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M. Ranadhir
Scientist S-3


Scientific researches of recent decades in fresh water fish culture in India have evolved a high yielding new technology popularly known as composite fish culture involving six Asiatic major carps like Catla catla, Labeo rohita, Cirrhinue mrigala, Hypophthalmichthys molitrix, Ctenopharyngodan idella and Cyprinus carpio. This new technology has been steadily gaining increasing adoption rate among Indian fish farmers. Production levels as high as 10,300 kg/ha/year have been obtained in certain experimental operations and in general, on an average a level of 4000–6000 kg/ha/year has been demonstrated in farmers ponds. In view of attainment of high production levels in composite fish culture, the prospects for its expansion seems to be very bright particularly as fish production level through traditional operations in India is estimated only around 600 kg/ha/year. Therefore, it is necessary that composite fish culture operations are subjected to micro-economic analysis which will indicate the factors affecting farm profitability and the way in which these factors of production are to be combined to maximise net returns.


Production function approach is a useful tool in finding answers to many aquaculture economics research problems. Fish production in composite fish culture like any other aquaculture system is a function of the quality and quantity of inputs applied in the production process. Apart from material inputs like mahua oil cake (Bassia latifolia), cowdung, chemical fertilizers, stocking material, feed, weed etc., management factors including labour and also soil, water and environmental characteristics play a vital role in determining the ultimate production. The way in which the species are mixed and the size at the time of stocking are also found to significantly affect production. Though most of the factors affecting fish production are theoretically known, an attempt was made initially to work out input-output relationships based on material inputs and fish production in order to draw some broad economic conclusions and to establish a simple workable model in field conditions.


Log-linear (Cobb-Douglas), linear and quadratic forms of production function were initially tried to consider their appropriatness in explaining output variation in composite fish culture. A form of linear-quadratic model fitted to the Indian carp culture data well with expected signs for production coefficients. The model for total production (all six species combined) is

YFISH=- 176013 + 83.2494 MAH - 0.0119558
MAH2 + 64.1404 COW - 0.00515717 COW2
+ 1502.58 CHE + 233.644 FEED
+ 14421.4 WEE - 22.9051 WEE2
+ 175.561 TONU


YFISH= Total fish in gm
MAH= Mahua oil cake in kg
COW= Cowdung in kg
CHE= Chemical fertilizers in kg
FEED= Feed in kg
WEE= Weeds in tonnes
ToNU= Total number

The above model explained 84% of variation in total output and the overall regression equation is significant as can be seen from F value given in Table I. (F9, 146 = 85.6442 > 2.72 at 5% level of significance). The model has expected signs, positive coefficient for linear terms and positive and negative coefficients for quadratic terms. Also it can be seen from Table I that the coefficients of CHE, FEED, WEE and TONU are significantly different from zero at 1% level of significance according to ‘t’ statistic.

Table I: Estimated coefficient, standard error, t statistic and level of significance for the model for total production

Independant variableEstimated coefficientStandard errorT-statisticLevel of significance

R2 = 0.8408 Adj R2 = 0.8309
F statistic (9, 146) = 85.6442
Durbin-Watson statistic = 1.555

From the production function output elasticities have been worked out. Output elasticities indicate the breakup effect of each variable on total production.

For linear terms, output elasticities (ex) are calculated as follows:

where is the estimated coefficient of the input variable, is the mean of the input and is the estimated production at means of inputs.

In case of quadratic terms,

where and is the same as defined above and 1 and 2 are estimated coefficients for x and x2 terms respectively.

Estimated production at means of inputs viz., MAH, COW, CHE, FEED, WEE and ToNU worked out to be 825 959 gm ( = 825959 )

Table 2: Production or output elasticities of inputs specified in the model.

Production or output elasticity of inputArithemetic mean of inputValue of production or output elasticity

The sum of production elasticities is 1.231 indicating that the production function exhibited increasing returns to scale. Putting it in a different way, if all the inputs specified in the production function are increased by a certain percentage, output will increase by a larger percentage. In this case, if all inputs are increased by 1%, output will increase by 1.231%.

The interpretation of production or output elasticities are

  1. A 10% increase in mahua oil cake application will produce a 0.35% increase in output.

  2. A 10% increase in cowdung application (organic fertilizer) will produce a 1.52% increase in output

  3. A 10% increase in chemical fertilizar application will produce a 1.81% increase in output.

  4. A 10% increase in feed will produce a 4.33% increase in output.

  5. A 10% increase in weeds will produce a 1.74% increase in output.

  6. A 10% increase in stocking number will produce a 2.56% increase in output.

Feed is the most powerful explanatory variable with highest output elasticity and this is the only item through which one can think of increasing production effectively because of biological limitation of increasing use of mahua oil cake, cowdung and chemical fertilizers.


To know the efficiency of input use, it is necessary to compare marginal physical product with input output price ratio. The norms of economics indicate that if MPP (marginal physical product) is greater than price ratio, use of that particular input should be increased. Also if MPP is less than price ratio, use of that input should be decreased. Equality implies optimum use of input.

If(Economic norm)
(Increase input use so that MPP will fall to such a level where quality occurs)
(Decrease input use so that MPP will raise so as to reach to such a level where equality occurs)
(Optimum input use)

where Px1 and Py are prices of input x1 and output respectively. Fish price was taken at farm gate on average at I.Rs 12/kg (Py = 0.012/gm). The input prices and output prices are to be taken as per the units specified in the production function.

Table 3: Marginal physical production (MPP), input price and input use in Indian composite fish culture.

InputMPPValue of marginal physical product
Cost of marginal unit
I. Rs
Input use
Mahua oil cake73.87440.891.701.70141.66Decrease
Cowdung (organic fertilizer)64.03620.770.100.108.33Increase
Chemical fertilizer (inorganic)1502.5818.032.002.00166.66Increase

Depending upon the relationship between the MPP and the respective price ratio, the decreasing or increasing use of inputs were outlined in Table-3. If use of inputs decreased, MPP will raise and if use of inputs increased MPP will fall. The extent of which the use of these inputs to be increased or decreased depends upon attainment of equality between MPP and price ratio of input and output. In case of feed, the logical conclusion of this analysis is that the farmers will benefit by increasing the use of feed to such an extent that MPP comes down to 166.66. Only in case of mahua oil cake, it is revealed as per current price level of mahua oil cake which is taken at I.Rs 1.70/kg, the use of mahua oil cake needs to be reviewed and may be kept at needed minimum prescribed dosage levels. Alternatively substitutes like bleaching powder may be tried if it is equally effective in view of cost factor of mahua oil cake and low quantities of bleaching powder required for the purpose as piscicide. Though the cost of cowdung is quite low, there are biological limitations of its increasing use in fish culture operations as any overdose of its application may cause oxygen depletion and thereby strain to fishes. This has been correctly revealed by the quadratic form of the relationship between cowdung and total production in the production function given in section 3.0


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