with the stability in prices and higher levels of income and employment.