Convergent cobweb. The Cobweb Model (With Equations) 2022-10-30
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A convergent cobweb is a graphical representation of a dynamic system that is used to analyze the behavior of the system over time. It is a useful tool for understanding how a system changes and evolves in response to different input conditions.
In a convergent cobweb diagram, the horizontal axis represents the value of a variable in the system, and the vertical axis represents the change in the value of that variable over time. The diagram is called a "cobweb" because it resembles a spider's web, with lines converging towards a central point.
To construct a convergent cobweb diagram, one must first choose a variable to track and determine the equation that governs its change over time. For example, in an economic model, the variable might be the price of a good, and the equation might describe how the price changes in response to changes in supply and demand.
Once the variable and equation have been chosen, the convergent cobweb diagram can be constructed by plotting the value of the variable at different points in time. As the value of the variable changes over time, the lines on the diagram will converge towards a stable point, known as an equilibrium point.
The shape of the convergent cobweb can reveal important insights about the behavior of the system. For example, if the lines on the diagram oscillate around the equilibrium point, it may indicate that the system is unstable and prone to fluctuations. On the other hand, if the lines on the diagram quickly converge towards the equilibrium point, it may indicate that the system is stable and well-behaved.
Convergent cobweb diagrams are often used in economics to study market behavior and to predict the effects of policy changes. They can also be used in other fields, such as biology, to study the dynamics of population growth and the spread of diseases.
Overall, convergent cobweb diagrams provide a useful tool for analyzing and understanding the behavior of dynamic systems over time. They help us to understand how different variables in a system interact and influence one another, and can help us to make more informed decisions about how to intervene in the system to achieve desired outcomes.
As already obtained, this will be the case if the demand curve is steeper than the supply curve. Nicholson, Microeconomic Theory, 7th ed. That is, p 0 is the market-clearing price in period 0. Futrell, ; Allan G. But, the price collapsed, leading to a big fall in the building of new housing.
For instance, an increase in demand will at once result in a spiral rise in price, since in the short period there can be no increase in supply. Cobweb theory and price divergence Price will diverge from the equilibrium when the supply curve is more elastic than the demand curve, at the equilibrium point If the slope of the supply curve is less than the demand curve, then the price changes could become magnified and the market more unstable. Commonsense tells that it cannot happen. Now go into the question of convergence or otherwise of the current price towards the equilibrium price. They treated the economy as of a point in time ignoring completely the movements of the economy through time.
Suppose that we start off with the supply which is not planned and the market is not in equilibrium. For instance, if the price of wheat increases say in September 2007 then supply will not increase instantaneously. Suppose that initially the supply of the good concerned has fallen short of the equilibrium amount because of some disturbance such as drought or flood. In global markets, supply fluctuations will be minimized by the role of importing from abroad. In practice the shape of the curves is such as to make continued divergence impossible. Thus the supply of wheat in 2008 will depend upon the price of wheat that prevailed in 2007 which offered the farmer inducement to devote more land to wheat cultivation.
These assumptions show that the theory is particularly applicable to agricultural products. Also, demand may vary. Starting with a large supply and low price in the first period, P 1 there would be a very short supply and high price, Q 2, and P 2, in the second period. In the case of continuous Cobweb the fluctuations in price and output continues repeating about equilibrium at same level. This high price calls forth a considerable increase in supply, Q 3 in the third period, with a resulting material reduction in price, to P 3.
If the supply curve is markedly less elastic than the demand curve. If producers plan their period2 production under the expectation that this high price will continue, then the period2 supply will be higher, at Q 2. That is why the price, p 0, of the initial period period 0 determines the supply of period 1, which is P 0N 1. . It was so named because the pattern traced by the prices and output movements resembled a cobweb. This time, taken by the supply to adjust itself to changes in demand is known as lag. To the extent the adjustments between supply and demand were assumed to take place instantaneously and not with a certain degree of time lag, the earlier approaches were static and could not furnish useful tools that could be applied with a fair degree of reliance for solving the problem of economic fluctuations in the dynamic economy where adjustments involved lags.
Agricultural markets are a context where the cobweb model might apply, since there is a lag between planting and This process is illustrated by the adjacent diagrams. This fifth period sees a still greater expansion in supply to Q 5 etc. As long as price is completely determined by the current supply, and supply is completely determined by the preceding price, fluctuation in price and production will continue in this unchanging pattern indefinitely, without an equilibrium being approached or reached. This model is known as the Cobweb model because, the path taken by the observed price and quantity resembles a cobweb. But in the unstable case, the farmers' errors get larger every period.
The farmer will, of course, devote larger farm acreage to wheat cultivation in the next crop season and so it will take one year before supply increases in response to increase in wheat price. The New Palgrave Dictionary of Economics 2nded. The divergent case occurs when the supply curve is more elastic than the demand curve, at the equilibrium point see Kaldor, 1934, page 135, propositions i and ii. Assuming that farmers look back at the most recent prices in order to forecast future prices might seem very reasonable, but this backward-looking forecasting which is called In the stable case, this may not be an unbelievable outcome, since the farmers' prediction errors the difference between the price they expect and the price that actually occurs become smaller every period. In: Vierteljahreshefte zur Konjunkturforschung, Verlag Reimar Hobbing, Berlin.
Continuing through Q 9, P 6 and Q 6, and P 6, production and price approach more and more closely to the equilibrium condition where further changes would occur. ADVERTISEMENTS: In this article we will discuss about the cobweb model to study market equilibrium. In this case, after several periods prices and quantities will come close to the point where supply and demand cross, and predicted prices will be very close to actual prices. Wellford, 'A Laboratory Analysis of Price Dynamics and Expectations in the Cobweb Model', Discussion Paper 89-15 University of Arizona, Tucson, AZ. On the basis of these values, the time-series graph for price in market I has been drawn in fig.
Now, even if the supply and demand functions and curves have their normal slopes i. In 1930 Cobweb Theory was advanced by the three economists in Italy. The names of Henery Schultz. What economic limits to oscillation are finally reached? The consequence is that if we have one year of low prices, next year farmers reduce the supply. Solution: a The demand and supply function for market I: The price-figure in market I in period 0 zero and in the next five period are obtained in 8 — 13 , respectively. Introduction to Cobweb Theory: The Cobweb Theorem attempts to explain the regularly recurring cycles in the output and prices of farm products. The following way is obtained.