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Demand and Supply Response of Cocoon Production in Jammu and Kashmir: A Cobweb Analysis.


Sericulture is the art and science of rearing silkworm for silk production. Silk is considered as the 'Queen of Textiles' in the world, because of high durability and shine. J&K state is known for producing bivoltine silk of international quality. Sericulture is labour intensive industry and helps in improving the economic condition of the landless farmers and weaker sections of the society and providing employment opportunities especially for women's during pre and post cocoon activities. Sericulture supplements the income of the farmers in addition to their returns from the other crops. With the increased economic needs due to changing social status and unpredictable market trend of different kinds of produces by the farmers of the state, sericulture has assumed special significance as an important subsidiary occupation. Presently about 29,300 rural families generating income worth Rs.2026 (J&K Economic Survey, 2013-14) lakh annually and one lakh man days in private reeling sector are associated with this profession (Ganie, 2012).

Sericulture industry in J&K despite having glorious history in the past do not own a bright name in silk production and export. Inspite of having suitable agro-climatic conditions for the development of silk industry, J&K produces negligible amount of silk products every year (Fatima, 2013). Due to this reason, this topic for research has been chosen to analyse the behaviour of demand and supply response by the application of cobweb model. This model has huge number of agricultural implication, because it shows the behaviour of equilibrium in that particular crop.

The regular recurring cycles in the production and prices of particular commodities have been recognised for many years by the economists. Finally three economists, in Italy, Holland, and the United States worked out the theoretical explanation which has come to be known as the 'cob-web theorem' (Ezekiel, 1938). The model is used to explain the dynamics of demand, supply and price over long period of time. There are many agricultural commodities whose price and output are determined in long periods. As prices move up or down, output produced also seem to move up and down in same manner. The models, where decisions in one period are based on variables in another period, such type of models are recognised by cobweb which is one of the forms of dynamic models (Shone, 2002). Cobweb model is a combination of two laws, the law of demand and law of supply; both are simultaneously determined by price and the relation between supply and price is lagged one whereas demand is directly related with price. The theorem states that price on a current market, under conditions of pure competition over a given limited period of time tends to be determined by the interaction of the supply and demand on that market. It means a farmer decides the crop to be cultivated by taking into consideration the prevailing prices but the production is completed after crop period (usually one year) (Yang, 2008; Ghatak et al., 1984).

Assumptions of Cobweb Theorem

* The production is completely determined by producer's response to price.

* Price is set by supply available and demand responding to price only.

* Time needed for production required at least one full period.

Cobweb theorem gives three types of cobwebs.

Convergent Cobweb

In this type of cobweb, elasticity of demand is greater than elasticity of supply. The slope of supply curve is greater than the slope of demand curve; we get the case of damped oscillations. The equilibrium can be established only through a series of adjustments that takes place over different consecutive time periods.

Divergent Cobweb

when change in prices and quantities move away from equilibrium, due to lesser elasticity of demand than elasticity of supply. This is an explosive or unstable type of equilibrium.

Continuous Cobweb

The cobweb may be of constant amplitude with perpetually oscillating price and quantities. When the prices completely depends upon current supply and supply completely depends on previous year prices, fluctuation in price and quantities will continue in this unchanging pattern without an equilibrium being approached or reached (Xu Lingling et al., 2012).


* To study the demand and supply response in cocoon market of J&K.

* To provide policy measures for the development of sericulture industry in the state.

Research Question

What is the behaviour of sericulture or cocoon market in J&K? Is sericulture a growing industry, if not then why?

Material and Methods

The study is wholly based on secondary data which has been collected from Directorate of Sericulture in J&K. The duration of the study is of eleven years from 2003-04 to 2012-13, because of data availability and 10 years is sufficient for drawing conclusion from this study. In the present study cobweb model was used to know the status of stability of equilibrium on the line of work done by Xu Lingling (2012), Ezekiel M. (1938), and Wellford Charissa P. (1989). The demand and supply function was estimated through simple linear regression, and then cobweb model was used to know equilibrium pattern whether there is convergent, divergent or continuous oscillations in cocoon market in J&K by the following way.

[Q.sub.s]=f (previous year cocoon prices)

[Q.sub.d]=f (current year cocoon prices)

Result and Discussion

Let us consider the following cobweb model which assumes that today's demand ([Q.sub.d]) for cocoon is a function of present price ([P.sub.t]), while today's supply of cocoon ([Q.sub.s]) depends yesterday's decisions of output based on anticipation of future prices. Hence cocoon output is naturally influenced by yesterday's cocoon price ([P.sub.t-1]).

It can be seen from the table 1 that during round 2 supply of cocoon depends upon previous year prices such as Rs. 215 and taking this constant for next year and producing 504.66 lakh kgs of cocoon, as a result of increasing supply for round 2, demand remains constant which leads to decrease prices from Rs. 215 to 197.37. As the theorem states farmers will keep this low price constant for round 3 and produce 487.73 lakh kg of cocoon which leads to increase prices from Rs 197.37 to Rs. 209.71 per kg because of decreased in cocoon supply during that particular year. The increased cocoon prices become incentive for farmers and they will make efforts to increase production either by embodied or disembodied technical progress to make gains, as a result supply of cocoon increases 503.30 lakh kgs during round 4, which leads to decease prices to Rs. 201.07 in the same year due to increase in supply of cocoon. This process always remains there as for as cobweb theorem is concerned, the whole process can be seen from the table 1.

Figure 1 and 2, reveals that the saw-tooth cycles of erratically fluctuating of cocoon prices and production continue indefinitely, but the magnitude of the movements become smaller and smaller as the cocoon market converges toward the equilibrium where the demand and supply curves of cocoon intersect. The cobweb model assumes that farmers base their production decision on the assumption that this year's price will be the same as last year's.

A low price last year (suppose time period 2 figure 2) leads cocoon rearers to produce a very small amount of cocoon production as shown in figure 1 during time period 3.

It happens because current years cocoon production is function of previous year cocoon prices, which at harvest time leads to a high price as seen in figure 2 during 3 period. Anticipating a high price, cocoon rearers produce huge crop expecting more gains due to high price. But the large crop pulls the cocoon price down, causing rearers to wind up with a low price. The cycle persists, but converges to equilibrium point.

Figure 3 shows the demand and supply of cocoon at different level of prices. The equilibrium is achieved where the demand and supply of cocoon intersect each other. It can be seen from the figure 3, E is equilibrium point where both curves intersect to each other. In the long run the cocoon output would settle at E in given figure 3 (497.64 lack kg) and at the same time long run cocoon prices would settle at the same point which is Rs. 203.63. The nature of the figure shows the convergent type of equilibrium, as the supply of cocoon increases leads to fall in price and next year supply will short fall, which push the prices up and so on. Thus fluctuations or oscillations will dampen and ultimately merge with the point of equilibrium (E in figure 3).

In the long run, the cocoon market in J&K will converge to the equilibrium at the stable price of Rs. 203.63 and cocoon production 497.64 lakh kgs predicted by the cobweb supply and demand model which is calculated as under.

Let [bar.P] be the equilibrium price, therefore

[mathematical expression not reproducible]

The equilibrium output in the long run would settle at;

[Q.sub.s] = 372 + 0.617[??]

[??] 497.64

[Q.sub.d] = 675-0.871[??]

[??] 497.64

The stability or convergent type of market is determined when the elasticity of demand is greater than elasticity of supply, and is also known as Marshallian stable equilibrium. The above analysis states that the slope coefficients (elasticities) of demand and supply are 0.871([beta]) and 0.617 (b) respectively the significant both at 1% and 5% level of significance. It clearly shows that among these coefficients that elasticity of demand is higher than elasticity of supply of cocoon in J&K, i.e., why there is Marshallian stable type of equilibrium in cocoon market in the State of J&K. The question arises why the cocoon market is convergent or stable type of equilibrium in J&K? The reason behind this is high elasticity of demand for cocoon market in the state. The important factors which lead to high elasticity of demand are as under:

* Low demand for cocoons because of lack of reeling units in J&K.

* High elasticity of substitution with artificial silk.

* Cheaper imports mainly from China.

* Nature of silk is luxurious.

The factors which make supply inelastic or less elastic are:

* Farmers can not store their produce even for a short period of time; otherwise caterpillar will come out from the cocoons, which leads to wastage of the produce.

* Due to the poor status of the growers they can not wait for better remunerative prices.

Classical economists states that stable markets are self correcting in nature and have important implications for economic policy. However, some scholars state that stability of equilibrium is a futile theoretical exercise without any economic significance, because growth is not taking place. Due to this static nature of cocoon market, sericulture industry is not growing in The state of J&K, irrespective of producing high quality silk and having strong historical background. In order to make it more remunerative activity, the convergence or damped oscillation has to break down. The suggestive or corrective measures to break this stable or static equilibrium are:

* Establishment of more silk reeling units.

* To organise more auction markets at tehsil or block level.

* Removal of intermediaries and facilitating direct contact between buyers and sellers.

* Reopen the existing silk factories in the state.

* Introduction of new techniques of cocoon production.

* Spread of knowledge about the prevailing prices at different auction markets.

* Providing incentives to unemployed youth to make their own reeling units.

If all these measures are taken into consideration, this industry will definitely grow in coming days. But this is not possible without the government and private sector intervention. As a result, on one side new avenues of income and employment will come out and on the other side poverty level will decrease.


Sericulture industry has not shown an increasing trend during past decades and is in a static state. As a result the contribution in terms of share in national cocoon production is only about 1 per cent. This static or slow pace of growth is contributed by high elasticity of demand for cocoon production as the cobweb analysis states. Therefore, due to this static state of cocoon market, the farmers are not getting remunerative prices for their produce; as a result the sericulture industry is not growing in the state. Since the sericulture industry has the potential to grow, a carefully orchestrated policy measures will definitely help the industry in bringing back its glorious past.


Branch William A. (2002) 'Local Convergence Properties of a Cobweb Model with Rationally Heterogeneous Expectations', Journal of Economic Dynamics and Control, P. 27.

Economic Survey (2010-11) Directorate of Economics and Statistics, Govt. of Jammu and Kashmir.

Ezekiel M. (1938) 'The Cobweb Theorem', Quarterly Journal of Economics, Vol. 52, No. 2.

Ganie Nisar, Kamili Afifa S., Baqual F.M., Sharma K.R., Dar A.K., and Khan I.L. (2012) 'Indian Sericulture Industry with Particular Reference to Jammu and Kashmir', International Journal of Advanced Biological Research, Vol. 2(2).

Ghatak Subrata, and Ingersent Ken (1984) Agriculture and Economic Development, Select Book Service Syndicate: New Delhi.

Gujrati Damodar (2004) Basic Econometrics, (4th edition) The McGraw-Hill Companies: Newyork.

Jhingan M.L. (2010) Macroeconomic Theory, Vrinda Publications (P) Ltd. Delhi.

Kaneez, F. (2013) 'Trends in Cocoon and Raw silk Production in Jammu and Kashmir State: A Case of Concern', International Journal of Recent Scientific Research, Vol. 4, issue 11, pp. 1826-1830.

Lekhi R.K., and Singh Joginder (2011) Agricultural Economics, Kalyani Publishers New Delhi.

Lovell Michael. (2004) Economics with Calculus. World Scientific Publishing Co. Pvt. Ltd.: Singapore.

Rana K.C. and Verma KN. (2011) Macro Economic Analysis, Vishal Publishing Co.: Jalandhar-Delhi.

Shone Ronald (2002) Economic Dynamics: Phase, Diagrams and Their Economic Application, Cambridge University Press, Second Edition, New York.

Wellford Charissa P. (1989) A Laboratory Analysis of Price Dynamics Expectations in the Cobweb Model, Discussion Paper No. 89-15, Department of Economics University of Arizona Tucson.

Xu Lingling and Wang Shuguang (2012) 'The Analysis of the Vegetables Price Fluctuation with Cobweb Model', Interdisciplinary Journal of Contemporary Research in Business, Vol. 4, No. 8.

Yang Jinbin (2010) Economic Analysis of Blueberry Investment in British Columbia, Thesis Submitted For Master of Science in Agriculture Economics, University Of British Columbia.


Let the supply function be:

[Q.sub.s] = a + b[P.sub.t-1] + [v.sub.1] and demand function is given as:

[Q.sub.d] = [alpha] + [beta][P.sub.t] + [u.sub.1]

For market equilibrium [Q.sub.d] = [Q.sub.s], it implies

[mathematical expression not reproducible]

This is the equation of the price [P.sub.t] on time path

if t=1, [mathematical expression not reproducible]

if t=2, [mathematical expression not reproducible] likewise the values of the other time periods can be calculated in the same manner. In the equilibrium, it is assumed that:

[bar.p] = [p.sub.t]= [p.sub.t-1]

Let [bar.P] the long run equilibrium price, therefore

[alpha]-[beta][??] = a + b[??]

[alpha] - a = [beta][bar.p]= (b + [beta])[bar.p] [??] [bar.p] = [alpha] - a/[beta] - b

Linear regression was used to estimate the demand and supply function given as under:

The demand function of cocoon is:

[Q.sub.d] = 675 - 0.871 [p.sub.t] 1

and the supply function cocoon is given as

[Q.sub.s] = 372 +0.617 [p.sub.t-1] 2

for market equilibrium [Q.sub.d] = [Q.sub.s]

372 + 0.617 [p.sub.t-1] = 675 - 0.871 [p.sub.t]


[p.sub.t] =347.87-0.70 [p.sub.t-1] 3

From the above equation, we get series of different prices (P) by substituting t=1, 2, 3, 4, 5......, the result is shown in table 1 above.
Coefficients    Std. Error  T-value  Significance

([beta]) 0.617  0.121       5.09     0.001
(b) 0.871       0.112       7.78     0.000

Tariq Ahmad Bhat (*) and Tapan Choure ([dagger])

(*) Ph.D. Research Scholar, School of Studies in Economics, Vikram University, Ujjain (M.P.)

([dagger]) Professor and Head, School of Studies in Economics, Vikram University, Ujjain (M.P.)
                               Table 1
Estimated Demand, Supply of Cocoon and its Prices during Different
Time Periods

Time Periods  [??] (Rs/Kgs)  [??] (Lakh Kgs)  [??] (Rs/Kgs)

 1                                            215
 2            215            504.66           197.37
 3            197.37         487.73           209.71
 4            209.71         503.3            201.07
 5            201.07         492.34           207.11
 6            207.11         499.86           202.88
 7            202.88         494.6            205.84
 8            205.84         498.29           203.77
 9            203.77         495.71           205.22
10            205.22         497.51           204.21
11            204.21         496.25           204.92

Time Periods  [??] (Lakh Kgs)

 1            504.66
 2            487.73
 3            503.3
 4            492.34
 5            499.86
 6            494.6
 7            498.29
 8            495.71
 9            497.51
10            496.25
11            496.51
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Author:Bhat, Tariq Ahmad; Choure, Tapan
Publication:Madhya Pradesh Journal of Social Sciences
Date:Jun 1, 2015
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