M. Ranadhir

Scientist S-3

1 INTRODUCTION

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.

2 PRODUCTION FUNCTION APPROACH

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.

3 INPUT-OUTPUT RELATIONSHIP

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 |

MAH^{2} + 64.1404 COW - 0.00515717 COW^{2} | ||

+ 1502.58 CHE + 233.644 FEED | ||

+ 14421.4 WEE - 22.9051 WEE^{2} | ||

+ 175.561 TONU |

Where

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.
(F_{9, 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 variable | Estimated coefficient | Standard error | T-statistic | Level of significance |

C | -176013 | 46546.7 | -3.78142 | 0.01 |

MAH | 83.2494 | 63.5639 | 1.30970 | N/s |

MAH^{2} | -0.0119558 | 0.00483385 | -2.47334 | 0.05 |

COW | 64.1404 | 33.8683 | 1.89382 | N/s |

COW^{2} | -0.00515717 | 0.00306915 | -1.68033 | N/s |

CHE | 1502.58 | 311.423 | 4.82489 | 0.01 |

FEED | 233.644 | 30.1363 | 7.75293 | 0.01 |

WEE | 14421.4 | 3826.29 | 3.76903 | 0.01 |

WEE^{2} | -22.9051 | 6.27375 | -3.65094 | 0.01 |

TONU | 175.561 | 46.0335 | 3.81377 | 0.01 |

R^{2} = 0.8408 Adj R^{2} = 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 x^{2} 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 input | Arithemetic mean of input | Value of production or output elasticity |

^{e}MAH | 392.071 | 0.035 |

^{e}COW | 1959.92 | 0.152 |

^{e}CHE | 99.3354 | 0.181 |

^{e}FEED | 1532.3 | 0.433 |

^{e}WEE | 10.292 | 0.174 |

^{e}TONU | 1207.56 | 0.256 |

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

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

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

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

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

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

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.

4 INPUT USE

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.

Input | MPP | Value of marginal physical product VMP I. Rs | Pxi I.Rs | Cost of marginal unit I. Rs | PxiPy | Input use |

Mahua oil cake | 73.8744 | 0.89 | 1.70 | 1.70 | 141.66 | Decrease |

Cowdung (organic fertilizer) | 64.0362 | 0.77 | 0.10 | 0.10 | 8.33 | Increase |

Chemical fertilizer (inorganic) | 1502.58 | 18.03 | 2.00 | 2.00 | 166.66 | Increase |

Feed | 233.644 | 2.80 | 2.00 | 2.00 | 166.66 | Increase |

Number | 175.561 | 2.10 | 2.00 | 0.20 | 16.66 | Increase |

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