Economics of the Philippine Milkfish Resource System (UNU, 1982, 66 pages) |

III. The transformation sub-system: cultivation to market size in fishponds |

The relationship between inputs and output in fishponds can be described mathematically through a production function of the following generalized form:

Y = f (X_{1},....................... X_{n})

where Y = output

X_{j} =inputs

Various specifications of the functional form could be used, including linear, polynomial, or power functions. For this paper, a Cobb-Douglas form was specified for the input/output relationship:

e

It was hypothesized that variation in output could be explained by 11 explanatory variables (inputs) as follows:

X_{1} = age of pond (years)

X_{2} = quantity of milkfish
fry stocked (pieces)

X_{3} = quantity of milkfish fingerlings
stocked (pieces)

X_{4} = acclimatization time before stocking
(hours)

X_{5} = hired labour (man-hours)

X_{6} =
miscellaneous operating costs (P)

X_{7} = milkfish culture
experience of operator (years)

X_{8} = pesticides,(P)

X_{9} = organic fertilizers (kg)

X_{10} = inorganic
fertilizers (kg)

X_{11} = farm size (land in ha)

= production coefficients to be estimated

e = error term

The absolute values of the production coefficients (Sb_{i}) can be
interpreted as the respective elasticities of production. The sum of the
coefficients (Sb_{i}) indicates returns to scale. Finally, the value of
the marginal product (VMP_{j}) for each input can be compared with the
input price (P_{i}) to determine the efficiency of the transformation
sub-system. If VMP_{j} <> P_{i}, the sub-system is not
efficient; that is, additional profits could be earned if the quantities of
input are changed. If VMP_{j} = P_{j}, the level of use of input
i is optimal.

Based on data collected from 324 producers in seven selected provinces, production functions were estimated on a per-farm and per-hectare basis, first for each of the seven provinces, and second, for the whole country. The latter national production functions are summarized in tables 17 and 18. Both the per-farm and per-hectare production functions are reported here to demonstrate that they are equally valid and have similar coefficients.

Before discussing the individual explanatory variables, their respective
production coefficients, and their significance or insignificance, it is helpful
to examine the nature of the estimated production functions. The predictive
value of the estimated production functions is satisfactory (given they are
based on cross-sectional data), as measured by the R^{2 }values, which
range from 0.39 to 0.77. The overall "fit" of the model, judged by the
F-values, is also very good. The absolute values of the estimated production
coefficients (not to be confused with their significance level) are low,
implying that the response of milkfish output to the application of supplemental
inputs is low.

Of the 11 explanatory variables hypothesized to explain variation in milkfish output, six are significant in the per hectare specification and seven in the per-farm specification. These are age of pond, milkfish fry, and fingerlings, miscellaneous operating costs, and organic and inorganic fertilizers. The seventh is farm size (land). The following discussion will focus on the two national functions estimated on a perfarm and per-hectare basis. Each of the significant explanatory variables will be first discussed in turn.

Age of Pond (X_{1}):

Age of pond is a significant variable in explaining variations in milkfish output. Based on the national production functions, it contributes 0.27-0.28 per cent to output for every 1 per cent increase in the age of pond, assuming that other inputs are held constant. The positive value of the coefficient is consistent with the general experience of milkfish producers. According to them, the older the ponds, the more productive they become. They attribute this to the organic matter build-up on the pond bottom, and the gradual reduction in the acidsulphate soil problem through pond draining, drying, and leaching. Some producers have even attempted to shorten the ageing period for the pond by incorporating mud press from sugar mills into their ponds, and claim that their milkfish ponds are positively affected. Mud press is the dirt accumulated from washing and processing the sugar-cane brought in from the fields, If this tendency as observed is useful, as claimed, one would then expect that as the pond becomes older, the need for fertilizers may level off to a certain extent with proper management of the pond system. It is only necessary to replenish the nutrients which have been removed from the pond in the process of rearing and harvesting fish.

Milkfish Fry (X_{2}):

Milkfish stocking rates of fry are highly significant in explaining milkfish output. This is to be expected since milkfish fry are the primary inputs in the production of milkfish. The estimated production coefficients for milkfish fry are 0.18 and 0.14 for the per-hectare and per-farm functions respectively. Again, this implies that for every 1 per cent increase in the milkfish-fry stocking rate, a 0.140.18 per cent increase in milkfish production can be expected, ceteris paribus.

Milkfish Fingerling (X_{3}):

Similarly, milkfish fingerlings as stocking materials are found to be significant in explaining milkfish output, For every 1 per cent increase in stocking rate, an increase of 0,10-0.14 per cent in output can be expected.

Miscellaneous Operating Costs (X_{6 }):

On the basis of the estimated production coefficient for miscellaneous operating costs, an increase of 1 per cent in expenditure of miscellaneous operating cost will increase milkfish output by 0.16-0.17 per cent. Because miscellaneous operating costs cover a wide variety of items such as repair and maintenance costs, food for labourers (but not labourer wages), depreciation, interest, rental, taxes, and other fees, it is not easy to pin-point the profitable use of additional expenditure on this input category, that is, which of the seven items to single out for additional expenditure. Miscellaneous operating costs as an input is, however, important in the production model because it represents 22 per cent of the production costs of milkfish. Stated differently, if this expenditure is reduced by 1 per cent, it means that output will be reduced by 0.160.17 per cent. The importance of this input category is, therefore, immediately apparent.

Organic and Inorganic Fertilizers ( X_{9}, X_{10} ):

To some extent, organic fertilizers can be used in place of inorganic fertilizers in milkfish production. In general, the absolute values of the estimated production coefficients for organic and inorganic fertilizers are small, though significant, implying that the application of fertilizers is not only not widely practiced but they are not generally being used in large enough quantities to affect yield in a big way. The estimated values for the two inputs range from 0.030.04 for organic and 0.09-0.12 for inorganic fertiIizers.

**TABLE 17. Estimated Per-Hectare Production Function (Cobb-Douglas),
Sample Means, and Estimated Output for the Philippines **

Explanatory variables |
Production
coefficients | Standard error | t-value | Significance level | Input Mean () | ||

GM | AM | ||||||

a | Intercept (antilog) | 7.01 | |||||

X_{1}
| Age of pond | 0.27* | 0.05 | 4.56 | 0.0001 | 12.84 | 21.57 |

X_{2} | Fry | 0.18* | 0.02 | 6.22 | 0.0001 | 3,543 | 5.940 |

X_{3}
| Fingerlings | 0.14* | 0.02 | 4.88 | 0.0001 | 2,346 | 5,892 |

X_{4} | Acclimatization | 0.05 | 0.04 | 1.22 | 0.22 | 3.74 | 14.09 |

X_{5} | Hired labour | -0,01 | 0.02 | - 0.35 | 0.72 | 123.26 | 228.71 |

X_{6} | Misc. operating costs | 0.17* | 0.05 | 3.36 | 0.0009 | 639.56 | 1,033.1 |

X_{7} | Culture experience | 0.04 | 0.06 | 0.55 | 0.58 | 10.28 | 15.72 |

X_{8}
| Pesticides | 0.02 | 0.03 | 0.46 | 0.64 | 27.79 | 62.46 |

X_{9} | Organic fertilizer | 0.04** | 0.01 | 2.24 | 0.02 | 630.44 | 2,178.8 |

X_{10}
| Inorganic fertilizer | 0.12* | 0.03 | 3.43 | 0.0007 | 74.77 | 172.3 |

X_{11} | Farm size | -0.02 | 0.04 | - 0.57 | 0.57 | 6.16 | 16.20 |

Sb_{i} | Returns to scale | 1.00 | |||||

R^{2} | Coeff. Of determination | 0.39 | |||||

Estimated output at = 1351.44 |

F-value = 18.3.

Note: GM is the geometric mean AM is the arithmetic
mean,

* Significant at 1 per cent.

** Significant at 5 per cent.

**TABLE 18. Estimated Per-Farm Production Function (Cobb-Douglas),
Sample Means, and Estimated Output for the Philippines**

Explanatory variables |
Production
coefficients | Standard error | t-value | Significance level | Input Mean () | ||

GM | AM | ||||||

a | Intercept (antilog ?) | 10.91 | |||||

X_{1} | Age of pond | 0.28* | 0.05 | 4 70 | 0.0001 | 1 2.84 | 21.57 |

X_{2} | Fry | 0.14* | 0.02 | 5 37 | 0.0001 | 3,543 | 5,940 |

X_{3} |
Fingerlings | 0.10* | 0.02 | 4.25 | 0.0001 | 2,346 | 5,892 |

X_{4} | Acclimatization | 0.04 | 0.04 | 1.00 | 0.32 | 3.74 | 14.09 |

X_{5} | Hired labour | -0.01 | 0.02 | - 0.29 | 0.77 | 123.26 | 228.71 |

X_{6
} | Misc. operating costs | 0.16* | 0.05 | 3.21 | 0.001 | 639.56 | 1,033.1 |

X_{7} | Culture experience | 0.04 | 0.06 | 0.65 | 0.51 | 10.28 | 1 5.72 |

X_{8} | Pesticides | 0.03 | 0.02 | 1.09 | 0.27 | 27.79 | 62.46 |

X_{9} | Organic fertilizer | 0 03** | 0.01 | 1.96 | 0.05 | 630.44 | 2,178.83 |

X_{10} | Inorganic fertilizer | 0.09* | 0.02 | 3.42 | 0.0007 | 74.77 | 172.3 |

X_{11}
| Farm size | 0.57* | 0.06 | 9.26 | 0.0001 | 6.16 | 16.20 |

Sb_{i} | Returns to scale | 1.47 | |||||

R^{2 }Coeff. of determination | 0.77 |

Estimated output at

= 2,577

F-value = 95.3

Note: GM is the geometric mean; AM is the arithmetic mean,

* Significant at 1 per cent.

** Significant at 5 per cent.

Farm Size (X_{11}):

In the per-farm model, farm size contributes 0.57 per cent to total output for each 1.0 per cent increase in land area. This coefficient is significantly different from zero. However, as discussed earlier, fertilizers can be made to substitute for land to a certain extent. Since Landsat imageries have shown that the scope for hectarage expansion is limited, the application of larger quantities of fertilizers is, therefore, suggested instead of bringing new areas under production.

Both dummy variables and independent specifications stratified by group were used to explain differences in productivity by province, climate type, ownership patterns, and farm size.

For comparisons among provinces, lloilo Province was used as the bench-mark. Productivity was lowest in Cagayan Province (37 per cent of lloilo's productivity). Milkfish producers in Pangasinan, Bulacan, Masbate, Bohol, and Zamboanga del Sur produce, respectively, 14, 4, 28, 43, and 34 per cent less than milkfish producers in lloilo. Although each province has its own inherent advantages or disadvantages, scope is available for milkfish producers in these six provinces to increase materially their per. hectare yields by using larger quantities of inputs. The above interprovincial output variations have conclusively shown that lloilo is the premier province in the country with the highest per hectare productivity. Interestingly, Bulacan milkfish farmers, contrary to some expectations that they would be more productive, produce slightly less than lloilo milkfish producers.

As expected, due to favourable climate, technical efficiency of milkfish producers in climate I is higher than that in climates III and IV (fig. 32). Technical efficiency in this case is interpreted as the difference in antilog of intercept (a) values for the production functions in each climate zone. In other words, the same level of input application in all three climate zones results in higher productivity per hectare in climate 1, due to inherent physical advantages of the climatic zone and/or to better management by producers Based on the antilog values of the intercepts, the inherent advantage (that is without supplementary inputs) of climate I over climates III and IV is approximately 50 kg and 48 kg per hectare respectively.

Milkfish producers owning private farms are also more technically efficient than producers leasing farms from the government. In addition, while a 1 per cent increase in farm size of privately-owned farms would increase output by 0.65 per cent, a 1 per cent increase in farm size of governmentleased farms would only increase output by 0.42 per cent. Besides, diminishing returns occur sooner on governmentleased farms than on privately-owned farms.

The difference in technical efficiency in terms of productivity per hectare
between small farms (<6 ha) and large farms (> 50 ha) is substantial.
However, further expansion of farm size in the latter category results in
diseconomies of scale while expansion of small farms is economically desirable.
Overall, using the national per farm specification, economies of scale are
definitely positive (Sb_{i}= 1.47). This means that the average size
farm (16.3 ha) can achieve economies of scale and increased profits by expanding
the level of input use.

While technical efficiency can be determined by a comparison among the intercepts of the various production functions specified, economic efficiency is determined for a given production function by comparing the marginal product with the input-output price ratio. At the point of optimum input combination, which maximizes net return, given a capital constraint, the ratio of the input output prices to marginal product must be the same for each of the inputs used. If capital is not a constraint, the value of the marginal product must be equated to the input price. This is written algebraically as follows:

or Mp_{i} x P_{0 }=P_{j}

or
VMP_{i}=P_{i}

where

MPj= marginal product of input i

Pj = price of input i (e.g.,
milkfish fry)

P_{0} = price of output (milkfish)

VMPi = value of
marginal product

Both the prices of inputs and output are known and the marginal products are
obtained by taking the first partial derivative of the estimated production
function with respect to the input i. If the value of the marginal product
(VMPj) is greater than the input price (Pi), then the use of that input should
be increased. If VMP_{i} < P_{i}, the use of input i should
be decreased. If VMP_{i} = P_{i}, producers are economically
efficient.

In the case of three of the four inputs for which prices are readily available (milkfish fry, organic fertilizer, and inorganic fertilizer), the value of marginal product is greater than the input price (table 19). For the country as a whole, application rates of these three inputs should be increased to raise the efficiency and profits of producers. The stocking rate of fingerlings is found to be optimum because the MVP of fingerlings and price of fingerlings is nearly equal. However, in the case where capital is limited, the above results show that the producer obtains a higher return from using inorganic fertilizer first and then organic fertilizer. This is because the use of P1 worth of inorganic fertilizer provides a higher return than a peso worth of organic fertilizer.

**TABLE 19. Value of Marginal Products and Input Prices for Selected
Inputs**

Input | VMP_{i} | P_{i} |
Optimum rate/ha |

Milkfish fry | 0.69 | 0.36* | 6,790 pieces |

Organic fertilizer | 0.82 | 0.29 | 1,750 kg |

Inorganic fertilizer | 20.20 | 1.66 | 1,124 kg |

Milkfish fingerling | 0.69 | 0.72* | 2,154 pieces |

* To be comparable with VMPi, which is based on output price per kg (4 pieces/kg), fry and fingerling prices shown are for 4 pieces. Individual fry and fingerling prices are P0.09 and P0.18 respectively.

The empirical analysis of the performance of the fishpond transformation sub-system using the input-output methodology, therefore, points to a general conclusion: Milkfish production in the Philippines can be more efficient and yields can be substantially increased. Present production methods with limited use of supplemental inputs grossly under-utilize the milkfish ponds under cultivation at present.

At the present low rates and levels of input application, the use of supplemental inputs show low marginal products for each of the inputs applied. The input-output relationship described, therefore, represents a lower production frontier than if the rates of input application were increased. In other words, if the use of all the inputs is increased at the same time (in either fixed or variable proportions), higher marginal products can be obtained. This is because, with the higher levels of input use, a higher input-output relationship is described. So instead of moving along the same production frontier there is a shift upwards to a new production frontier.

Diminishing marginal returns set in only when one input is increased without a simultaneous increase in all the other inputs, that is, a movement along the same production function. The implication is that if the milkfish producers in the country switch to the use of larger quantities of all supplemental inputs, output will likewise increase as they move up to a new production frontier.