Technical, Economic, and Allocative Efficiency of Corn Farming In South Lampung Regency

South Lampung Regency is the center of corn production in Lampung Province. However, the low productivity of corn due to the suboptimal allocation of production factors has affected the efficiency of corn farming production. This research aims to analyze the level of technical, allocative, and economical efficiency corn farming in South Lampung Regency


INTRODUCTION
Increasing of broiler farming business has triggered an increase in animal feed industry activities. The raw material for the animal feed industry is corn. The total use of corn for animal feed industry activities in 2012 was 4.32 million tons and increased to 5.22 million tons in 2016 (Kementerian Pertanian, 2017). This shows that corn farming has prospects for continuous development, considering that corn has a fixed market.

RESEARCH METHODS
The study used a survey methodology. South Lampung Regency served as the site of this study's research. A purposeful selection was made for the research region, taking into mind that South Lampung Regency is one of the major hubs for corn production in Lampung Province.  Table 1 shows that Ketapang District and Penengahan District are the primary corn-producing subdistricts in South Lampung Regency. Therefore, this research was conducted in Ketapang District and Penengahan District , which are assumed to represent South Lampung Regency. The object of research is corn farmers who cultivate corn on dry land at the research location. The number of samples 71 peoples. Sample are selected by simple random sampling method. The information gathered for this study is both primary and secondary. Primary data was obtained using a survey method, namely by directly interviewing corn farmers using a list of questions (a questionnaire) that has been provided. Secondary data were obtained from institutions or agencies related to this research. The stochastic frontier Cobb-Douglas production function and the dual cost function from the homogeneous Cobb-Douglas production function are employed in the analytical method to address the study objectives.
Technical Efficiency and Inefficiency Analysis. The stochastic frontier Cobb-Douglas production function is used to study factors that affect corn output, technical efficiency, and factors that cause technical inefficiency. This function is used to determine the potential production of each farmer. The Cobb-Douglas Stochastic Frontier production function is converted to the following natural logarithmic linear form (Fadwiwati et al., 2014), then processed using the Frontier 4.1 program. : LnY = ln β0 + β1 ln X1 + β2 ln X2 + β3 ln X3 + β4 ln X4 + β5 ln X5 + β6 ln X6 + β7 ln X7 + vi -ui ........ (3) Description : Y = actual production of dry shelled corn (kg) X1 = land area (ha) X2 = number of seeds (kg) X3 = amount of N (kg)  Element N is calculated from the use of NPK and Urea fertilizers. X4 = amount of P (kg)  Element P is calculated from the use of NPK an SP-36 fertilizers. X5 = amount of K (kg)  Element P is calculated from the use of NPK fertilizers. X6 = pesticide amount (gba) herbicides and insecticides X 7 = labor (HKP) 1 HKP = 7 hours of work/day vi = unpredictable variables associated with environmental elements like weather, pests, and illnesses, as well as modeling flaws. ui = random variable is non negative and is assumed to affect the level of technical inefficiency and is related to internal factors. β0 = constant β j = regression parameter/coefficient, j = 1,2,3,4,5,6, dan 7.
The expected parameter/coefficient value is positive, namely j > 0, because the addition of input will increase corn production. Measurement of the level of technical efficiency of corn farming using the following formula: The technical efficiency value is between 0 ≤ ET ≤ 1.
Technical efficiency is only utilized for functions that have a specific number of outputs and inputs, and its value is inversely proportional to the value of the effect of technical inefficiency Coelli (1996) dalam Rohi, (2018) and Ismail et al., (2017). The effect of technical inefficiency is measured by the variable Ui, which has a normal distribution with N values and is considered to be independent. To determine the distribution parameter value (Ui ) of the effect of technical inefficiency, the following formula is used: = farmer's age (years) Z2 = number of family members (person) Z3 = dummy participation in counseling (1 = attending counseling, 0 = not participating in counseling) Z4 = credit access dummy (1 = have access to credit, 0 = do not have access to credit) Expected parameter/coefficient values : δ1 > 0, δ2, δ3 δ4 < 0. A positive coefficient indicates that this factor increases the technical inefficiency of farming. If the coefficient is negative, it indicates that this factor reduces the level of technical efficiency.
Allocative and Economic Efficiency Analysis. The dual cost function is derived from the homogeneous Cobb-Douglas production function to measure allocative efficiency and economy. This method has been used in several studies, there is Nursan (2016); Rohi (2018); Chiona et al. (2014); dan Abdulai et al. (2015). The Cobb-Douglas production function uses the following two inputs: The dual cost function is derived with the assumption of cost minimization with output constraints Y = The dual cost function must be obtained from the value of the expansion path (expansion of business scale) through the langrange function as follows: To obtain the values for X1 and X2 expansion paths, the langrange function is derived from the first order condition as follows: The ratio of the observed minimum total production costs (C*) to the actual total production costs (C) is what is known as the economic efficiency, and this is how the equation looks: Allocative efficiency (EA) of farming per individual is obtained from technical efficiency and economic efficiency as follows:

RESULTS AND DISCUSSION
Characteristics of Respondents. Table 1 describe that most of the farmers are of productive age (23-44 years), but the majority of their education is elementary school graduates. Most of the farmers' experience in corn farming is not too long, which is < 12 years. This shows that the knowledge and skills of farmers in corn farming are not very good. The agricultural family's number of dependents is not excessive. Mostly 3-4 people per family, so the burden of spending for family needs is not too big. The majority of the land used by farmers to grow corn is in the range of 0.25 to 1.17 ha. The area of land to cultivate corn depends on the amount of capital owned by the farmer and the land available for planting. Use of Corn Farming Input. According to Table 2, farmers do not use seeds in accordance with the suggested rate of 20 kg/ha. This is due to the high price of corn seeds. The average price of corn seeds reaches IDR 88,380.28 per kilogram. Urea fertilizer should be used at a rate of 250 kg per hectare, but farmers often use it at a rate of 544.48 kg per hectare. The use of Urea fertilizer is far above the recommendation because Urea fertilizer is a subsidized fertilizer so the price is the cheapest. In addition, farmers consider the use of Urea fertilizer to be very good for corn plants, because corn plants are greener. The use of SP-36 fertilizer is also excessive, that is as much as 243.53 kg/ha, even though the recommendation is 100 kg/ha. However, the use of NPK fertilizer is still less at 206.31 kg/ha compared to the recommended 250 kg/ha. Lack of use of NPK fertilizers causes corn plants to lack K elements, even though K plays a role in improving the quality of corn seeds.

Estimating the Stochastic Frontier Production Function of Cobb-Douglas. The South
Lampung Regency corn farming production function model has seven inputs: land area, number of seeds, quantity of element N, quantity of element P, quantity of element K, quantity of pesticide, and quantity of labor. Element N comes from Urea and NPK fertilizers, where the N content in Urea fertilizer is 46% and the N content in NPK fertilizer is 15%. Element P were obtained from SP-36 fertilizer and NPK fertilizer, where the SP-36 fertilizer content was 36% and the P content in NPK fertilizer was 15%. Element K comes from NPK fertilizer, where the K content in NPK fertilizer is 15%. Calculation of the amount of element N used by each farmer was obtained from the use of Urea and NPK fertilizers per farmer. Element N from Urea fertilizer is 46% of the average use of Urea fertilizer per farmer, while the amount of element N from NPK fertilizer is 15% of the average use of NPK fertilizer per farmer. The calculation of the amount of element P used by each farmer is 36% of the average use of SP-36 fertilizer per farmer, while the P amount of NPK fertilizer is 15% of the average use of NPK fertilizer per farmer. The total use of P fertilizer per farmer is element P from SP-36 fertilizer plus element P from NPK fertilizer. Calculation of the amount of element K used by each farmer is 15% of the average use of NPK fertilizer. Estimating the Stochastic Frontier Cobb-Douglas production function model using the Maximum Likelihood Estimator (MLE) method with the help of the Frontier 4.1 program. The results of the approximation of the Stochastic Frontier production function are presented in Table 3. The significant of the effect of each variable is based on two levels of significant, namely the 1% and 5% significant levels. The use of these two levels of significant shows that a variable with a significant level of 1% is more influential than a variable with a significant level of 5%.
According to Table 3, the gamma value of 0.97 has a considerable impact with a 99% significance level. which means that 97.6% of the variation in production between farmers is caused by differences in technical efficiency, while the remaining 2.4% is due to stochastic effects that are out of the model, there is: climate influence, natural disasters, pests and plant diseases, and others. This study has a gamma value that is smaller than the research of Sahara et al., (2019) on corn farming in Kendal Regency that is 0.99, but it is greater than the gamma value in Rohi (2018) research on corn farming in East Kupang District, Kupang Regency which is equal to 0.68. The value of the Generalized Likelihood Ratio (LR) in the stochastic frontier corn production model is 19,179. Compared to the Code and Palm tables, this value is higher, which is 11.91 which is significant at = 5%. This demonstrates the effects of farming's technical efficiency and inefficiency. LR Test 19,179**** Description : *** Significant level with α = 1% (t tabel = 2,66028) ** Significant level with α = 5% (t tabel = 2,00030) Land area (X1) has a significant effect with significant level 95% and a coefficient value of 0.249. If the land area is added by 1%, it will increase corn production by 0.249%. This is in accordance with research by Nursan (2016) Abdulai et al. (2015), that land area has a positive effect on corn production. Thus corn production can be increased by escalate the area of arable land for corn farming.
The number of seeds (X2) has a significant effect with significant level 95%, and the coefficient value is 0.373. This shows that, increasing the number of seeds by 1% will increasing corn production by 0.373 %. These results are in accordance to research by Situmorang et al. (2020) 2019), that corn output is positively impacted by the amount of seeds. The recommended use of corn seed is 20 kg/ha (Paeru & Dewi, 2017), but the average use of seed by farmers is 17.46 kg/ha. Increasing the use of corn seeds in appropriate with the recommended dose can increase corn production at the research site. The use of corn seeds which is still below the recommendation is due to the high price of corn seeds, with an average price of around Rp. 98,486.49 per kilogram.
Element K (X5) is significantly influential, with a significant level of 99% and a coefficient value of 0.014. If the amount of element K is increased by 1%, it will increase corn production by 0.014%. Increasing element K by using NPK fertilizer (K content 15%) The average use of kalium (K) elements by farmers is 30.95 kg/ha, while the recommended K element is 37.5 kg/ha. The function of element K is to improve the quality of crop yields, increase plant resistance to pests, diseases, and drought, facilitate photosynthesis, and harden plant stems. The highest K element is found in KCl fertilizer, which is as much as 60%. However, KCl fertilizer is not subsidized, so farmers prefer to use NPK fertilizer, which contains small amounts of K elements (15%).
The number of workers (X8) has significantly influential with significant level of 99%, with a coefficient value of 0.392. If the use of labor is added by 1%, it will increase corn production by 0.392 %. This is in appropriate with the research of  (2016). The addition of labor can be done in soil processing activities. The majority of farmers in the research location carry out farming activities without tillage. Farming without tillage is carried out because tillage activities require a lot of labor, so it will increase labor costs if tillage is done manually. The use of agricultural machinery such as plows and tractors has not been evenly distributed, because the number of plows and tractors owned by farmer groups is limited, so farmers must take turns to use them.
The estimation of the Stochastic Frontier production function indicate that optimal land use is required. The use of seeds and K elements in accordance with the recommendations is expected to increase corn production. In addition, it is necessary to optimize the use of labor for land management activities so that the land is ready to be planted and can provide maximum results.

Corn Farming Technical Efficiency and Inefficiency. Technical efficiency in this research was
analyzed by using the Cobb-Douglas Stochastic Frontier production function, namely by using the Maximum Likelihood Estimate (MLE) estimation method, with Frontier 4.1 program. The distribution of technical efficiency is divided into 3 categories based on the area of arable land, namely narrow, medium and large land.  Table 4 shows that the technical efficiency's average level on medium land is the lowest, while the highest average technical efficiency on narrow land is 0.84 which exceeds the overall average technical efficiency. So there is a tendency that the narrower the corn farming area, the more efficient it will be technically, because the production factors uses is not too much, so it is still within the limits of the ability of farmers to provide production factors. The value of the technical efficiency ranges from 0.36 -0.96, with an average of 0.82. The average technical efficiency > 0.70 indicates that most of the corn farming has been technically efficient. So corn farming in South Lampung Regency can increase technical efficiency at the level of technology and existing inputs by 15% (1-0.82/0.96). The achievement of different levels of technical efficiency in each farmer shows the level of mastery and application of technology that differs between farmers. Based on Table 5, the coefficient of farmer age, participation in extension, and dummy access to credit are positive and the factor coefficient of the number of family members is negative. The age of the farmer and the number of family members have a 95% significant impact on the inefficiency of maize growing. The farmer's age factor has a positive effect, meaning that the older the farmer, the higher the inefficiency of corn farming. This is related to the physical ability of farmers which decreases with age. Deteriorating physical conditions can increase the use of labor outside the family, so that it will increase the cost of farming. This is in accordance to the research by Sahara et al. (2019), on corn farmers in Kendal Regency and research by Chiona et al. (2014) on corn farming in the Central Province of Zambia, which states that the farmer age variable has a positive effect on corn farming inefficiency. The factor of the number of family members has a negative effect on the inefficiency of corn farming, meaning that farmers who have more family members will decrease the level of technical inefficiency or increase the technical efficiency of corn farming. Corn farming activities require a lot of labor, because of the many activities that must be carried out from planting preparation to harvesting. The large number of family members can be used to help corn farming activities. The use of labor in the family will reduce the cost of farming corn. This is in accordance with the research of Anggraini et al. (2016) regarding the efficiency of cassava farming production in Central Lampung Regency, Yoko et al. (2017) regarding the efficiency of rice farming production in Central Lampung Regency, and Sihlongonyane et al. (2014) on the economic efficiency of corn farming.

Economic Efficiency and Allocative Efficiency of Corn Farming. Allocative and economical
efficiency were analyzed from the input side using input prices prevailing at the farm level, by deriving the stochastic frontier production function by using equation (17) Table 6.  Table 6 shows that the average economic efficiency of corn farming is 0.22 with the value of economic efficiency in the range of 0.20 -0.34. If farmers want to get maximum economic efficiency, they must save costs by (1-0.22/0.34 ) which is 35 percent. The value of economic efficiency based on land area shows that narrow land area has a higher average value of economic efficiency compared to narrow land and medium land. This is because the ability of farmers to reduce farm production costs is higher than farmers with larger lands. Narrow land area will make it easier for farmers to manage land, where farming on narrow land does not require too much labor, so farmers can maximize the use of labor in the family. In addition to saving on the use of labor, farmers can save on the use of herbicides. Narrow land makes it easier for farmers to control weed growth, weeds can be eradicated manually by hoeing. Based on the average value of the overall economic efficiency, which is 0.70, it can be seen that corn farming in South Lampung Regency is not yet economically efficient. The cause of the economic inefficiency is that corn farming requires a large amount of labor, seeds, and fertilizers, while the price of seeds and labor is quite high. The fertilizer subsidy policy was able to reduce the production costs of corn farming (Lestari et al., 2020), but resulted in the application of fertilizers outside of the recommended dosage.. In addition, the unstable price of corn causes the income of corn farmers to be uncertain. Based on Table 7, the level of allocative efficiency of corn farming is quite low, with an average of 0.28. If farmers want to get maximum allocative efficiency, they must save costs by (1-(0.28/0.59)x100), which is 53 percent. Based on the area of land, the average allocative efficiency on narrow land is the same as the average allocative efficiency of all respondent farmers. The average allocative efficiency on medium land was 7.1 percent higher than the average allocative efficiency for all respondent farmers. The average allocative efficiency on a large area of land is 3.6 percent lower than the average allocative efficiency of all respondent farmers. Farming on large land has the smallest average allocative efficiency, because the wider the area that cultivated, the more inputs are used, while farmers have not been able to allocate inputs by paying attention to the prices of the inputs themselves, not based on needs or recommendations. All respondent farmers have an allocative efficiency value of 0.70, which indicates that corn farming in South Lampung Regency is not allocatively efficient. Farmers use inputs while still paying attention to the prices of the inputs themselves. This can be caused by the low purchasing power of farmers, because farmers have to wait long enough to start farming in the first planting season (MT-I). The waiting period for planting is long enough that the income that farmers have from harvests in the previous II (MT-II) planting season has been used by farmers to meet their daily needs. So that when starting planting in the next growing season, farmers lack farming capital. As a result, there is excessive use of inputs that have low prices, namely Urea and SP-36 fertilizer, where the use of Urea fertilizer is 544.48 kg per hectare of land and the use of SP-36 fertilizer is 243.53 kg per hectare. Meanwhile, the recommendation for the use of Urea fertilizer by field extension officers in South Lampung Regency is 250 kg per hectare of land and for SP-36 fertilizer as much as 100 kg per hectare. The excessive use of Urea and SP-36 fertilizer is the effect of the subsidized price of Urea Fertilizer and SP-36 fertilizer which is cheaper than other fertilizers, so farmers use Urea fertilizer and SP-36 fertilizer in higher quantities. In addition to excessive use of fertilizers. The use of NPK fertilizer is less than the recommended amount, which is 206.31 kg per hectare, while the recommended use of NPK fertilizer is 250 kg per hectare. The existence of subsidy policies can have both negative and positive effects on farming activities. According to Lestari et al., (2022), the elimination of fertilizer subsidies is still able to provide benefits to corn farming, but the selling price of corn remains stable. The increase in allocative efficiency caused by farmers focusing on input prices is by using inputs as recommended, so that there is no excessive or insufficient use of inputs. This situation will increase the efficiency of the use of farming capital.

CONCLUSION
Land area, number of seeds, quantity of K elements, and labor force are inputs that significantly influence corn production in South Lampung Regency. Corn farming in South Lampung Regency is technically efficient; the average level of technical efficiency is 82%. Factors that can reduce the level of technical efficiency at the research location are the age of the farmer and the number of family members. However, corn farming is not efficient either economically or allocatively. The average level of economic efficiency is 22%, while the average level of allocative efficiency is 28%. The low level of economic and allocative efficiency is due to the high price of corn cultivation inputs, so farmers have not allocated inputs according to the recommended dosage.
Farmers are expected to use fertilizers in accordance with the recommendations or recommended doses, namely 250 kg of urea per hectare, SP-36 fertilizer of 100 kg per hectare and 250 kg of NPK fertilizer per hectare. The use of fertilizers according to the recommended dose can reduce farming costs and can increasing the efficiency of corn farming production in South Lampung Regency. Income certainty will encourage farmers to use inputs appropriately and efficiently. The use of inputs appropriately and efficiently will reduce the use of excessive inputs to be allocated to other inputs that are less used, with the aim of achieving allocative and economic efficiency.