1. INTRODUCTION
Agricultural commercialisation is a process of alteration in agricultural characteristics. As a process, it is restricted to not only cashtraded commodities but is an effort to develop agricultural production systems in the process of transforming subsistence agriculture into commercial agriculture (von Braun, 1995;Saparita, 2005;Woldeyohanes et al., 2017;Evertsson N., 2012). The process of commercialising subsistence agriculture can be divided into two parts. Firstly, from the production input side, for example through the increase of purchase and use of input. Secondly, from the production output side, such as by obtaining marketed surplus with higher marketing margins. Therefore, it can be concluded that the commercialisation of agriculture is limited not only to a cash crop but more functionally to the development and expansion of agricultural activities towards commercial agriculture.
Commercialisation aims to increase the income of smallholder farmers assuming there is a surplus of agricultural production from the basic consumption needs of farmers. This advantage can be achieved if the area of agricultural land is sufficient for farmers. It is an indicator of agriculture commercialisation shifting from subsistence level to commercial agriculture. In line with this argument, several studies have been conducted (Witherup and Verrecchia, 2019;Awotide et al., 2016;Abdullah et al., 2019;Carletto et al., 2017;Kopackova and Libalova, 2019;Witherup and Verrecchia, 2019). The approaches used to investigate commercialisation in previous studies are varied, but most focus on one aspect, such as input or output. Figure 1 shows the theoretical framework adapted from Abdullah et al. (2019), von Braun (1995), Matenga and Hichaambwa (2017), Rahman (2003), and Tirkaso (2013). The novelty in this study concerns our method for analysing commercialisation that uses a duality method through values of production efficiency. The analysis of the role of institutions and government in the production process of rice input and output policies could be increasing cost efficiency and selling prices of rice at the level of farmers and retail traders.
2. THEORETICAL MODEL
The theoretical model used in the study is neoclassical and assumes the CobbDouglas production model, which can be described as follows (Kumbhakar and Lovell, 2004;Saada and Suifan, 2020):
In Equation (1), q denotes rice production, x_{ji} stands for rice production input, i.e. labour (x_{1}), processing machinery (x_{2}), harvested area (x_{3}), seeds (x_{4}), fertiliser (x_{5}) and pesticide (x_{6}). β_{ij} = regression coefficient, i≠j dani=1, 2,…6 .
2.1 CostMinimising Model
For examining the research objective, the three equations are solved using the optimal cost model. This model is derived from the CobbDouglas production function. Production function consists of inputs x_{ji}, and input prices are w_{i,j}. Following Yi and Reardon (2015), the first order of the Langrangian Equation (3) can be written as follows:
Based on the constraint and the objective function, the equation for the conditional input demand for inputs i, j can be derived as follows:
Substituting the two conditional equations input demand into objective functions and dividing the input prices (w_{ij}) with the rice price p, hence the optimal cost equation is obtained. The stochastic frontier model is derived by adding the compound error term u_{i} −v_{i} where i=1,…, n and u_{i} are nonnegative disturbances associated with technical inefficiencies, while v_{i} is the white noise. Hence, the optimal cost frontier model can be written as follows:
The optimal cost stochastic frontier or cost frontier model states that the error term ε = v−u is composed of two components that are independent of one another that indicate the level of inefficiency, if u≥0 indicates technical efficiency (Aigner et al., 1977;Meeusen and van Den Broeck, 1977;Jondrow et al., 1982;Coelli et al., 2005;Shayakhmetova and Chaklikova, 2018). The cost frontier model is estimated in the form of nonlinear specification. Theoretically, the cost function is not linear (see: MasCollel et al., 1995) due to the use of the input price ratio data to the output price. The model estimation has been carried out by Farsi et al. (2005) and Filippini and Greene (2016). For analysing the estimated parameters, it is necessary to calculate the elasticity of each parameter produced, because the results of nonlinear parameter estimation that cannot directly be interpreted as elasticity, different profit frontier models and supply frontiers in this study are estimated in linear form. Elasticity is evaluated using the marginal effect approach (Greene, 2012;Shahbakhsh et al., 2019).
2.2 Profit Maximising Model
The cost function model minimises the costs of rice production factors. Accordingly, this model emphasises production input. The profit function is used to analyse the output side. This maximum profit model answers the second research objective, that is, to analyse the level of profit of rice farmers in Indonesia. It is derived in Equation (10).
By inserting the cost and profit equations into Equation (10), indirect profit is obtained $\pi ({w}_{ij},\hspace{0.17em}p)$. Then, the model is transformed into natural logarithms and algebraic manipulations by multiplying by (pq)^{−1} and adding the compound error term component ${u}_{i}{v}_{i}$ so that the profit frontier model to be estimated is:
2.3 Supply and Farmer Surplus
The supply model used to examine welfare of farmers can be derived from the maximum profit process and minimum costs, with the assumption of MC ≤ P and using cost equations (9) then the farmers’ rice supply function is obtained as follows:
By integrating Equation (12), we obtain a surplus model of farmers to show the level of welfare of farmers from different rice prices and policies issued by government institutions.
where:

p = dry unhusked rice (GKG) prices at the farm level

p = dry unhusked rice prices on average at the mill level and government purchase prices.
It is assumed that w_{ij} constant, so the integral solution is written in Equation (14):
3. METHODOLOGY
The analytical model used in the study is the Stochastic Frontier Analysis Model. This model is used to measure inefficiency (Coelli et al., 2005). In this case, it is used to analyse inefficiency of rice production as an indicator of the commercialisation of agriculture. By utilising crosssection data from farmer households in Indonesia, this study assumes rice farmer production in the form of the CobbDouglas production function in Equation 1 (Coelli et al., 2005;Mercadier et al., 2016;Greene, 1982). The three stochastic frontier models were estimated using the Ordinary Least Square Estimation (OLSE) and Maximum Likelihood Estimation (MLE) methods. Residuals σ_{v} and σ_{u} are instruments to detect production inefficiency and calculate the ratio of the two error components, so it can be expressed as lambda value or $\lambda ={\sigma}_{v}/{\sigma}_{u}$ (Coelli et al., 2005;Seok et al., 2018).
In the second step, after the minimum cost function is obtained, the profit function estimation is carried out using the same estimation method to analyse the profitability of farmers. If both technical inefficiencies occur with the farmer, it indicates the low commercialisation of farmers and vice versa. The final step is to analyse the level of farmers’ welfare. The analytical method is used by considering the price variable, i.e. the price change (Δp) of the transaction price between the farmer and the buyer with the average market price (p) as welfare realisation. The method for looking at the commercialisation of the supply side of rice and its impact on the welfare of farmer households is to analyse the difference in market prices with farmer transaction prices. If the estimated result has a positive sign, it indicates that a farmer surplus occurs. In other words, paddy has shown a positive direction, or there has been commercialisation to benefit from any amount of rice or grain produced by farmer households in Indonesia and vice versa. Accordingly, based on this perspective, the welfare of farmers will be analysed.
4. RESULTS AND DISCUSSION
The estimation of the cost frontier model shows that the processing machinery component is not statistically significant other than the explanatory variables that determine the variation in the optimal cost structure of rice production with the significance level of 1%. The estimation results in Table 1 indicate that an important component of the SFA (Suitability, acceptability, feasibility) model is two error terms v_{i} and u_{i} which have their respective variants. ${\sigma}_{u}^{2}$ is an error distribution term inefficiency based on the estimation results showing normally distributed with a 1% significance level and ${\sigma}_{v}^{2}$ the distribution of error term components which are interpreted as white noise, such as technological issues and others. The estimation results show that this v_{i} is also normal in terms of both significance at the level of 1% (Figures 2 and 3).
Unlike the cost frontier, the estimated profit frontier is in the linear double log. The coefficient sign expectation for production input is negative where an increase in input prices will reduce optimal profit which can be achieved by farmers, while the explanatory variable of rice prices at the household level is expected to be positive. Overall, the estimation of profit frontier shows that all variables that explain variations in optimal profits changes are inelastic, where the coefficient is < 1. The variables that most influence the optimal profit of farmer households is the rice price at the farm level; if the rice price increases by 10% at the farm level, it will increase the farmer’s optimal household profit by 8%.
The ratio σ_{v} to σ_{u} is 1.7727, which shows technical inefficiency from the optimal profit potential of rice production caused by a random component of white noise such as technology. In other words, the optimal potential profit from reduced rice production due to the technical inefficiency of rice farmers is significant at the level of 1%. This can be explained that the effect of green revolution such as the discovery of superior seeds and the use of nonorganic fertilisers was the result of a green revolution in the late 1960s which reduced the quality of land by the use of nonorganic inputs. Also doubts the continuity of agricultural management that adopts nonorganic technology that shows the symptoms of the law of diminishing returns on nonenvironmentally friendly agricultural management.
The estimation results of the profit frontier are found only as processing machines as part of the positive production inputs. However, as explained earlier, the positive sign shows that the increase in the price of processing machinery by 10% will increase the farmer‘s household profit by 0.4 with the significance level of 1%. In contrast to Rahman (2003) from the descriptions of the data obtained where BPS survey data also estimate the price of processing machines such as tractors, rice threshing as the price of the rent of the machine itself. This positive sign can be attributed to farmers’ households contributing to rent payment processing machinery to increase the income of the households of rice farmers or farmer groups. The novelty of this study is contributing theoretically and methodologically from the approach to estimating the optimal function of profits for farmer households.
Also, the wage rate has a positive effect on the optimal income of rice farm households with the significance level of 1%. Experiencing the same thing with processing machinery, different sign coefficients should be negative based on theory. However, it can be explained that this condition is a characteristic of subsistence agriculture carried out by the farmers themselves. Therefore, every 10% of the increase in the wages of workers, the head of the farmer’s household will increase profits by 0.1523. However, the participation of unpaid workers indicates the low level of commercialisation of the rice subsector that agricultural transformation from subsistence is a condition of commercialisation (von Braun, 1995;Deluchey and Dos Santos, 2018). This was proposed by Saparita (2005) in its projections about the commercialisation of agriculture in Indonesia until 2050 on the importance of subsistence transformation to modern agriculture.
In view of this, another empirical finding as well as novelty from this study is that processing machines and the wage rates of farmer workers turned out to have a positive effect on the composition of optimal farmer household’s profits but had a different impact on the degree of commercialisation of agriculture, especially in the rice subsector. Processing machinery has the potential to improve commercialisation while the wage rates of agricultural workers diminish the degree of commercialisation of rice agriculture in Indonesia. The estimation results of Equation (13), as shown in Table 1 are estimated in linear specifications. The price of rice, which is the main component, indicates that the estimated results are theoretically and statistically consistent. Overall, the estimated results of the supply frontier model test used by the Wald test results χ^{2} denote that this model is quite robust in explaining the various changes in the rice supply inefficiency with the significance level of 1%.
The estimated value of the ratio σ_{u} to σ_{v} is 1.7727, indicating technical inefficiency in the supply of rice. Because the ratio is greater than one, it shows σ_{v} > σ_{u}. It means that the random component of white noise that is above the frontier regression line is due to technological factors, the level of knowledge and experience of farmers that cause technical inefficiencies in the supply of the households of rice farmers. The inefficiency factor in the supply of rice is 0.6208, meaning that the potential for reduced rice supply is 62.08% due to technical inefficiencies of rice farmers. In the supply analysis, the price issue is one of the important components in explaining variations in changes in rice supply, besides infrastructure facilities such as distribution channels, transportation and several other components. The results of the supply frontier estimation indicate that the loss from profits that should be received by farmers or deadweight loss from the impact of price changes each year in the period from 2014 to 2017 has a negative impact on the welfare of farmers. This condition implies that the impact tends to increase every year that additional farmers lose additional profits that should be received during that period.
The estimation results from the supply frontier model can be simulated using Equation (14) to develop conditions of the welfare of farmer households. The 2013 census data was utilised to estimate supply frontier parameters. It was exercised as an estimator to calculate variations in price changes before the census and after the agricultural census was carried out during the period from 2010 to 2017. In the next step, the price simulation component is divided into three simulation conditions, i.e. first, the farmer level price; second, the government purchase price (HPP); and finally, the price of the mill level. Prices at the farm level, with the price of milled rice or unhusked rice prevailing at that time IDR 3,547.00, the farmer’s surplus is positive. In other words, from each kilogram of the marketed rice, the benefits are received to the household farmers. However, compared to the government’s purchase price, the farmer’s surplus condition is below the government’s purchase price, so farmers should still be able to get 862.88 rupiahs from each grain sold. While the price at the milling price (GKG) that can be received by farmers is lower than that at the farm level or even far below the governments purchase price.
Initially, in 2010 and 2011, the price level at that time applied at various levels had a positive impact on the condition and welfare of farmer households. However, after 2013, the level of the welfare of farmers, which has been shown in the simulation results, decreased. Therefore, in 2015, the government issued Inpres No. 5 to overcome this problem by regulating and controlling the purchase price of milled dry grain. Price control policies through government purchase prices proved effective until 2017.
5. DISCUSSION AND CONCLUSIONS
The dualistic approach to analyse cost and profit inefficiency provide complementary research results. The cost frontier approach aims to minimise costs, and profit frontier aims to maximise profits. The supply frontier can obtain both, particularly to investigate the efficiency and price changes that have an impact on the welfare of farmer households. Both conjointly explain a connection, i.e. the processing engine variables that are not significant in estimating the cost frontier model but significant in the estimation of the profit frontier model which is also the novelty of this study. Likewise, the wages of agricultural workers contribute more significantly to profit compared to the optimal cost. Both of these represent the contribution of this research to the theoretical framework and the factors which influence profit and optimal costs in rice commercialisation.
The three models proved the technical inefficiencies caused by the elasticity coefficients of each production input. They were mostly inelastic indicating the input response to variations in changes in cost composition and optimal profit is not responsive. It is coupled with a stochastic error factor that causes inefficiencies that boost costs and reduce the profit of rice production from the rice subsector of farmer households. On the supply side, rice prices at the farm level are inelastic. It is consistent with the prevailing theoretical basis of supply. When viewed from the impact of each price change, the factor of price becomes an important determinant in determining changes in farmers’ and income; this indicates from the supply side that the determinant of prices at the farm level still does not reach commercialisation. It can still be increased by IDR 1,360.52 so that a farmer’s surplus can be attained.
Regarding the benefits of commercialisation based on our findings, the recommendations that can be given from this research are policy implications to authorised institutions and the development of theories and studies in agricultural economics along with the development of theories and implementation of the concept of commercialisation of agriculture in Indonesia. The commercialisation of the rice subsector at the level of farmer households needs to be improved. In terms of commodities in the form of stable rice prices through institutions at the farm level with double functions in terms of capital or financing and purchasing or distributing of rice production at the micro level, the increase in the use value of production factors utilisation can increase the income of farmer households in the rice subsector.
The role of farmer households is very important as an economic unit in achieving commercialisation, increasing efficiency, and economy of scale. It can be done with a note that there is a need for strong institutions in the rice subsector, especially in overcoming the problems in financing the production and marketing distribution of crops. The last recommendation that can be given is related to environmental issues to implement and review of longterm organic farming techniques through the development of local seeds, fertilisers, and several other production inputs, to obtain increased rice production in both quantity and quality of this national staple food source.