Assessment of Profit Efficiency for Spinach Production under Small-Scale Irrigated Agriculture in the Eastern Cape Province, South Africa

Improving profit efficiency in vegetable farming, especially for Spinach, is vital in enhancing income, livelihoods, and nutrition security and reducing the poverty of smallholder farmers, particularly in developing countries like South Africa. Despite the country’s potential, spinach production faces major challenges, including unreliable markets, low adoption of modern production systems, and production inefficiencies that affect farm returns. This has been attributed to a lack of adequate and reliable information to guide producers on measures for improving productivity through cost effective production systems and efficient market systems, eventually leading to profit inefficiency. Therefore, this study sought to assess the profit efficiency of smallholder spinach producers under irrigated agriculture in the Eastern Cape Province, South Africa. The study made use of multi-stratified sampling procedures to select 150 spinach producers under irrigation. The stochastic profit frontier function was applied to assess the profit efficiency of smallholder spinach farmers. The results indicated that most farmers operated in farm sizes of 3 ha with an average age of 48 years. The estimates of the stochastic profit frontier function showed that farm size, cost of fertilizer, seed, and pesticides increased profit while labour used decreased profit. Findings indicated a 10% profit loss due to a mixture of technical and allocative inefficiency in the production of spinach, while farmers were able to attain an average profit inefficiency of 90%. Moreover, findings revealed numerous factors that positively affected the profit efficiency of spinach farmers, including socioeconomic, institutional, and cultural. The study findings imply that profit efficiency can increase significantly through the use of high-quality fertilizer, seeds, and pesticides. The allocative efficiency results indicate that improvement in access to extension services, farmers’ level of education, and farm experience can result in the increased allocative efficiency of spinach farmers in the study site. The study further suggests that smallholder farmers must adopt innovative technology to enhance their agricultural productivity, and this is likely to improve household income and nutrition security. Thus, the study recommends that policymakers and government must invest in farmers’ education through effective extension delivery programs and the provision of credit to help farmers increase their profit efficiency.


Introduction
Spinach (spinacia olereracca) is a leafy vegetable rich in vitamins, and mostly grown during the cool weather of either Spring or Autumn (Fall) [1]. Spinach is a widely distributed and limits smallholder farmers' ability to advance the prospects that presently exist in the global food system [13]. Thus, an increase in production is viewed as a possible solution to high food prices and spinach shortage incidences. The afore-mentioned challenges can be addressed through improving technology usage, application of effective production methods, and efficiency of smallholder farmers producing spinach. Hence, studying profit efficiency and identifying the factors influencing profit efficiency is necessary to develop efficiency-enhancing processes targeting smallholder farmers. The factors affecting profit efficiency have indirectly influence the criteria for selecting development approaches and meeting Sustainable Development Goals (SDGs). Calculating efficiency is imperative since it could lead to sizable resource savings, which have important effects on the management of farms and the formulation of policies [4]. Efficiency measurement enables the identification of potential output increases given the existing technology.
The majority of smallholder farmers in the Eastern Cape province produce spinach for food consumption, which plays a vital role in improving their diets. Moreover, spinach production provides an economic incentive to smallholder farmers through income from sales. This means that smallholders also use spinach as their cash crop to improve their income and food security. The capability of spinach farmers to adopt new technology to accomplish long-lasting and efficient outputs solely depends on their level of profit margins, which in turn depends on input and output prices, and the cost of fixed factors of production. Other variables would operate to bring about changes in profit levels and efficiency in farms.
Determining these factors and the magnitude of their effects on farm-level profit efficiency establishes the practical questions this study sought to answer. However, there are no studies that have been carried out to measure either the profit or technical efficiency of spinach production in the Eastern Cape. Most studies conducted previously in South Africa and other countries, in general, focused exclusively on the technical efficiency of cereals [15,16] or economic efficiency of other food crops [17,18]. Profit efficiency is inclusive of all technical efficiency, allocative efficiency, and economic efficiency. None of these studies focused on analyzing the profit efficiency of spinach production in a smallholder farming system. The limitations of previous studies lie in the fact that they did not account for factors influencing the profitability and profit efficiency of smallholder farmers, and only assumed technical efficiency in terms of input use and production technology [2,16]. As a result, smallholder farmers have low productivity, resulting in very low incomes, because they rely on obsolute techniques for production. Farm productivity is low compared to the national average, which indicates the presence of farming inefficiency. There is low adoption of technologies among smallholder farmers, resulting in low annual yields and incomes. According to the literature, the profit efficiency of spinach farming is still insignificant and very little is known concerning whether smallholder spinach farmers are efficient or not in the Eastern Cape Province [13,14]. Additionally, smallholder farming faces several restrictions, such as a lack of access to production inputs and efficient produce markets. There is a wide gap in knowledge on the profit efficiency of smallholder spinach producers and it needs to be addressed. Determining the efficiency levels in each system can guide policy to develop targeted strategies on how to improve efficiency in spinach farming since blanket approaches may not yield the desired results. This study, therefore, focused on allocative efficiency, which looks at the ability of spinach farmers to produce the maximum possible output (technical efficiency) at the least possible cost (economic efficiency) [19]. The above boundaries make the study important because efficiency is assessed and studied for its actual and potential influence on profitability, competitiveness, and the factors affecting them. Therefore, this paper aimed to assess the profit efficiency of spinach among smallholder farmers in the Eastern Cape. An assessment of spinach profit efficiency is essential given that this crop is generally produced under intensive cropping system practices with high input costs. Moreover, vegetables are generally vulnerable to poor weather and climate conditions. Spinach also falls under the category of highly perishable products, requiring expensive storage facilities.

Conceptual Framework
Although productivity and efficiency are two contrasting concepts, these concepts fall under the assumption of a constant return to scale. Productivity is a ratio of production output that is needed or necessary to produce it (inputs) [20,21]. The measure of productivity is defined as a total output per one unit of total input. Productivity fluctuates depending on the scale of operation, functioning environment, production innovation, and operating efficiency [22]. On the other hand, efficiency is defined as the success achieved when a farm uses its resources to produce output [23]. In simpler terms, productivity is the measure of the productive efficiency of the farm. Agricultural productivity relies on how factors are efficiently used in the production process. As a result, efficiency is accomplished by either lessening the resources obligatory for producing a specified output or maximizing output produced from given resources. Thus, productivity and efficiency are directly correlated, which implies that to increase productivity means there must be an efficient use of resources to intensify agriculture as farmers increase the use of technology in production.
Consequently, through innovative production techniques, productivity will improve, resulting in increased farm returns and uplifting farmers' economic well-being. The use of innovative production techniques enables high output production from restricted resources, such as land preserved by farmers [24]. The main aim of promoting increased technical efficiency in the farm is to decrease the cost of production while enhancing farm yields. Given these sentiments, it is imperative to measure the levels of technical efficiency of farmers to assess the losses in production that are credited to inefficiency due to different factors, such as socio-economic characteristics, cultural norms, and management practices. Based on consumer production theory, farmers' inefficiency is influenced by countless factors, including technology, cultural norms, socioeconomic factors, policy, research, and institutional factors. Thus, it is necessary to understand these factors as efficiency is imperative in fast-tracking SDGs, especially the first objective, which focuses on eradicating all forms of poverty and malnutrition.
Farmers are faced with the challenge of producing more food to meet the growing population, especially in developing countries. The efficiency of input conversion is not only dependent on the number of resources used, but also on production systems adopted by farmers, farms, and farmer characteristics [14]. However, farming is challenged by many factors, such as weather conditions, cultural norms, lack of innovation, and transaction costs, which affect the efficiency of farmers. The efficient use of resources by farmers is the only solution that farmers can use to improve their productivity and enhance farm returns. Farmers intend to attain efficient markets, and farmers pursue an expanded market system that enables them to diversify and discover numerous markets as a measure of reducing risks, uncertainties, and inefficiencies.
Production in agricultural enterprises entails the transformation of inputs into outputs. The spinach production includes farm inputs, such as farm size, labour availability, fertilizer cost, pesticides, and seeds, jointly used at different scales to yield the expected output. Figure 1 indicates that the anticipation was that when the farmer increases the application of any input in the farm, spinach yields might increase without considering the result of a negative effect of overuse in surrounding areas. The optimal level is reached when crucial factors of production are applied to enhance output [25]. The profit efficiency levels have affected the efficiency of production of a farmer.  The socio-economic and institutional factors, farmers' efforts, and intervening variables were factors influencing farmers' efficiency. The profit efficiency and its influencing factors influence policy decisions. The policy decisions play an important role in providing feedback effect to spinach farmers in enhancing profit efficiency and profit levels. The enhanced income and food security levels of spinach farmers affect profit efficiency and its determining factors through the improved and informed use of inputs. The socio-economic and institutional factors, farmers' efforts, and intervening variables were factors influencing farmers' efficiency. The profit efficiency and its influencing factors influence policy decisions. The policy decisions play an important role in providing feedback effect to spinach farmers in enhancing profit efficiency and profit levels. The enhanced income and food security levels of spinach farmers affect profit efficiency and its determining factors through the improved and informed use of inputs.

Study Area
The study was conducted in two district municipalities, namely Chris Hani and Amatole, in the Eastern Cape Province of South Africa. These municipalities were chosen because of their agricultural activities, mainly in Intsika Yethu and Ngqushwa, situated in the former homelands, Transkei and Ciskei, respectively. These local municipalities are home to Qamata and Tyhefu irrigation schemes, which are contributing immensely to rural households' livelihoods in the Eastern Cape Province. Qamata and Tyhefu irrigation schemes were considered for this study because they are amongst the largest smallholder irrigation schemes that produce crops and vegetables and are still operational in these selected local municipalities. The study selected these two irrigation schemes as they are situated in different district municipalities in the province that represent the range of agro-ecological and climatic characteristics suitable for spinach production in the province. Eastern Cape is one of the poorest provinces in South Africa where the majority of people are living below the national average poverty level as the province sits at 74.9% while food insecurity is very high at 78% [26][27][28] Figure 2. This has resulted in high food insecurity and a high risk of poverty in the province. As a result, living below the poverty line contributed immensely to decreasing agricultural productivity due to farm labour shortages. Conducting the study in these two-former homeland areas is very significant in permitting comparative analysis as they are from different environments yet contribute immensely to the agricultural economy of the province.

Study Area
The study was conducted in two district municipalities, namely Chris Hani and Amatole, in the Eastern Cape Province of South Africa. These municipalities were chosen because of their agricultural activities, mainly in Intsika Yethu and Ngqushwa, situated in the former homelands, Transkei and Ciskei, respectively. These local municipalities are home to Qamata and Tyhefu irrigation schemes, which are contributing immensely to rural households' livelihoods in the Eastern Cape Province. Qamata and Tyhefu irrigation schemes were considered for this study because they are amongst the largest smallholder irrigation schemes that produce crops and vegetables and are still operational in these selected local municipalities. The study selected these two irrigation schemes as they are situated in different district municipalities in the province that represent the range of agroecological and climatic characteristics suitable for spinach production in the province. Eastern Cape is one of the poorest provinces in South Africa where the majority of people are living below the national average poverty level as the province sits at 74.9% while food insecurity is very high at 78% [26][27][28] Figure 2. This has resulted in high food insecurity and a high risk of poverty in the province. As a result, living below the poverty line contributed immensely to decreasing agricultural productivity due to farm labour shortages. Conducting the study in these two-former homeland areas is very significant in permitting comparative analysis as they are from different environments yet contribute immensely to the agricultural economy of the province.
Smallholder farmers in these irrigation schemes (IS) produce various crops and vegetables, such as cabbage, spinach, maize, carrot, maize, and potatoes, to name a few. Farmers in these IS practice farming for commercialization and home consumption. The production of spinach is widely increasing as farmers are generating a lot of income from its marketing. The moderate climate conditions in these irrigation schemes accommodate the production of spinach. The study made use of a cross-sectional research design in collecting data due to its efficiency in terms of time and resources as well as high precision and accuracy [29].

Sampling Procedure, Frame, and Sample Size
The target population was the smallholder farmers producing spinach in the Eastern Cape irrigation schemes. The smallholder spinach farmers formed the sampling frame, and the sampling unit was the household head. The IS are practising not only vegetable farming, but also crop production within their establishment. The study made use of Smallholder farmers in these irrigation schemes (IS) produce various crops and vegetables, such as cabbage, spinach, maize, carrot, maize, and potatoes, to name a few. Farmers in these IS practice farming for commercialization and home consumption. The production of spinach is widely increasing as farmers are generating a lot of income from its marketing. The moderate climate conditions in these irrigation schemes accommodate the production of spinach. The study made use of a cross-sectional research design in collecting data due to its efficiency in terms of time and resources as well as high precision and accuracy [29].

Sampling Procedure, Frame, and Sample Size
The target population was the smallholder farmers producing spinach in the Eastern Cape irrigation schemes. The smallholder spinach farmers formed the sampling frame, and the sampling unit was the household head. The IS are practising not only vegetable farming, but also crop production within their establishment. The study made use of multi-stratified sampling procedures to survey the Eastern Cape. This approach is sensible and offers a perfect representation of the target population [14]. Firstly, the two district Sustainability 2022, 14, 2991 7 of 17 municipalities in the Eastern Cape were mainly selected due to their active participation and involvement in agriculture. Within the district municipalities, two municipalities where the irrigation schemes are located were chosen as the study sites based on the concentration of vegetable production. Secondly, smallholder farmers were stratified into crop producers and vegetable producers to allow the researcher to draw upon the desired sample size. The basis for the selection was the concentration of spinach production because this vegetable is the third most popular staple crop after maize and cabbage in the province. Finally, smallholder spinach farmers were purposively selected. The study sample size was 150 smallholder spinach farmers from both irrigation schemes.

Data Collection
The study used the primary data that were collected from spinach farmers between January 2016 and August 2017 using pretested close-ended questionnaires administered by trained enumerators in structured interviews. The questionnaire included short and precise questions regarding the production, market diversity, and efficiency of spinach. Information on demographic, institutional, physical, and socioeconomic factors, yields, and inputs used to grow spinach by smallholder farmers in the 2016-2017 cropping season was also collected. In addition, face-to-face meetings with the respondents were held to attain in-depth information essential to realize the main objective of the study. The secondary data were extracted from various sources for this study, including scientific publications, annual government reports, and other internet sources. These data were useful for comparison with survey data and to improve the questionnaire results to validate the survey.

Data Analysis
The study used the stochastic production frontier analysis. Descriptive statistics were also used in the study to describe demographic characteristics and production information of smallholder vegetable farmers. The study made use of frequencies, percentages, means, and graphs to describe the characteristics and production information of vegetable farmers.

Analytical Framework
The study made use of stochastic profit frontier (SPF) to estimate the technical efficiency of smallholder spinach farmers in the study area. The study adopted the SPF model to postulate a profit function that is assumed to behave in a manner consistent with the stochastic frontier concept [30,31]. This approach has been extensively used to estimate the technical and profit efficiency of small-scale farmers across the globe [30][31][32][33][34]. The preference of this approach emanates from its parametric nature and superiority compared to other methods. The SPF preference over non-parametric data envelopment analysis (DEA) is based on its use of the maximum likelihood method that yields robust results, unlike DEA, which depends on mathematical programming [19].
Profit efficiency, in this study, is defined as a profit gain from operating on the profit frontier, considering farm-specific prices and factors. A spinach farm ensures maximum profit despite the perfectly competitive input and output markets and singular output technology. The profit function approach allows the combination of technical and allocative efficiency concepts in the profit relationship and assumes that the production decision errors are transformed into minimum profits and revenue for the farmer. Thus, profit efficiency is defined as the farms' ability to attain maximum profit given the variable input prices and the level of fixed factors of the farm. Profit inefficiency, therefore, is referred to as the loss of profit for not operating at the maximum level possible [35]. The stochastic production frontier model suggests that the inefficiency effects can be expressed as a linear function of explanatory variables, reflecting farm-specific characteristics [36]. The advantage of this model is that it enables the estimation of farm-specific efficiency scores and causative factors of the efficiency derivatives among farmers in a one-phase estimation procedure. The approach involves computing the technical efficiency (TE) and economic efficiency (EE) scores for the farming households, and these scores are then used to estimate AE as a ratio of EE to TE. The TE was estimated through stochastic production function (SPF), while EE was computed from the stochastic cost function. To achieve the objectives of this study, the stochastic frontier production and profit function models were used to analyse the socio-economic characteristics and EE, respectively, of the farmers. The stochastic profit function is defined as: where: π * = normalized profit of i-th farmer; π ρ = description of the normalized profit, q i = vector of variable inputs; z = vector of fixed input(s); P = price of the output that is used to normalize variables in the model; π = profit of the farmer is defined as total income after deducting the total cost of production; exp(v i − µ i ) = composite error term.
The profit/economic efficiency (EE) of an individual farmer in the context of stochastic frontier profit function was derived as a ratio of the predicted, observed or actual profit π i to the corresponding predicted maximum profit π * . For the best farm or frontier, profit is given the price of variable inputs and the level of fixed factor(s) of production of that farmer. Mathematically, it is expressed following Kaka et al. [36] and Sunday et al. [32] as: Then, The stochastic disturbance term e i consists of two independent elements: "v" and "u". The symmetric two-sided error term (v) accounts for random variation in profit attributed to factors outside the farmer's control (random effects, measurement errors, omitted explanatory variables, and statistical noise). The one-sided component µ is a non-negative error term accounting for the inefficiency of the farm. Thus, it represents the profit shortfall from its maximum possible value that the stochastic profit frontier will give. However, when µ = 0, it implies farm profit lies on the efficiency frontier (i.e., 100% profit efficiency), and µ < 0 implies that the farm profit lies below the efficiency frontier. Both v and µ are assumed to be independently and normally distributed with zero mean and constant variance.

Empirical Stochastic Profit Frontier Model Specification
A multiple regression model based on the stochastic frontier profit function adopts the Cobb-Douglas functional form to determine the profit efficiency of spinach producers in the study area. The frontier model estimated following Kaka et al. [36] and Sunday et al. [32] was therefore specified as follows: where: π * = normalized profit computed for the i-th farmer, In = natural log, X * 1 = price of seed (ZAR/kg) normalized by the price of spinach, X * 2 = price of fertilizer (ZAR/kg) normalized by the price of spinach, X * 3 = price of labour (ZAR/man-day) normalized by the price of spinach, Sustainability 2022, 14, 2991 9 of 17 X * 4 = price of herbicides (ZAR/lt) normalized by the price of spinach, X k = area of land cultivated (ha), β 0, β 1,....4, β K , are parameters to be estimated, v i represents statistical disturbance term and µ i = represents the profit inefficiency effects of the i-th farmer.

Socio-Economic Characteristics of Spinach Farmers
The socio-economic characteristics of sampled farmers are presented in Table 1. The most frequently observed gender is male, with 68%. These results were in line with the finding of Mujuru and Obi [13] that male farmers dominate irrigation schemes as females are responsible for the households' chores. The mean average age of farmers was 48 years with an average household size of four persons in the households. These findings agree with the work of Okello et al. [19], who found that younger farmers dominate smallholder farming. This has a positive effect on spinach efficiency, given that younger farmers are more risk-takers than older farmers, which makes them adopt innovative technology that will enhance spinach production methods compared to older farmers who are risk-averse. Moreover, young farmers, in general, are physically strong enough to perform farm activities, unlike older farmers. The household size was used as a proxy for farm labour, and farmers were using their family members to work in the field, which played a crucial role in enhancing production and contributing to the profit efficiency of spinach. The study found that 65% of respondents were married. The average years spent in school was seven years, which is equivalent to primary education and thus means spinach farmers were literate. This means that spending many years in school provided spinach farmers with managerial competence and the ability to implement innovative techniques and marketing practices [34]. Educated farmers can make informed decisions to increase production, unlike uneducated farmers [15]. The average farm size utilized by spinach farmers was 3 ha, with an average farm experience of 10 years in farming. This suggests that most of the farmers have crucial insights concerning spinach agricultural production, and farmers were making use of the available land to optimize production and maximize their profit. Access to extension services played a significant role in increasing the profit efficiency of farmers, at 66%, and spinach farmers were members of farm organizations, at 65%. Spinach farmers had no access to financial support (access to credit, 64%), and spinach farmers were using social grants, farm income, and salaries to finance their farms. The most frequently observed household income was R6 890.13 per month. Spinach farmers resided approximately 8 km from the closest business centre. Spinach farming generated farm returns with an average of R1 243 per production season cultivated with an average farm size of 3 ha using on average 40 kg of fertilizer.

Profit Efficiency Function Estimates
The profitability parameter estimates for spinach production for the stochastic profit function are presented in Table 2. The profit inefficiency of spinach is measured by the value of gamma (γ) and was estimated using the generalized log-likelihood ratio test. The results reveal that the value of gamma is greater than zero, implying that discrepancies in profit efficiency are a result of both production inefficiency and external factors that are uncontrolled by the farmer (policies, random shocks, and measurement errors). This suggests that variations in spinach production in the province are primarily a result of profit inefficiency on the part of the spinach farmers. Note ** and *** represent significant level at 5% and 1% respectively.
The estimated model had a log-likelihood value of −221.943 and a Wald chi 2 of 52.78, which was strongly significant at the 1% level. This shows that the model was properly stated and that the explanatory variables were jointly able to explain the variations. The implication is that most of the variations in maize output emanate from farmers' practices as opposed to random variability. The profit inefficiency effects in spinach production in the study area as established by the gamma value of 0.66 were significant at the 1% level, according to analysis. The gamma (γ) (which is the ratio of the variance of the inefficiency component to the total error term) value of 0.66 implies that about 66% of the variation in the output of spinach farmers was due to differences in their profit efficiencies (the total variation in output is due to the presence of production inefficiency). These results correspond with the works of Nyam et al. [35] and Kamu [36] in that profit efficiency (PE) is a substantial contributor to the total deviation of output. This suggests that the one-sided random inefficiency factor strongly outweighs the measurements error and other random disturbances.
All the inputs demonstrated positive coefficients (elasticities of production), which positively influenced the profit. The fertilizer cost showed the highest positive elasticity (0.387 rand per litre), which was statistically significant at the 1% level, and this was revealed to be the most important variable determining profit efficiency. This implies that with a 1% increase in the cost of fertilizer purchased, the profit obtained from spinach production will increase by 0.39%. This implies that an increase in the use of fertilizer by the farmer increases the normalized profit of the farmer. Fertilizer is important for an increase in spinach output and soil conservation, and as such, an increase in fertilizer use is critical for farm sustainability. Fertilizer ensures the availability of micronutrients, such as Nitrogen and Potassium, for the successive vegetable. These results concur with the work of Mukwalikuli [37], Kaka et al. [30], and Chcha [25], who found that the cost of fertilizer used in paddy production played a significant role in increasing the profitability of a paddy.
Pesticides influenced spinach output at a 5% significance level, and the elasticity was 0.339. The implication is that a 1% increase in the cost of pesticides purchased led to a 0.34% increase in profit obtained from spinach production. The cost of pesticides will increase to complement the farm size, which will increase spinach production. Pesticides influenced output at the 5% significance level. Pest invasion in this regard could significantly compromise spinach productivity if farmers did not apply pesticides within the farms. These results accord with those of Dlamini et al. [38], who carried out a study in Swaziland and found that pesticides influenced profit and output levels. Pest invasion could significantly threaten spinach productivity should farmers fail to apply the pesticides within the wetlands. The cost of seeds was positive (0.453 rand per kilogram), which was statistically significant at the 1% level. This means that 1% increase in the price of seeds purchased, the profit obtained from spinach production will increase by 0.45%. The seed rate was a positive factor of output on spinach farming in EC province. The fact that elasticity of seed price was the second highest may also suggest that seed quantity used was the most limiting factor to spinach production, which constrained farmers from attaining maximum productivity. These results correspond with the work of Kamu [36], Okeyo et al. [19], Ahmed et al. [39], and Kibirige [40], who infer that seed purchase was the determining factor in the maize output and profit obtained by farmers in East African Wetlands, Central Ethiopia, and Masindi district of Uganda, respectively.
Land area is an essential factor in the production of spinach. The area planted had a positive coefficient and was significant at 1% level. This suggests that with a 1% increase in the area planted, the profit obtained from spinach production will increase by 0.29%. This indicates that spinach farmers were operating at the smallholder level. Hence, increasing their cultivated land area (0.289 hectares) will improve profit. This implies that land expansion led to an increase in the marginal output of spinach. Land availability had elastic implications on spinach production. These results were in line with the work of Okeyo et al. [19] and Kaka et al. [30] in that increased land area plays a crucial role in increasing smallholder farmers' output and profit. Labour used had no significant influence on spinach profit. The non-significance of labour used to spinach profit might be attributed to the direct relationship between the quantity of labour used and land area planted. Table 3 displays profit efficiency scores for spinach production in the Eastern Cape Provinces. The results probably support the conclusion of the technical and economic inefficiency of the smallholder farmers in the production of spinach. The smallholder farmers' efficiency levels were below 100%. The mean TE, AE, and EE were 90%, 75%, and 59%, respectively. The research results reveal that profit efficiency differs extensively among farmers, ranging from 43.3% to 88.3%. This variation can be attributed to the differences in the allocation and inputs' use amongst the farmers. The study estimated the mean profit efficiency of 90.1%, implying that spinach producers in the study areas have room to expand their profit by 9.9% through the adoption of the existing innovative production methods employed by efficient farmers. These findings were similar to those obtained by Okello et al. [19] and Tanko and Alidu [41], who found that smallholder farmers do not attain maximum efficiency from their production.  Table 4 presents the estimates of the determinants of profit inefficiency of spinach production in the study area. Subsequently, the parameters of the inefficiency levels are used in the production model as dependent variables. A variable with a negative sign in the inefficiency parameters is considered to either decrease inefficiency or increase efficiency, while a positive variable in the inefficiency model is viewed to have a negative effect or influence on efficiency. Significance at *** p < 0.01, ** p < 0.05.

Determinants of Farm-Level Resource Allocative Efficiency of Spinach Production
Years spent in school has a negative relation to profit efficiency and was significant at the 5% level. This implies that the additional year spent in school by the farmers enhances farmers' knowledge and management capabilities, assisting farmers in becoming more efficient. These farmers have improved their ability to interpret, adopt new technology to enhance production, and utilize information about markets by spending more years in school. This might be due to the fact that educated farmers were eager to disseminate technology that they were able to receive and interpret information, disseminating new information and making use of improved technologies, such as improved seeds, fertilizers, and pesticides for farming. These results concur with Nyam et al. [35] and Kaka et al. [30]. Education plays a crucial role in farming. As farmers are exposed to more agronomic practices and innovative techniques used in farming, they increase their spinach productivity, enhancing farm returns.
Access to extension services has a negative coefficient and is significant at the 1% level. This suggests that improved access to extension services will increase the profit efficiency of spinach farmers. This is because extension personnel disseminate information and provide farmers with better production methods and market information, which subsequently increases profit efficiency. A lack of visits by extension agents affected farmers negatively as they were restricted in their access to new information, techniques of production, understanding new practices, and use of modern inputs, which in turn would improve their profit efficiency. These results were in line with the work of Nyam et al. [35] and Mukwalikuli [37]. Access to extension services decreases profit inefficiency in spinach production among smallholder farmers as farmers lack knowledge of which agricultural techniques to use and lack market information important for improving farm returns. Access to credit had a positive coefficient, and it was significant at the 5% level. This implies that an increase in access to credit will lead to a decrease in the profit efficiency of the smallholder spinach farmers while increasing technical efficiency. A positive relationship between access to credit and profit inefficiency implied access to credit increased inefficiency and hence decreased the profit efficiency of spinach farmers. Access credit is important to farmers as it assist in buying proper agricultural inputs (such as high yielding seeds, fertilizer, agrochemicals, technologies and other production inputs) are able to increase their efficiencies. Spinach farmers who accessed credit had 7.9% higher technical efficiency compared to those without access. These results were in line with the work of Chacha [25]. A lack of financial support to farmers substantially contributes to the loss of profits of spinach producers as farmers use obsolete technology that reduces spinach output.
Household size has a positive and significant coefficient at the 5% level of significance. Household size positively influences the profit inefficiency, meaning that it increases the inefficiency of spinach farmers, therefore reducing their profit efficiency levels. This implies that an increase in household size reduces profit efficiency and thus increases the technical efficiency of farmers. This is because farmers in the study area depend on family labour to increase spinach production. As the workforce increases, this will have numerous effects on spinach output. However, if it were not correctly managed, it would have an adverse effect on production and productivity. The advantages of farm labour include affordability, availability, and ease of allocation in different farm activities [30,35,42]. The large household size tends to restrict the attainment of higher profits because the income derived is consumed in ensuring that the numerous needs of the household are met, thereby drawing on the financial resources beneficial to the farm.
Distance to the market center is a crucial indicator for market accessibility for both input and outputs for smallholder farmers. The results found a positive relationship between distance to the nearest market center and the efficiency of spinach production. This suggests that an increase of 1 km in the distance to the marketing center is associated with a 0.25% decrease in the efficiency of spinach farmers. The reduced efficiency due to the long distance to the market arises from the additional costs incurred during the transportation of the produce to the market. Longer distances between spinach farming and marketing centers as well as input providers reduced farmers' efficiency. Since markets are far from farmers' locations, they were unable to find the most current market information (such as price, demand, and supply of spinach) and expand seed on time. As a result, farmers that were closest to the market were more profitable than those who are far from the markets. These findings agree with those of Kamu [30] in that farms are located in inaccessible areas (rural areas) where access roads are obstructed such that the extension personnel find it difficult to frequently visit the farmers.
An inverse relationship exists between farm size and the efficiency of spinach. Specifically, an increase in farm size can potentially decrease the efficiency of spinach while increasing profit efficiency for spinach production by 0.7%. This implies that smallholder farmers are more productive in producing spinach than larger farms. These results agree with the work of Okello et al. [19], who proposed that the efficiency of resource use that small farms can attain increases the technical efficiency and reduces profit efficiency. Farm experience had a negative influence on efficiency at the 5% significance level. This suggests that an additional year spent on spinach production offered farmers an opportunity to increase profit efficiency levels by 2.84%. These results agree with those of Kaka et al. [30] and Oumarou and Huiqiu [43]. Farm experience can accurately predict what is needed in the farm, whether and when to plant or spray, and what types and amounts of inputs to use to increase their production, which ultimately increases their profit.
Fertilizer quantity used by farmers has a positive coefficient and was significant at the 5% level. This suggests that a 1% increase in the fertilizer quantity increases the efficiency of spinach production by 0.75%. This means the use of fertilizer quantities in spinach farming increases yields. The application of a greater quantity of fertilizer ensures that productivity is enhanced, thus improving efficiency.

Conclusions
The study investigated smallholder spinach producers under irrigated agriculture in the Eastern Cape. The study made use of Qamata and Tyhefu irrigation schemes as study sites due to their effectiveness in spinach production from different ecological regions. A cross-sectional research design was used to collect data from spinach farmers. The study used multi-stratified sampling procedures to collect data from 160 small-scale spinach farmers under irrigation. An SPF model to assess the profitability of spinach farmers and to identify the determinants of profit efficiency. Spinach production was found to be a profitable enterprise, and farm size significantly explained the profit efficiency of the farmers. The results indicated that spinach farmers are mostly profit efficient but can improve by up to 9.9% using the available technology. In conclusion, the use of innovative farming methods and technologies will help spinach farmers to increase their agricultural output. The positive coefficient of these parameters indicates that the increased use of these inputs will increase the spinach production level to a greater extent. Hence, if inputs are used to their maximum potential, there will be considerable gain from improvements in profit efficiency. The analysis of profit efficiency in this study indicates that years spent in schools, household size, distance to the market center, fertilizer quantities, farm size, farming experiences, access to credit, and access to extension services positively influenced the profit efficiency of spinach farmers. Based on the study result, the study recommends establishing financial support and investment in rural education through an effective extension delivery program that will assist farmers in overcoming their inefficiency. Young people and women need to be encouraged to participate in farming to enhance the vegetable production system. Farmers can be further supported through input acquisition, fertilizer application, and the marketing of spinach produce. For further research, one can look into assessing profit efficiency for spinach production under small-scale irrigated agriculture in other provinces of the country, since this study was only limited to the Eastern Cape province. This may assist in enhancing the information availability for spinach production efficiency in the country as a whole. Participants were informed about their right to ask questions relating to the research. Confidentiality and privacy were ensured throughout.

Data Availability Statement:
The datasets used or analyzed during the current study are available from the corresponding author on reasonable request.