THE ANALYSIS OF PRODUCTION FUNCTION AND ALLOCATIVE EFFICIENCY OF SEED WATER SPINACH IN SUMURCINDE VILLAGE SOKO DISTRICT TUBAN REGENCY

The Analysis of Production Function and Allocative Efficiency of Seed


INTRODUCTION
Human life in its daily life can not be separated from fulfilling the needs of clothing, food, and boards that must be met. That is why agricultural activities are an essential part of life. Agricultural activities considerably reduce unemployment in Indonesia and develop the country, so agricultural activities cannot be ignored. Indonesia itself is a country that is fertile with soil and rich in natural resources, so it has excellent potential for developing its agricultural business.
The agricultural sector is frequently researched because it forms the foundation of Indonesia's economic development. National development has also focused on the farm sector, mainly on using and processing agricultural products. It is hoped that the utilisation and expansion of this product's results will be done with maximum effort and utmost efficiency for the Indonesian population to appreciate them. In Indonesia, the agricultural sector has an essential role because Indonesia has relatively large and diverse potential resources and is one of the drivers for the national economic system.
Vegetables are horticultural commodities that have added value for national development because vegetables significantly contribute to increasing income and people's welfare (Lama & Kune, 2016). In economic development, horticulture has a significant role. On the other hand, horticulture also fulfils human nutritional needs as a complement to staple food (Gleyn et al., 2020). Horticultural products are one of the agricultural commodities that have an excellent opportunity to be developed because horticultural products are needed by the community every day for consumption and can improve the welfare of farmers, both types of fruits, vegetables, medicines, and ornamental plants. In meeting human food needs, vegetables play a significant role in human health because vegetables contain various sources of vitamins, minerals, fibre, provitamins, and carbohydrates.
Seed Water Spinach is one of the most well-known vegetable plants and is widely consumed as daily food by the people of Indonesia. For every 100 grams of seed water spinach, there are 29 calories, 3 grams of protein, 0.3 grams of fat, 5.4 grams of carbs, 50 mg of phosphorus, 50 mg of calcium, 3 mg of iron, 6300 IU of vitamin A, 0.07 mg of vitamin B1, and 32 mg of vitamin C. (Hidayati et al., 2017). Seed Water Spinach is a food ingredient that is easy to get at an affordable price, making Indonesian people like Seed Water Spinach vegetables.
Seed Water Spinach farming is one type of farming that interests farmers, particularly in Sumurcinde Village, Soko District, Tuban Regency. This type of Seed Water Spinach farming is different from other types of Seed Water Spinach farming. Seed Water Spinach farming generally uses leaves as the main ingredient for consumer sale. However, this seed water spinach farming business in Sumurcinde Village, Soko District, Tuban Regency, uses the seeds for sale. The business of farming Seed Water Spinach in Sumurcinde Village, Soko District, Tuban Regency, has been carried out since 2019. During the dry season, farmers' land cannot be planted with rice which requires quite a lot of water. So farmers choose Seed Water Spinach to be cultivated because Seed Water Spinach is a vegetable that is easy to care for and can generate significant income for farmers.
Previously, research on water spinach farming had been carried out, such as studies addressing the variables that affect the production of seed water spinach. The research results showed that seed variables, ponska fertiliser, urea fertiliser, and za fertiliser all simultaneously affect the manufacturing of water spinach seed production in Ds. Dapet, Kec. Balongpanggang, Kab. Gresik. Partially, seeds, urea fertiliser, za fertiliser, and super sip affect water spinach seed production. Meanwhile, ponska, virtako, and labour had no significant effect. Seed use was inefficient (e = 66,689.65) in water spinach seed production. The urea fertiliser produced water spinach seeds inefficiently (e = -386.58). Fertilizer Za was inefficient (e = -167.70) in planting water spinach seeds. The service of Supersip was inadequate (e = 100301.04) in producing water spinach seeds.
Research on the application of production factors was carried out by (Silitonga et al., 2018) regarding the analysis of economic efficiency for several types of vegetable farming in Sungai Gelam District, Muaro Jambi Regency, where one type of vegetable is Seed Water Spinach. The probability values for the production factors of land area (x1), seeds (x2) and manure (x3) were smaller than alpha (0.05) at the 95 per cent confidence level, which means that partially or individually, these independent variables are significant significantly affect the production of Seed Water Spinach. While the probability value, which includes urea fertiliser (x4), pesticides (x5) and labour (x6), is more significant than alpha (0.05) at the 95 percent confidence level, which means that partially or individually, these independent variables have no affect spinach. The analysis of the economic efficiency of seeds and manure shows that the results are not yet efficient. In contrast, the land area shows the results are not economically efficient.
The production of Seed Water Spinach is expected to continue to increase from year to year. However, farmers in Sumurcinde Village face constraints on production factors, including seeds, phonska fertiliser, urea fertiliser, power grow fertiliser, pesticides, and labour. This makes farmers strive to be efficient in using production factors to increase efficiency and productivity. Calculating allocative efficiency is one way to find out the factors of farming water spinach. Allocative efficiency is the relationship between output and input. Achieve allocation efficiency if they can increase intake while minimising results. In Sumurcinde Village, Soko District, Tuban Regency, this study examines the effects of production factors on the productivity of seed water spinach farming and the allocative effectiveness of using production factors in this sector.

MATERIALS AND METHODS
The location of the study was chosen on purpose, namely in Sumurcinde Village, Soko District, Tuban Regency by considering that Sumurcinde Village is one of the villages where the characteristics of most of the farmers are farmers and one of the villages that produce Seed Water Spinach. This study was carried out in December 2022 and January 2022. Data retrieval in this study with interviews, recording, and observation techniques. In this research, a descriptive quantitative methodology was applied. This research using a descriptive quantitative method only explains a variable's contents in a study and is not used to test hypotheses (Marlina, 2020). The selection of respondents (samples) used in this study has a total population of 206 farmers. The sample used was 67 farmers with a total land area of 19.2 ha. Sampling aims to get a descriptive picture of the observation units included in the sample and to generalise and estimate population parameters. This study determined the selection using the Slovin formula, which has a 10% error rate (e).
Methods of data analysis using Cobb Douglas production function analysis. Analysis of factors thought to influence the production of Seed Water Spinach, namely: seeds, phonska fertiliser, eISSN: 2656-4270 urea fertiliser, power grow fertiliser, pesticides, and labour (HOK). The workforce used comes from within and outside the family, and the workforce's size in a farming business is expressed in HOK (Working Day) (Elinur & Heriyanto, 2019). The Cobb-Douglas function was chosen because of its simple shape and the ability to minimise multicollinearity (Thamrin, 2014). The Cobb-Douglas function equation can be written as: Where: Y = production of Seed Water Spinach (kg/period); A = intercept value; X 1 = Seed (kg); X 2 = Phonska Fertilizer (kg); X 3 = Urea Fertilizer (kg); X 4 = Powergrow Fertilizer (ml); X 5 = Pesticide (ml); X 6 = Labor (HOK); b 1 ,b 2 ,b 3 ,b 4 ,b 5 ,b 6 = variable regression coefficients X 1 ,X 2 ,X 3 ,X 4 ,X 5 ,X 6 ; u = error ; e = natural logarithm, b i = model coefficients.
The equation is converted into a linear form by logarithm: The production function connects the inputs (factors of production) and outputs (products of production) (Damayanti, 2013). The production function can be used for two purposes: maximising output and minimising the input used. This study uses the OLS method as a parameter estimator. Therefore, before the analysis results are used to draw conclusions, the classic assumption test required in the OLS has been carried out beforehand. The classic test includes: testing for normality, heteroscedasticity, and multicollinearity are examples of each. The Normality Test measures whether the data obtained is normal or not so that statistics can be selected correctly ). The regression model's correlation is tested using the multicollinearity test. One way to detect a high correlation in the independent variables is to use the Tolerance and Variance Inflation Factor (VIF). If VIF > 10 and Tolerance value < 0.10, multicollinearity occurs; If VIF < 10 and Tolerance value > 0.10, multicollinearity does not occur. The aim is to test whether there is a difference in the regression model (Rukayat, 2018). To determine whether the regression model has an inequality in variance from the residuals of one observation to another, the heteroscedasticity test with the Glejser test method is utilised (Nugraha Billy, 2022). The basis for decision making: If the significance value is > α = 0.05, the conclusion is that there is no heteroscedasticity; If the significance value < α = 0.05, the decision is that there is heteroscedasticity. The model is then analysed to determine how accurate the estimation is. The statistical criteria in this stage will be tested for the calculated F, t, and R² values by looking at the significance level at α = 5%.
The usage of inputs can be efficient if farmers endeavour to ensure that the Marginal Product Value (NPM) is the same. (Arta et al., 2016).
Where b = Regression coefficient; Y = the Average number of production; PY = selling price of production; X= Average number of x; PX = price X with the criteria NPMx = Px or NPMx/Px = 1. If the situation is NPMx/Px = 1, then the use of input x is efficient, NPMx/Px < 1, then the use of the input is inefficient, and you have to reduce the use of inputs, NPMx/Px>1, the use of input is not efficient, so you have to add the use of input.

Characteristics of Respondents
The traits that farmers have will affect the maturity level of farmers in managing a farming business (Burano & Siska, 2019). The characteristics of farmers illustrate the ability to farm based on effective and efficient planning according to the technical cultivation of a plant. Seed Water Spinach farmers' attributes are essential to a study. The aim is to determine the observed farmers' condition and condition. Characteristics of Seed Water Spinach farmers observed included age, education level, and area of land planted.
Age is one measure of the success of a farming business. Based on the research, there were three respondents aged 31-40 years, 17 respondents aged 41-50, 31 respondents aged 50-60, and 16 respondents aged >60. From these data, the age of farmers from 31-60 years 51 respondents. This shows that productive farmers (Susanti et al., 2016) argue that farmers in the practical age range of 30-59 years have muscular physical and mental strength in developing farming and self-potential. eISSN: 2656-4270 Productive age owned by farmers usually affects good performance compared to no longer practical farmers. Farmers aged > 60 will tire easily compared to younger farmers. Even though young farmers lose in terms of experience, young farmers are more innovative in running their farming business and are brave enough to take risks. (Silitonga et al., 2018) Argues that age affects the physique and way of thinking of farmers. Based on Table 1, the degree to which the majority of Sumurcinde Village attained was the Elementary School level of 59.7% with 40 respondents. This shows that the education level of respondents in Sumurcinde Village was deficient, below the primary education of nine years. A bad economy is one of the reasons why Seed Water Spinach farmers cannot continue their education. In essence, education is essential for the sustainability of a farming business. A well-educated individual will be more willing to accept and try new things. (Maramba, 2018). The same thing was stated: highly educated farmers have broad and future-oriented thinking compared to low-educated farmers. The causes of poverty in the agriculture sector are a lack of technical expertise and poor knowledge. The respondent's level of education will determine how effectively the farm is managed.
Productivity yields of a Seed Water Spinach farming business are influenced by land and land area (Hastuti et al., 2022). The wider the land used for a farming business, the greater the productivity results. And income will also increase even though other factors affect the productivity of this Seed Water Spinach. Seed Water Spinach farmers have the status of their land, meaning that farmers in Sumurcinde Village can rely on the agricultural sector to meet family needs from farming income (Simanjuntak et al., 2019). Based on the table above, 56 respondents, with a percentage of 83.6, have a land area of 0.1 -0.73 ha. This shows that the land used by farmers is narrow.
The production factors used by Seed Water Spinach farmers are seeds, urea, phonska, power growth, pesticides, and labour. The two types of sources used by Seed Water Spinach farmers are varieties 04 with medium leaves and broad leaves. The seeds used in this cultivation are based on the average land area of 0.5 ha is 2.7 kg/ha. In the use of fertilisers, water spinach farmers use three fertilisers, namely urea fertiliser, phonska fertiliser, and power grow liquid fertiliser. Urea fertiliser is the fertiliser used in large quantities by water spinach farmers (117.7 kg/ha) compared to phonska fertiliser (72.7 kg/ha) and power grow fertiliser (105.8 ml/ha). This is because urea fertiliser is a source of nitrogen nutrients for plants (Mahrus & Raksun, 2020). The use of pesticides in this Seed Water Spinach farming business is 84.7 ml/ha. The dose of pesticide applied to the Seed Water Spinach plant depends on the area and needs of the plant itself. The workforce used in this Seed Water Spinach farming business consists of workers in the family with an average HOK cost of IDR 1,515,009/ha.
Meanwhile, outside family labour is IDR 1,087,333/ha. Seed Water Spinach farmers, in carrying out their farming, mostly use the power in the family itself because while they can do it themselves, they don't need to use other people's labour. Meanwhile, outside labour is used during the planting season and harvest season.

Classic Assumption Test
Normality test results using the One Sample Kolmogrow method. This method has a higher level of normality for the same data size (Purnomo, 2017). The data are said to be normally Multicollinearity does not occur if the VIF value is less than ten and the tolerance is more than 0.1. The evidence in Table 2 demonstrates that none of the independent variables exhibits multicollinearity symptoms.
The method used for this heteroscedasticity test is the Glejser test. Regression analysis performs the Glejser test between the independent variables and the residual absolute value (ABS_RES). In Table 3, the six independent variables have a significance > 0.05. Suppose the parameter coefficient values for the independent variables have a sig. > 0.05; the regression model does not have heteroscedasticity (Riyanto & Andhita, 2020).

Analysis of the Coub-Douglass Production Function
Regression analysis is required to ascertain the link between production parameters and the productivity of water spinach seeds. Table 4 displays the findings of the regression study of farming productivity in Sumurcinde Village. The Cobb-Douglass production function is a function with two or more variables, where the independent variable is referred to as the X variable and the dependent variable is represented by the letter Y (Imran & Indriani, 2022). The F-count value is 35.047, and a significance value of 0.00 <0.05 means, which means that there is a significant effect between all the independent variables (seeds, phonska fertiliser, urea fertiliser, power grow fertiliser, pesticides, and labour) on the variable dependent (Seed Water Spinach production).
The coefficient of determination test shows how well the independent variables explain the results (multiple correlation coefficient). In Table 4, the value (R square) is 0.778. This means that the independent variables (seeds, phonska fertiliser, urea fertiliser, power grow fertiliser, pesticides, and labour) affect the dependent variable (Seed Water Spinach) is 77.8%. And the remaining 22.2% is influenced by other variables not observed in this study.
Based on the regression analysis performed, the following equation is obtained: LnY = 2.510 + 0.055 X 1 +0.155 X 2 + 0.003 X 3 + 0.576 X 4 -0.076 X 5 + 0.334 X 6 (4) The regression analysis's findings are significant if the value is more than 0.05 (0.816 > 0.05). The production of Seed Water Spinach is thus not significantly impacted by the seed variable. In this case, the use of inappropriate seed varieties will result in the production of Seed Water Spinach not being optimal (Hartina et al., 2018). The seeds will grow normally if they are in a good environment. Both from the place of germination, water source, light, humidity and temperature with a regression coefficient value of 0.055, the seed variable shows a positive link with the production of Seed Water Spinach. This indicates that each additional seed of one percent will increase output by 0.055%, assuming other variables that are not observed are considered fixed.
Based on the results of the regression study, the phonska fertiliser variable has no apparent effect on the growth of Seed Water Spinach. As shown (0.416 > 0.05 ), the significance value is higher than the α value. Fertilisation is one way to improve the quality of vegetables by fulfilling the nutrients these plants need. Fertilisation is done by adding substances unavailable or lacking in places where plants grow (Putra et al., 2022). Fertilisation is also done to grow and develop water spinach plants to increase maximum yields. However, these Seed Water Spinach farmers use Phonska fertiliser only as a complementary fertiliser. Like the research done (Siswanti et al., 2016) in their study, farmers only use Phonska fertiliser in small quantities because it is only a complement to urea fertiliser. The regression coefficient for the phonska fertiliser variable is 0.155, indicating a positive association. This means that every one percent addition of Phonska fertiliser will increase production by 0.155% and vice versa.
Urea fertiliser contains 46% Nitrogen (N) that farmers commonly use to fertilise vegetables, including Seed Water Spinach. For plants to create amino acid molecules that can be turned into protein, nitrogen is required. Nitrogen is also needed to form chlorophyll, enzymes and nucleic acids. Therefore, nitrogen is required in large quantities during the vegetative growth stage of plants, especially Seed Water Spinach. Using urea fertiliser for water, spinach farmers use quite a large amount. However, the fertiliser is not absorbed optimally because the land is dry during the dry season. Seed water spinach production was not affected by urea fertiliser. As shown (0.985 > 0.05), the significance value is higher than the α value. The urea fertiliser variable has a regression coefficient value of 0.003. This signifies the positive correlation between urea fertiliser and water spinach seed production. It's the same with research (Rarasati & Prihtanti, 2020), which states urea fertiliser has no significant effect on land Seed Water Spinach production risk.
The power growth fertiliser variable impacts seed water spinach production. The significance value is less than (0.024 < 0.05) in weight. This is because power grows fertiliser is liquid so plants can absorb it more optimally. Powergrow fertiliser has a regression coefficient value of 0.576, which means that the correlation with the production of Seed Water Spinach is positive. Adding one percent of power grow fertiliser will increase production yields by 0.576% with other assumptions considered constant.
Water spinach seed production was not affected by pesticide variables. In Table 4, the significant value (0.619 > 0.05) is greater than the α value. The regression coefficient value of the pesticide variable is -0.076, which means that the correlation between the pesticide variable and the production of Seed Water Spinach is negative. This means that if there is an addition of one percent of pesticides, it will cause a decrease in output by 0.076 and vice versa. If there is a one percent reduction in pesticides, it will increase production by 0.076%. Pesticides, if used in the wrong dosage, happen because pesticides contain dangerous chemicals. Using pesticides not in the proper dosage will damage natural resources, cause soil, water, and air pollution and the danger of poisoning (Irfan, 2016).
Considering the analysis, Seed water spinach production is unaffected by the labour variable. This opinion does not align with (Mufriantie & Feriady, 2014), which stated that labour affected Seed eISSN: 2656-4270 Water Spinach production. In a farming business, all the work carried out during the production process up to the harvest must be considered by women, men and children. Factors include age, farming experience, the number of workers, and the wages determining the amount of work outpouring (Salim et al., 2019). The significance value is smaller than the value of α (0.052 > 0.05). Farmers are less intensive in processing and maintaining Seed Water Spinach. The association between labour and the production of kale seeds is positive, as indicated by a regression coefficient of 0.334. This means that if there is an addition of one percent of the workforce, it will increase production by 0.334, and vice versa.

Allocative Efficiency Analysis
Water spinach seed farming production factors can be known for their efficiency level using an allocative efficiency test. Table 5 below shows the findings of the allocative efficiency analysis of the utilisation of production factors for cultivating Seed Water Spinach.  Table 5 shows that the NPMxi/Px value is 3.1, which means that the NPMxi/Px value is greater than 1 (3.1 > 1). Therefore, the use of Power Grow fertiliser is inefficient. Seed Water, Spinach farmers use power grow fertiliser to provide nutrients to the leaves of Seed Water Spinach. The nutrient content in the foliar fertiliser results in better vegetative growth because the foliar fertiliser contains N nutrients which can increase leaf growth and photosynthetic activity. The use of powergrow fertiliser in water spinach farmers are still lacking, so it is necessary to increase the use of power-grow fertiliser to get maximum production of Seed Water Spinach.

CONCLUSIONS AND SUGGESTIONS :
Overall, the observed variables (seed, phonska fertiliser, urea fertiliser, power grow fertiliser, pesticides, and labour) significantly affect the production of Seed Water Spinach. Meanwhile, partially the variables of seed, phonska fertiliser, urea fertiliser, pesticides, and work did not have a significant effect on the production of Seed Water Spinach. In contrast, the power growth fertiliser variable significantly affects the output of Seed Water Spinach. Using power grow fertiliser production factors in Seed Water Spinach farming of 105.8 per farm is still inefficient. Farmers can optimise production factors (seeds, phonska fertiliser, urea fertiliser, power grow fertiliser, pesticides, labour) in water spinach seed farming so that the resulting product can increase and increase farmers' income. The production of Seed Water Spinach will increase if the use of power grows fertiliser is raised again and still considering other factors such as pest control so that the farming of Seed Water Spinach carried out by farmers in Sumurcinde Village will increase.