Cobweb pattern

The cobweb-like model ( theorem ) is a microeconomic model , the mechanism of which, under perfect competition, sets prices based on fluctuations in supply and demand , and the production and prices of goods with a short shelf life, coming out of equilibrium, do not necessarily return to it. The model got its name in 1934 thanks to the economist Nicholas Caldor on the basis that the graph of the curves reflecting changes in prices forms a web .

Creation History

Regularly repeated production cycles and commodity prices were noted in the works of S. Benner “Benner's prophecy of future ups and downs of prices” ^[1] 1876, and Haas G. “Factors affecting prices pork " ^{[2] of} 1926 and articles by Arthur Hanau " Forecast of pork prices " ^{[3] of} 1927, which formed the , on the basis of which Kitchin’s cycles were opened ^[4] .

Constant price fluctuations in product markets, whose production takes a considerable time, and storage with a short period, where the quantity produced depends on the price expected at the time of sale, as well as the offer at the time of sale determines the current price, were investigated and simultaneously for the first time for the first time in 1930 in the articles of the Dutch economist Jan Tinbergen "The definition and interpretation of the supply curves: the description" ^[5] , the American economist Henry Schultz "static demand values" ^[6] and the Italian economy that Umberto Richie "Synthetic Economy" ^[7] . In 1934, an article by the American economist N. Caldor “Determining Statistical Equilibrium” ^{[8] was} published, in which the model was called spider-like based on the fact that the graph of the curves reflecting price changes form a web ^[9] .

Assumptions

The model has a number of prerequisites ^[10] :

perfect competition .

Approval

Prices are set on the basis of fluctuations in supply and demand, and out of equilibrium they do not necessarily return to it ^[11] .

Model Illustration

Convergent spiral

Spinning spiral

Constant fluctuations

Nonlinear vibrations

Manufacturer based on current price $P$ ${\ displaystyle P}$ determines the amount $Q$ ${\ displaystyle Q}$ products that will put on the market in the coming period. If the current price $P$ ${\ displaystyle P}$ high, then manufacturers begin to increase their production volume, in order to make the delivery of their products to the market at the end of their production cycle. Manufacturers, within the framework of their own supply curve, act late, as they associate their quantity of the subsequent period based on the current price, and the period is the production cycle of the batch ^[10] .

The equilibrium of the model is fixed at the intersection of the supply curve $S S$ ${\ displaystyle SS}$ and demand curve $D D$ ${\ displaystyle DD}$ at the point $E$ ${\ displaystyle E}$ where the quantity $Q^{*}$ ${\ displaystyle Q ^ {*}}$ , which will be required by buyers, coincides with the amount that manufacturers are ready to supply ^[10] .

Convergent spiral

If the steepness of the supply line is greater than the steepness of the falling demand line, then the fluctuations gradually fade, the spiral twists inward, equilibrium is reached until the next exogenous push:

{\frac {dQ^{S}/Q}{dP^{S}/P}}<\left|{\frac {dQ^{D}/Q}{dP^{D}/P}}\right|,

{\ displaystyle {\ frac {dQ ^ {S} / Q} {dP ^ {S} / P}} <\ left | {\ frac {dQ ^ {D} / Q} {dP ^ {D} / P} } \ right |,}

In case of change (drop) in the quantity of production to the level $Q_{1}$ ${\ displaystyle Q_ {1}}$ that matches the point $E$ ${\ displaystyle E}$ on the demand curve equal to the price $P_{1}$ ${\ displaystyle P_ {1}}$ which is higher than the equilibrium price $P^{*}$ ${\ displaystyle P ^ {*}}$ . The new price encourages manufacturers to produce more equal points $F2$ ${\ displaystyle F2}$ on the supply line, but buyers are willing to buy only at a price $P^{2}$ ${\ displaystyle P ^ {2}}$ that corresponds to the point $E2$ ${\ displaystyle E2}$ on the demand curve, which means manufacturers decide to reduce production to a level $F3$ ${\ displaystyle F3}$ on the supply curve, which allows you to raise prices to the level $P^{3}$ ${\ displaystyle P ^ {3}}$ that corresponds to the point $E3$ ${\ displaystyle E3}$ on the demand curve and so on to the equilibrium point $E$ ${\ displaystyle E}$ ^[10] .

Spinning spiral

If the supply line has less steepness than the demand line, then the spiral unwinds, the fluctuations increase ^[11] :

{\frac {dQ^{S}/Q}{dP^{S}/P}}>\left|{\frac {dQ^{D}/Q}{dP^{D}/P}}\right|.

{\ displaystyle {\ frac {dQ ^ {S} / Q} {dP ^ {S} / P}}> \ left | {\ frac {dQ ^ {D} / Q} {dP ^ {D} / P} } \ right |.}

Constant fluctuations

If the line of supply and demand have the same steepness, then uniform fluctuations are constant, oscillating endlessly around the equilibrium position ^[11] :

{\frac {dQ^{S}/Q}{dP^{S}/P}}=\left|{\frac {dQ^{D}/Q}{dP^{D}/P}}\right|.

{\ displaystyle {\ frac {dQ ^ {S} / Q} {dP ^ {S} / P}} = \ left | {\ frac {dQ ^ {D} / Q} {dP ^ {D} / P} } \ right |.}

Nonlinear vibrations

The supply and demand curves can take such forms that the steepness of the supply curve at the equilibrium point is less than the demand curve. With minor changes, the vibrations unwind, and with significant changes, the vibrations have damped vibrations to a certain level, where they have constant vibrations ^[10] .

Application

A positive application of the model is noted in the analysis of the corn and pork market at the beginning of the 20th century, monetary theory and the theory of economic cycles in the 1950s, the labor market of lawyers, doctors and engineers in the 1970s ^[12] , the Russian pharmaceutical market ^[13] .

Criticism

A number of researchers have noted the model’s weaknesses ^[12] :

continued production in the context of manufacturers expecting their losses;
lack of clear definitions and transition from short-term to long-term supply curve;
an expectation mechanism in which manufacturers can improve the accuracy of their estimates by discovering the forecast error pattern themselves and incorporating them into their forecasts;
the reason for using the forecasting mechanism by manufacturers;
the lack of correlation of errors in the forecast, in which the example of past forecast errors cannot be used to improve the accuracy of forecasts;
the model predicts a shorter price cycle than the one that is observed.

Notes

↑ Benner S. Benner's Prophecies of Future Ups and Downs in Prices // Cincinnati. - 1876.
↑ Haas GC, Ezekiel M. Factors Affecting the Price of Hogs // US Department of Agriculture. - Washington, DC, 1926. - No. 1 Ag84B no. 1400 . - S. 67-68 .
↑ Hanau A. Die Prognose der schweinepreise // Reimar Hobbing. - Berlin, 1927.
↑ Tinbergen J. Development Cooperation as a Learning Process // International Bank for Reconstruction and Development. - Washington, 1982. - S. 313-334 .
↑ Tinbergen J. Bestimmung und Deutung von Angebotskurven: Ein Beispiel // Zeitschrift für Nationalökonomie, Band 1, Heft 5. - Wien, 1930 .-- S. 669-679 .
↑ Schultz H. Der Sinn der Statistischen Nachfragen // Kurt Schroeder Verlag Heft 10. - Bonn, 1930 .-- S. 255-280 .
↑ Ricci U. Synthetische Okonomie // Zeitschrift fuir Nationalokonomie Band 1, Heft 5. - Wien, 1930 .-- S. 656 .
↑ Kaldor N. A Classificatory Note on the Determinateness of Equilibrium // The Review of Economic Studies Vol. 1, No. 2. - 1934. - February. - S. 122-136 .
↑ Ezekiel M. The Cobweb Theorem // The Quarterly Journal of Economics Vol. 52, No. 2. - 1938. - February. - S. 255-280 . Archived on June 16, 2015.
↑ ¹ ² ³ ⁴ ⁵ Samuelson P. Economics. - M .: Progress, 1964 .-- S. 470-472.
↑ ¹ ² ³ Halperin V.M. , Ignatiev S.M. , Morgunov V.I. Microeconomics. In 3 volumes . - SPb. : School of Economics, 2004. - T. 1. - S. 63-66. - ISBN 5-902402-04-2 .
↑ ¹ ² Pashigyan P. Spider-like model // Economic theory / ed. Itwell J. - M .: INFRA-M, 2004 .-- S. 70-73 . - ISBN 5-16-001750-X. Archived March 11, 2016.
↑ Fomin A.V. The dynamic equilibrium model of the pharmaceutical market // The dissertation for the degree of candidate of economic sciences. - M .: HSE, 2013.

[:1-1] Benner S. Benner's Prophecies of Future Ups and Downs in Prices // Cincinnati. - 1876.

[:2-2] Haas GC, Ezekiel M. Factors Affecting the Price of Hogs // US Department of Agriculture. - Washington, DC, 1926. - No. 1 Ag84B no. 1400 . - S. 67-68 .

[:3-3] Hanau A. Die Prognose der schweinepreise // Reimar Hobbing. - Berlin, 1927.

[:4-4] Tinbergen J. Development Cooperation as a Learning Process // International Bank for Reconstruction and Development. - Washington, 1982. - S. 313-334 .

[:5-5] Tinbergen J. Bestimmung und Deutung von Angebotskurven: Ein Beispiel // Zeitschrift für Nationalökonomie, Band 1, Heft 5. - Wien, 1930 .-- S. 669-679 .

[:6-6] Schultz H. Der Sinn der Statistischen Nachfragen // Kurt Schroeder Verlag Heft 10. - Bonn, 1930 .-- S. 255-280 .

[:7-7] Ricci U. Synthetische Okonomie // Zeitschrift fuir Nationalokonomie Band 1, Heft 5. - Wien, 1930 .-- S. 656 .

[:8-8] Kaldor N. A Classificatory Note on the Determinateness of Equilibrium // The Review of Economic Studies Vol. 1, No. 2. - 1934. - February. - S. 122-136 .

[:9-9] Ezekiel M. The Cobweb Theorem // The Quarterly Journal of Economics Vol. 52, No. 2. - 1938. - February. - S. 255-280 . Archived on June 16, 2015.

[:10-10] ¹ ² ³ ⁴ ⁵ Samuelson P. Economics. - M .: Progress, 1964 .-- S. 470-472.

[:11-11] ¹ ² ³ Halperin V.M. , Ignatiev S.M. , Morgunov V.I. Microeconomics. In 3 volumes . - SPb. : School of Economics, 2004. - T. 1. - S. 63-66. - ISBN 5-902402-04-2 .

[:12-12] ¹ ² Pashigyan P. Spider-like model // Economic theory / ed. Itwell J. - M .: INFRA-M, 2004 .-- S. 70-73 . - ISBN 5-16-001750-X. Archived March 11, 2016.

[:13-13] Fomin A.V. The dynamic equilibrium model of the pharmaceutical market // The dissertation for the degree of candidate of economic sciences. - M .: HSE, 2013.