Resource Use Efficiency of Potato Production among Smallholder Irrigated Farmers in the Eastern Cape Province of South Africa

Abstract

Potato (Solanum tuberosum L.) is Africa’s second most-grown crop and is widely used as the staple food after maize. The demand for potato production is increasing and growth in the area under production is estimated at 1.25% a year. Potato has great potential when it comes to food security and farm returns for many smallholder farmers. However, potato productivity is relatively low due to many factors that contribute to the low yield (including drought, poor production practices, and limited access to high-quality seed) and inefficient use of resources. Potato farmers have no access to formal markets, which may reduce the profitability of their enterprises. Additionally, while many studies have been conducted on the resource aspect of vegetable crops, very little is known about the profit efficiency of potato producers in the country. At the same time, efforts to commercialize potato production have not delivered the expected outcomes. This study aimed to estimate the profitability of potatoes, evaluate farm-level efficiency, and identify the factors that influence the efficiency levels of potato farmers in the Eastern Cape Province who engage in irrigation farming. The study used multi-stage and snowball sampling to select 150 smallholder potato farmers from whom primary data were collected using close-ended questionnaires. The data were analyzed using descriptive, gross margin analysis and translog stochastic profit frontier (SPF) modelling. The study found potato production to be profitable by as much as ZAR 7027.11 per annum. It is shown that farm size under potato, seed, pesticides, and fertilisers contribute positively towards the improvement of efficiency while labour and hired tractors negatively affect efficiency. The average technical efficiency of potato production among irrigated smallholder farmers was 89%, indicating that potato farmers could increase output by 11% without increasing inputs. Potato farm size, years spent in school, access to extension services, family size, and non-farm income are socio-economic and institutional factors influencing the farmers’ technical efficiency. However, the farmer’s age, access to credit, and cold storage had a negative effect on their productivity. The study recommends that government and non-governmental organisations strengthen the existing extension service provided to smallholder farmers and make efforts to provide farmers with long-term training and education to increase their productivity.

1. Introduction

Potato (Solanum tuberosum L.) is a versatile and widely cultivated crop that holds significant importance in global food production. It is considered the most productive crop and ranks as the third-largest source of food worldwide, following maize and rice [1,2]. In Africa, potato stands as the second most-grown crop, and South Africa is one of the top four producers where it plays a crucial role as a staple food alongside maize. The farming of potato is frequently carried out by smallholders who are predominately producing it using intensive smallholder farming and this is widely practised under irrigated farming [3,4].

The demand for potato production has been steadily increasing due to population growth, changing dietary preferences, and urbanization. As a result, there has been a gradual expansion in the area dedicated to potato cultivation, estimated to grow at a rate of 1.25% per year [5,6]. This expansion reflects the recognition of potatoes’ potential to contribute to food security and provide economic returns for smallholder farmers.

Despite its potential, potato production faces various challenges, particularly in the context of smallholder farming. Significant threats to potato crops are posed by abiotic factors such as temperature swings and soil salinity [2,7]. Potatoes are sensitive to climate change including temperature extremes, with frost damaging the foliage, soil salinity, and excessive heat inhibiting tuber development. Soil salinity, resulting from poor irrigation practices or high salt content in the soil, can negatively impact potato growth and yield [8].

Additionally, the production of potatoes among smallholder farmers is constrained by limited access to resources and technology. Small-scale farmers often face challenges in acquiring quality seeds, fertilisers, and pesticides, which can limit their ability to achieve optimal yields [9,10,11]. Furthermore, the lack of mechanization and advanced farming techniques hinders the efficiency and productivity of potato farming. This suggests that the contribution of potatoes to the national economy will progressively decline unless measures are taken to enhance potato production. Significant advancements in potato production contribute not only to local economic development but also to the producers’ and international community’s standard of living. Bajracharya and Sapkota [11] and Al-Hachami et al. [12] specified that smallholder potato productivity’s main problems are the unavailability of quality seeds, lack of fertilisers at the right time, scarcity of labour, poor market, lack of technical acquaintance with pest management, and geographical barricades. These challenges lead to a limited level of production and lower prices [13]. As a result, smallholder farmers are unable to effectively engage in competitive markets. Additionally, the issue of land fragmentation has caused a delay in the process of commercialization. Smallholder potato farmers are subsistence farmers who lack enhanced technologies, adequate extension services, adequate road networks and infrastructure, and adequate market facilities, all of which result in less productive potato production, decreased profitability, and inefficient resource utilisation.

Efficient resource utilisation is crucial for the ecological and financial sustainability of potato production. This includes effective management of water, fertilisers, and pesticides to minimize waste and environmental impacts. The production, packaging, and transportation of these products are influenced by energy costs, which contribute to their overall price [14]. Moreover, the rising prices of fuel and electricity have direct implications for the cost of operating machinery and irrigation systems in potato farming. The efficiency of agricultural resource use is crucial, particularly in developing nations such as South Africa, where production frequently occurs on vulnerable lands and is characterised by small-scale subsistence agriculture [15]. Therefore, improving resource use efficiencies can help optimize yields, reduce production costs, and minimize negative effects on the environment.

Potato is a significant food crop in developing countries and is often grown at a significant scale. While potato holds immense potential in addressing food security and generating income for smallholder farmers, its production is vulnerable to shocks and upset, effective and inefficient utilisation of inputs, and technological constraints [16]. Addressing these challenges through improved agricultural practices, access to resources, and enhanced technology adoption can enhance the sustainability and productivity of potato farming, ultimately benefiting both farmers by improving the efficiency of agricultural resource usage will lead to increased productivity, livelihoods, and sustainability in the agricultural sector and the broader population [17]. Therefore, it is essential to work towards strengthening and establishing the market participation of potato farmers in order to ensure higher-quality incomes to finance their increased access to technologies that will drive the transformation process forward in earnest. The aim of this study is to analyze the resource efficiency and profitability of potato production in the Eastern Cape Province. It focuses on how input and output market conditions drive profit efficiency on potato farms. By considering factors such as strategic planning, knowledge of local conditions, and continuous improvement, farmers can optimize resource allocation and management to improve efficiency and profitability [17]. The study sought to identify the major factors influencing farm profit efficiency and provide recommendations to overcome constraints and increase productivity and income from potato cultivation. Overall, the study aims to understand the relationship between market dynamics and profitability in potato farming to enhance resource utilisation and farm management.

2. Methodology

2.1. Theoretical and Conceptual Framework: Production Theory and Efficiency Theory

Production theory and efficiency theory provide frameworks for understanding and analyzing the production process and resource efficiency in potato smallholder farming. Theories of production and efficiency aim to maximize the output of potato production while minimizing input requirements.

Efficient potato production ensures an adequate supply of potatoes, which is crucial for food security. Production theory focuses on understanding the relationship between inputs and outputs in agricultural production. It helps explain how various inputs, such as land, labour, capital, and technology, combine to produce agricultural goods like potatoes [18]. By implementing efficient production techniques, farmers can achieve higher potato yields, contributing to increased food production and availability.

Efficiency theory, as highlighted by Liberto [19], focuses on resource utilisation and the achievement of maximum output with minimum inputs. In the context of this study, efficiency theories can be used to assess the extent to which potato producers in the Eastern Cape Province are utilising their resources effectively. By analyzing efficiency in potato smallholder farming, farmers can identify bottlenecks, inefficiencies, and areas for improvement. Efficiency theories also consider various factors that affect production efficiency, such as farm management practices, technological adoption, access to irrigation infrastructure, availability of skilled labour, farm size, market access, and government policies.

To gain a comprehensive understanding of the profitability, efficiency, and factors influencing potato production under irrigation farming in the Eastern Cape Province, the study integrated production and efficiency theories by employing an econometric model called Stochastic Frontier Analysis (SFA).

SFA is a widely econometric technique that measures the technical efficiency of production in the presence of random errors or inefficiencies. The general form of the stochastic frontier production function for potato smallholder farming can be written as:

$$Y=f{\left(X,\beta \right)}^{*} \left(-\mu \right)$$

where

• $Y$ is the observed potato output (dependent variable).
• $X$ is a vector of inputs, including land, labour, capital, technology, and other relevant factors (independent variables).
• $\beta$ is a vector of parameters to be estimated.
• $f{\left(X,\beta \right)}^{*} \left(-\mu \right)$ is the functional form representing the production technology or production function.
• $\mu$ is the random error component representing inefficiency.
• Exp $\left(-\mu \right)$ is the efficiency term, which varies between 0 and 1, where 1 represents perfect efficiency (no inefficiency).

The researcher can estimate the parameters (β) of the production function and the inefficiency term (u) simultaneously using the econometric software STATA 15 because it permits the error term (v) to be set from a two-side normal distribution N (μv, σv) with μv = 0 and σv = 1 and the inefficiency term (u) to be varied in absolute terms and distributional form in the subsequent simulations. This software facilitates the two measures that have been used to evaluate the performance of the proposed model against both the simulated frontier and the SFA and QR methods: the mean squared error (MSE), i.e., the average squared difference between the simulated and the estimated values, in order to verify the accuracy of the frontier estimate; the average of the absolute value of the differences (mean abs diff.) between estimated and true efficiencies in order to evaluate from the perspective of efficiency estimation. The estimated inefficiency term will provide insights into the extent of inefficiencies in potato production and how much output could potentially be improved by adopting best practices.

By integrating SFA into the study, the researcher can quantitatively assess the efficiency levels of potato producers in the Eastern Cape Province. The model will help identify factors that contribute to inefficiencies in potato production and determine the impact of various inputs on potato output.

The findings from the Stochastic Frontier Analysis can provide valuable insights for policymakers, extension services, and farmers to implement targeted interventions and improve the overall productivity, profitability, livelihoods, and sustainability of potato farming in the region and the agricultural sector. This knowledge can contribute to evidence-based policy recommendations, improve resource allocation, and ultimately enhance the food security and accessibility of potatoes in the Eastern Cape Province.

2.2. Description of the Study Area

The study was conducted in South Africa’s Eastern Cape Province (ECP), the second largest province in the country after Northern Cape. ECP is known for its natural beauty and unmatched diversity compared to other provinces. However, it also has a high poverty rate, with many people living below the country’s food poverty line of ZAR 624 [20]. Sixty per cent (60%) of the region’s 6.6 million inhabitants reside in rural areas characterised by extreme isolation, poverty, and destitution, with approximately 2.5 million inhabitants being unemployed. As a result, the majority reside in rural areas and rely on agriculture for their livelihoods. With a land area of approximately 170,000 km², larger than many countries, ECP offers favourable conditions for agribusiness and tourism [21]. The ECP is rich in agroecology which favours highlands, midlands, and mountainous hills which permit forestry. The climate of the province is classified as BSk (middle-latitude steppe). The province’s annual average temperature is 17.38 °C (63.28 °F), which is −3.84% lower than the national average. The annual average amount of precipitation in the Eastern Cape is 900 mm. This climate is conducive to agricultural production due to its high humidity and moderate temperatures, particularly for potato cultivation.

The study area was chosen for the study because it has existing irrigation schemes on which black farmers have been settled within the last decade and for which no previous studies have been undertaken to measure the productive efficiency of staple crops. However, the study only focused on smallholder farmers who practice farming under irrigation schemes and these farmers are few as compared to commercial farmers. The study was conducted in the Qamata and Tyhefu irrigation areas as they have a large number of smallholder farmers engaged in various agricultural practices for agribusiness purposes. These schemes were selected out of the eight existing ones in the entire province of Eastern Cape because they were the only revitalized schemes with significant agricultural activity taking place. The reason for this was mainly due to the fact that the South African government invested a lot in irrigation schemes as they are seen as one of the approaches that can be used to enhance food security, water security, nutritional security, and reduce poverty among rural areas. This was the motivation to see, in their production, how efficient smallholder potato farmers are and to check their profit efficiency. These farmers are not as large as commercial farmers but they practice potato farming using 1 Ha to 3 Ha where they produce for home consumption and surpluses for markets.

Agricultural production in the province involves both commercial and smallholder farmers, with smallholder farming dominating crops, vegetables, and livestock. Smallholder farmers engage in farming to sustain their households and support agribusiness activities. Most farmers increase soil fertility with organic and inorganic fertilisers. The province’s climate, as highlighted by Sibanda et al. [22], is suitable for citrus, livestock, vegetables, and crop farming, thanks to good summer rainfall and a moderate climate that becomes more subtropical in the northwest. Consequently, there are numerous functional smallholder irrigation schemes in the province, contributing to its GDP. The study area was selected based on the availability and functionality of these irrigation schemes, which are primarily operated by black smallholder and emerging farmers as part of the South African government’s strategy to improve food security, employment, and farm returns in rural areas.

However, no previous studies have measured the productive efficiency of essential crops in the province. Therefore, the study aimed to fill this research gap. It adopted a cross-sectional study design to collect data from potato producers, allowing measurement of both profit efficiency (the outcome) and resource use efficiency (the exposures) among smallholder farmers in the study area. This design facilitated data collection from various smallholder potato farmers at a single point in time.

2.3. Sampling Procedure, Frame, and Sample Size

The study made use of a multi-stage and snowballing sampling procedure to collect data from smallholder potato farmers. The study made use of a multi-stage sampling procedure to simplify data collection as the data were collected from a large group of smallholder irrigation schemes in the province and from various geographical settings. This sampling procedure was used because it allowed us to subdivide the smallholder potato producers into clusters based on their geographic settings to include all smallholder potato farmers from functional irrigation schemes in the Eastern Cape Province. The first stage of multi-stage sampling involved selecting district municipalities within the ECP with functional smallholder irrigation and also practising potato farming. The Amatole (Zanyokwe Irrigation Scheme) and Chris Hani District (Tyefu and Qamata irrigation schemes) municipalities were chosen purposively as study sites as they have functional smallholder irrigation schemes engaging with vegetable farming, especially potato production. The second stage involves grouping the smallholder farmers into strata for easy selection of the desired group of farmers for this study. The study had two strata, crop farmers (maize farmers) and vegetable farmers. The study then chose the potato farmers after stage two was completed. Stage 3 and the last stage involved snowballing sampling to choose the desired sample size of potato farmers, which was 150. Snowballing was used because it made things easier for researchers as it allowed potato farmers to refer researchers to the next potato farmers as they present specific traits and know each other within the irrigation schemes. The unit of analysis was smallholder potato farmers. The study made use of the following formula to come up with the sample size:

$$n=\frac{Z^{2}pq}{e^2} =\frac{1.95\times 0.5\times 0.5}{{\left(0.08\right)}^2} =150$$

where n is the sample size; Z is the confidence level (α = 0.05, hence, Z = 1.96); p is the proportion of the population containing the major interest, q = 1 − p, and e is the allowable error. The study sample size was 150 smallholder potato farmers.

2.4. Data Collection

The study employed primary data collection methods to gather information from smallholder potato farmers in the designated research area. The primary data were obtained using structured interviews using close-ended questionnaires. In Raymond Mhlaba Municipality, a pre-testing phase was conducted prior to the official data collection. This pre-testing served two purposes: to assess the questionnaire’s relevance, appropriateness, and the time required for respondents to complete it, and to train the enumerators who were recruited to administer the questionnaires. The feedback received during the pre-testing phase was utilised to enhance the questionnaire and ensure its alignment with the desired data. The primary data collected from smallholder farmers encompassed various aspects, including demographic information, potato production by farmers, resources utilised in potato production, farm returns from potato cultivation, challenges encountered by potato producers, and factors related to potato production. In addition, secondary data sources included the Department of Agriculture Gazette, Potato SA, RegenZ, the National Agricultural Marketing Council, peer-reviewed publications, and farm organisation reports.

2.5. Data Analysis

The collected data underwent a coding process and were entered into an Excel spreadsheet. Subsequently, the data were exported from the Excel spreadsheet to STATA 15 and SPSS version 24 for analysis. In this study, descriptive statistics, Farm Budgeting, and stochastic profit frontier modelling were performed. The demographic characteristics of smallholder potato farmers and the difficulties they faced were evaluated using descriptive statistics. Percentages, frequencies, means, t-tests, and chi-square tests were employed to analyze the data and draw meaningful insights from them.

2.5.1. Gross Margin Analysis

The study employed gross margin analysis to assess the profitability of smallholder potato farmers in the research area. This analytical approach utilises gross margin and net farm income as measures of farm profit. The gross margin analysis is widely recognized and preferred because it not only considers total revenue and total variable costs when measuring farm returns but also incorporates fixed costs to calculate net farm income. By including factors of production such as land, capital, and management as fixed costs, this technique provides a comprehensive evaluation of farm returns. Previous studies have also utilised the budgetary technique due to its ability to account for various factors influencing farm profitability.

Gross margin analysis was utilised to determine the profitability of smallholder potato farmers in the research area. This method employs gross margin and net farm income as indicators of farm profit. The gross margin is the product of the difference between total revenue (TR) and total variable costs (TVC). This tool was used by Bahta and Baker [23], Kebede et al. [24], and Aliyi et al. [25] to measure the farm returns of smallholder farmers. It is commonly used in agricultural enterprises for organising and comparing producers with similar characteristics. The costs of production were measured in Rands (ZAR) per hectare (Ha). The gross margin was calculated as follows:

$$GM \left(\pi \right)=\sum (T{R}_i-TV{C}_i)$$

(1)

where

• GM—means gross margin per potato irrigated farmer.
• TR is the total revenue from the production of potatoes i measured in terms of:
• TVC, which is the total variable cost of the production of potatoes i, measured in terms of direct and indirect costs. This includes transport, water, hired labour, seeds, chemicals, and fertilisers.

The total revenue, which is equivalent to potato income or gross income from each potato, was calculated as:

$$T{R}_i=P_i x Q_i$$

(2)

where $P_i$ is the farm gate price of the potato, $Q_i$ is the total quantity produced for each potato.

Total variable costs were calculated using the following expression:

$$TV{C}_i={{\displaystyle \sum }}_{i=1}(K_{it}+S_{it}+L_{it})$$

(3)

where $K_{it}$ is the fertiliser expenditure, $S_{it}$ is the total expenditure on seed, and $L_{it}$ is the total labour expenditure in each potato enterprise.

The paper went a step further in measuring farm profit by estimating Net Farm Income. This was undertaken purposively as it involved factors of production (land, capital, and management) in its calculations. This method provides important information about the results of the operating activities of potato enterprises over a given period. The NFI is often defined in collective terms and is an important and highly visible statistic when used to define the fitness of the farming enterprise. Net Farm Income is derived as follows:

$$NF{I}_i=G{M}_i-TF{C}_i$$

(4)

where $NF{I}_i$ is the Net Farm Income/profit of potato production, $G{M}_i$ is the farm’s gross margin of potato production, and $TF{C}_i$ is the total fixed cost of the potato farm.

2.5.2. Model Specification

The study employed the stochastic profit frontier (SPF) approach to analyze farm-level efficiency and identify the factors influencing the efficiency levels of potato producers engaged in irrigation farming. Noteworthy studies such as Bajrachary and Sapkota [11], Sultana et al. [2], Mezgebo et al. [26], and Kadakoğlu and Karl [27] have also utilised the stochastic profit frontier to estimate resource efficiency among smallholder farmers. The SPF method is widely recognized for assessing resource efficiency due to its ability to capture the functional relationship between explanatory variables (e.g., input, output, and ecological factors in potato production) and dependent variables such as cost, profit, and production. This approach assumes that certain enterprises do not effectively utilise their resources. It aligns with the current study’s objectives as it allows for the comparison of potato farmers’ performance under different technological regimes, considering variations in irrigation schemes and environmental conditions. The stochastic profit frontier approach addresses stochastic noise and facilitates statistical hypothesis testing related to production structure and inefficiency levels. In this study, researchers employed a truncated SPF model, utilising the log form of the approach due to its multiplicative nature. The use of truncated SPF regression allowed the study to conduct a polynomial regression with squared variables and interaction effects. Polynomial regression excels at estimating a single output, but its application to multiple outputs necessitates data disaggregation and price data that are difficult to obtain in transition economies [28].

STATA software was used to conduct a one-step assessment of technical efficiency and its determinants based on a normalised translog profit function. The profit function model is specified as follows:

$$ln{\pi }^{*}=ln{\alpha }_0+{\displaystyle \sum }_{i=1}^n{\alpha }_i{D}_i+{\displaystyle \sum }_{i=1}^n{\alpha }_{1}ln{P}^{*}+\frac{1}{2} {\displaystyle \sum }_{i=1}^n{\displaystyle \sum }_{h=1}^n{Y}_{ih}ln{P}_i^{*}ln{P}_h^{*}$$

$$\leftrightarrow \leftrightarrow \leftrightarrow \leftrightarrow$$

$$\mathit{A} \mathit{B} \mathit{C} \mathit{D}$$

$$+{\displaystyle \sum }_{i=1}^n{\displaystyle \sum }_{k=1}^m{\delta }_{ik}ln{P}_i^{*}ln{Z}_k+{\displaystyle \sum }_{k=1}^m{\beta }_{k}ln{Z}_k+\frac{1}{2}{\displaystyle \sum }_{k=1}^m{\displaystyle \sum }_{j=1}^m\Phi ln{Z}_{k}ln{Z}_j+v+u$$

$$\leftrightarrow \leftrightarrow \leftrightarrow \leftrightarrow$$

$$\mathit{E} \mathit{F} \mathit{G} \mathit{H}$$

where π∗ is the normalized restricted profit calculated as $\frac{TR-TC}{P_{Qi}}$, with TR and TC being total revenue and total cost, respectively, and $P{Q}_i$ is the output price for potato I. $P_i$ is the price of variable input $X_i$, which is also normalized by output price, $Z_k$ being the $k^{\mathit{th}}$ fixed input, whereas i = h = 1,2,3……..n; k = j = 1,2,3……m and ${\alpha }_0$, ${\alpha }_i$, ${\gamma }_{ih}$, ${\delta }_{ik}$, $\beta { }_k$ and Φ are parameters to be estimated. The equation has been segmented into parts from A to H and these represent constant terms, dummies, input prices, input–output prices, price-factor interactions, fixed factors, factor interactions, and the random-technical inefficiency effect.

The equation has been divided into sections A through H, which represent constant terms, variables, input prices, input–output prices, price-factor interactions, fixed factors, factor interactions, and the random-technical inefficiency effect. The variable inputs consist of labour, fertilisers, pesticides, tractor rentals, and fertiliser. Because location influences land quality, it was deemed necessary to include it as a dummy variable. The land is the only fixed factor measured in the study. Awunyo-Vito et al. [29] specified that the normalized profit functions with fixed inputs are occasionally referred to as normalized limited profit functions. Following Hossain et al. [30], the inspirational logarithmic model for estimating the economic efficiency of Eastern Cape potato enterprises was stated as follows:

$$\begin{array}{ll}\ln \mathsf{\pi } * = \mathsf{\beta }0+ \mathsf{\beta }1& \ln \left(\mathrm{Areait}\right)+ \mathsf{\beta }2\ln \left(\mathrm{Seedit}\right)+ \mathsf{\beta }3\ln \left(\mathrm{Fertit}\right)+ \mathsf{\beta }4\ln \left(\mathrm{Labit}\right)+\mathsf{\beta }2\ln \left(\mathrm{Pesticidesit}\right)\\ & + \mathsf{\beta }2\ln \left(\mathrm{Hired} \mathrm{TRactorit}\right)+1 2 [\mathsf{\beta }11 \ln \left(\mathrm{Areait} 2 \right)+ \mathsf{\beta }22\ln \left(\mathrm{Seedit} 2 \right)+ \mathsf{\beta }33\ln \left(\mathrm{Fertit} 2 \right)\\ & + \mathsf{\beta }44\ln \left(\mathrm{Labit} 2 \right)+ \mathsf{\beta }55\ln \left(\mathrm{Pesticides} 2\right)+\mathsf{\beta }66\ln \left(\mathrm{Hired} \mathrm{tract} 2\right)]+ \mathsf{\beta }12\ln \left(\mathrm{Areait}\right) * \ln \left(\mathrm{Seedit}\right)\\ & + \mathsf{\beta }13\ln \left(\mathrm{Areait}\right) * \ln \left(\mathrm{Fertit}\right)+ \mathsf{\beta }14\ln \left(\mathrm{Areait}\right) * \ln \left(\mathrm{Labit}\right)+\mathsf{\beta }15\ln \left(\mathrm{Areait}\right) * \ln \left(\mathrm{Pesticidesit}\right)\\ & +\mathsf{\beta }16\ln \left(\mathrm{Areait}\right) * \ln \left(\mathrm{Hired} \mathrm{tractors} \mathrm{it}\right)+ \mathsf{\beta }23\ln \left(\mathrm{Seedit}\right) * \ln \left(\mathrm{Fertit}\right)+ \mathsf{\beta }24\ln \left(\mathrm{Seedit}\right) * \ln \left(\mathrm{Labit}\right)\\ & + \mathsf{\beta }34\ln \left(\mathrm{Fertit}\right) * \ln \left(\mathrm{Labit}\right)+\mathsf{\beta }35\ln \left(\mathrm{Seedit}\right) * \ln \left(\mathrm{Pesticidesit}\right)+\mathsf{\beta }35\ln \left(\mathrm{Seedit}\right) * \ln \left(\mathrm{Hired} \mathrm{tractit}\right)\\ & + \mathsf{\beta }5\mathrm{DLOC} +{ \mathrm{v}}_{it}\end{array}$$

where π∗ is the normalized profit per potato enterprise in Rands. $The are{a}_{ it}$ is the area under cultivation for potato i in hectares, where i is potato.

$See{d}_{it}$ is the normalised price of seed for potato i in Rands/Kg.

$La{b}_{it}$ is the normalised price of labour in Rands.

$Fer{t}_{it}$ is the normalised price of fertiliser for potato i in Rands/Kg.

$Pesticide{s}_{it}$ is the normalised price of pesticides for potato i in litres

$Hired tracto{r}_{it}$ is the normalised price of hired tractor in Rands.

$v_{it}$ is the systematic error component.

$u_{it}$ is technical inefficiency. From the point of view of technical efficiency, the systematic error component and technical inefficiency terms in the preceding model were used as the basis to calculate the quantity of the total variance contributed by the variance component. An equation can be detailed in the form:

$${\mathrm{Y}}_{it}={ \mathrm{X}\prime }_{it}\mathsf{\beta } +n_i-u_i+v_{it}$$

The error components are:

$n_i$ ≥ 0 is a time-invariant farm effect.

$u_i$ ≥ 0 represents the inefficiency term.

$v_{it}$ is the noise (random) error term.

The values of lambda (which is the ratio of the variance of u to that of v) are the leader in the decision regarding the disparity in profit and inefficiency and what quantity of the variations is enlightened by the idiosyncratic error or the fixed effects. Post-estimation tests completed on STATA were intended to guarantee that the model parameters gratify equivalence restrictions in line with economic theory.

2.6. The Data

This section shows the data collected to fit the study. The data used were collected as primary data obtained through means of structured interviews with farmers or heads who were in the position to make decisions on resource allocation for their households.

Table 1. Description of the variables used.

Variable	Description	Measuring Type	Expected Priori
Gender	The sex of the farmer (male/female)	Dummy	+/−
Age	Age of the farmer in years	Continuous	+/−
Family size	Number of the family household of the farmer	Continuous	+
Farm size	Land area under cultivation by the farmer	Continuous	+
Occupation	Is farming the main occupation for the farm (self-employed, employed by the government)	Dummy	+/−
Education	Number of years spent in school by the farmer	Continuous	+
Marital status	The marriage status of the farmer (married/single/window)	Dummy	+/−
Household monthly income	This is the household monthly income in Rands (farm income, grants, and remittances)	Continuous	+
Irrigation member	Is the farmer a member of an irrigation scheme	Dummy	+
Mode of acquisition of land	The mode of acquisition	Dummy	+
Irrigation	Whether or not the farmer applied irrigation	Dummy	+
Total Labour Intensity	Number of persons employed	Continuous	+
Family Labour Intensity	Family members working per unit of land cultivated	Continuous	+
Fertiliser	Quantity of inorganic fertiliser used on potato (kg)	Continuous	+
Cost of tractor	Amount paid (hired) for tractors to prepare and spray cultivated land (Rand)	Continuous	+
Cost of land	Amount paid (rent) for the land under cultivation (Rand)	Continuous	+
Cost of seed	Total expenditure on seeds (Rand)	Continuous	+
Cost of pesticides	Total expenditure on pesticides (chemicals) (Rand)	Continuous	+
Cost of labour	Amount paid for use of labour	Continuous	+
Total Revenue	Total amount realized from sales of output	Continuous	+
Total Variable Costs	Total amount from the inputs used in the farm	Continuous	+
Value of Output	Market value of physical potato output	Continuous
Access to Extension	Frequency of Extension Visits	Continuous	+
Access to credit	Availability of accessible credit (yes/no)	Dummy	+/−
Member of farm organisation	Is the farmer a member of a farm organisation	Dummy	+

presents a description of the variables used, their measurement types, and their hypothesized relationship with the dependent variables. The field data were subsequently cleaned and coded in a spreadsheet to simplify the process of entering the data into Stata version 15 and SPSS version 26 for analysis. Some transformations were also performed to generate the interaction terms. Costs and time constraints made it necessary to limit the study to the Eastern Cape Province.

3. Results and Discussion

3.1. Socioeconomics and Distribution of Farm Characteristics

The socioeconomic characteristics of potato farmers play a crucial role in the analysis of economic data as they significantly influence farmers’ economic behaviour. These variables serve as key indicators, providing insights into the farmers themselves and enabling a comprehensive socioeconomic analysis of potato systems. In

Table 2. Summarized descriptive statistics of selected farmer characteristics.

Variable	Sample Size	Units	Mean	Standard Deviation	Minimum	Maximum
Gender: Male	150	Dummy, 1 = male, 0 otherwise	0.74	0.52	0	1
Occupation: Self-employed	150	Dummy, 1 = self-employed, 0 otherwise	0.58	0.33	0	1
Access to extension services: Yes	150	Number of visits	0.68	1.86	0	6
Membership of farm organisation: Yes	150	Dummy, 1 = member of farm organisation, 0 otherwise	0.70	0.48	0	1
Access to credit: No	150	Dummy, 1 = access to credit, 0 otherwise	0.62	0.44	0	1
Marital status: Married	150	Dummy, 1 = married, 0 otherwise	0.58	0.34	0	1
Age of the farmer	150	Years	48.23	8.40	24	68
Family size	150	Person	5.32	2.15	2	13
Farm size	150	Hectares	2.47	0.54	0.53	5.20
Years spent in school	150	Years	11.43	4.29	4	15
Household income	150	ZAR	4389.12	43.86	520.13	8365.45
Potato experience	150	Years	8.40	4.78	1	30
Irrigation membership	150	Dummy, 1 = irrigation member, 0 otherwise	0.68	1.23	0	1

below, the demographic characteristics of potato farmers are presented, along with their corresponding Standard Deviations (SD).

The descriptive results presented in Table 2 showed that potato farming was dominated by males, with 74% of respondents identifying as male. These results were not surprising due to African societies’ cultural norms and patriarchy, which prevent females from participating in farming and instead they focus on household chores. These findings were consistent with those of Tapera et al. [31], who identified that males tend to be the sole proprietors of economic resources and have more energy to work the land than women. According to the results, the average age of the farmers was approximately 48 years, with minimum and maximum ages of 24 and 68 years, respectively. These results were in line with Kadakoğlu and Karli [27] and Mezgebo et al. [26], who showed that smallholder farming is dominated by active aged farmers who are energized in operating the farm and knowledgeable about potato farming, and are thus anticipated to be productive. Marriage was a determining factor among potato farmers, with 58% being married. This marital status significantly influenced their decision-making processes concerning the farm. Married farmers tended to make choices that would enhance farm productivity, thereby contributing to the availability of food for their households as compared to single farmers. As a proxy for family labour, family size was considered. The average household size was five people, and they played an essential role in supplying family labour for potato production. As the majority of potato producers rely primarily on family labour, a larger family size was advantageous for providing additional labour to the farm from family members. Potato farmers demonstrated a level of literacy, having completed an average of 11 years of schooling, which is equivalent to secondary education in South Africa. These results revealed that potato farmers were knowledgeable and were able to interpret agricultural information that was beneficial for potato production. These results were in line with Mengui et al. [32] and Wassihun et al. [33], who showed that a significant portion of the farmers had attained secondary education, highlighting their ability to read and write, which are foundational skills for effective farming. Among these farmers, those involved in potato cultivation had an average of 8 years of practical experience in farming. The average farm size used for potato production was 2 hectares, which shows that these farmers were smallholder farmers.

The average household monthly Income was ZAR 4389.12 per month, with minimum and maximum household incomes being ZAR 520.13 and ZAR 8365.45. The household income was accumulated from multiple sources, including social security such as social grants, earnings from farming activities, and remittances. These results were in line with Kebede et al. [24]. Potato farmers were members of the irrigation scheme, with 68% reporting membership, and this played a crucial role for farmers as they were provided with agricultural information and water for irrigation. Potato farmers had access to extension services (68%) and were members of farm organisations (70%). These benefited farmers as they provided agronomic practices and technology used for production as well as relevant training to enhance agricultural productivity. Potato farmers had no access to credit (62%), which hampered the potato production in the study. These results were in line with Sultana et al. [2], who showed that smallholder farmers struggle to purchase inputs and hire labour due to a lack of financial support. This lack of finance is hindering the progress of potato production in terms of purchasing storage facilities and refrigerators since potatoes are perishable. The study results reveal that potato farming is their sole occupation as they are self-employed.

3.2. Descriptive Production Function

Potato farmers in the study area cultivated potatoes on an average of 2 hectares of fertile land within the boundaries of irrigation schemes. The production data presented in

Table 3. Summarized statistics of variables used in the SPF model for technical efficiency analysis.

Variable	Mean	Standard Deviation	Minimum	Maximum
Output
Potato quantity (Bags of 10 kg)	536.38	26.39	0.41	120
Input
Farm size (ha)	2.34	3.65	0.5	5.13
Fertilisers (kg)	140.75	3200	0	220.68
Seed quantity (kg)	450.89	476.41	20	1600
Potato labour used (Man-days)	11.23	7.34	1.53	30
Pesticides (kg)	130.46	144.32	0	780
Hired tractor (ZAR)	670.25	840.29	300	1200

revealed that, on average, farmers were able to produce 536 kg of bags (10 kg) of potatoes per season. However, this production level remained limited, potentially due to the insufficient use of quality inputs resulting from financial constraints. Notably, the average amount of fertiliser utilised by farmers was 140 kg, with some farmers not using any fertiliser at all due to financial limitations. The cost of fertiliser influenced its usage among potato farmers. Additionally, farmers used an average of 450.89 kg of seed for potato production. The choice and quantity of seed employed by potato producers have implications for the resulting yield. Financial constraints and high prices compelled farmers to opt for cheaper seedlings. The study found that potato farmers employed labour for an average of 11 days, which had an impact on potato production. To combat diseases and pests, farmers used an average of 130.46 kg of pesticides. In terms of mechanization, the average cost of hiring a tractor per hectare amounted to ZAR 670.25, with a minimum cost of ZAR 300 and a maximum cost of ZAR 1200.

3.3. Profitability of Smallholder Potato Farmers

In the Eastern Cape Province, potato production maintains a significant position among vegetable practices. Farmers engage in potato cultivation because it serves as the second staple food in Africa, following maize. Smallholder farmers not only grow potatoes for household consumption but also generate farm returns and enhance their overall well-being. In this study, it was deemed crucial to assess the profitability of potato production before delving into profit efficiency estimation. Evaluating farm returns is essential for assessing the performance and effectiveness of the agricultural enterprise per annum (per year). The average costs and returns of the potato enterprise in the Eastern Cape Province are presented in

Table 4. Gross Margin analysis of potato farming.

Cost and Revenue	Amount in Rands (ZAR)		Percentage (%)
Gross Revenue
Potato gross income at average prices	19,850.41
Variable Costs
Costs of seedling	2578.68		23.30
Family labour	1860		22.55
Hired labour	90.41		1.12
Total labour	1950.51		9.03
Fertiliser (NPK) (inorganic)	1740.68		22.43
Hire a tractor to prepare the land	2269.17		23.28
Pesticides (chemicals)	795.12		18.29
Total variable cost	9334.16		100
Gross Margin of Potato		10,516.25
Returns to variable costs		1.13
Less fixed cost (land rent, depreciation of farm assets and farm tools)
Total fixed costs (ZAR)		3489.14
Net farm returns		7027.11

.

The findings indicate that farmers practised potato production on an average farm size of 2 hectares, yielding a maximum of 120 bags of potatoes on average. The gross margin of the potato enterprise was calculated at ZAR 10,516.25 per year (per annum), with a gross margin per 100 of 1.13. These results align with previous studies by Oluwatayo et al. [34] and Kebede et al. [24], who also found profitable returns for potato producers. The profit ratio of 1.13 suggests that for every ZAR 1.00 invested in potato farms, farmers stand to make a profit of ZAR 1.13.

Furthermore, the study estimated the net farm profit to determine whether potato farmers could cover their expenses. The results revealed a net farm income (NFI) of ZAR 7027.11 per annum. The positive NFI indicates that smallholder potato producers in the Eastern Cape Province were able to cover their operational expenses, thus highlighting the profitability of potato production for these farmers. However, as much as potato farmers are making a profit, they are not generating the profit they should be making due to a lack of market information which limits farmers in meeting retail standards and they end up selling most of their produce at farm gates at a lower price. This will be explained in the challenges section below.

3.4. Distribution of Technical Efficiency of Potato Enterprise

Table 5. Frequency distribution of technical efficiency of the potato enterprise.

Variable	Frequency of Farms	Percentage (%)
Technical efficiency
0.01–0.15	0	0
0.016–0.25	3	2.27
0.26–0.50	18	22.05
0.51–0.75	25	24.11
0.76–0.99	33	46.57
0.89–100	7	5.0
Total	86	100
Minimum	0.22
Maximum	0.99
Mean TE	0.891

below presents the distribution of technical efficiency scores for the potato enterprise in the Eastern Cape Province. The study made use of efficiency scores to determine the average technical efficiency of potato production in the study. The efficiency scores range between 0 and 100% as the scores are expressed in percentage terms. In this study, efficiency was expressed as a percentage, which indicates that the cumulative probability distribution of bias-corrected technical efficiency scores (frequencies and percentages) was utilised. The findings indicate that the minimum distribution of potato enterprise efficiency averaged 22%, while the maximum distribution averaged 99%. These results align with previous studies by Rahman [35] and Mengui et al. [32]. The study results also show that out of 150 sampled potato farmers, 33 (46%) farmers were technically efficient based on the frequency distribution of technical efficiency (TE) scores.

Table 5 reveals that the estimated technical efficiencies for smallholder potato farmers ranged from 22% to 99%, indicating a significant disparity in the technical efficiencies of potato farmers who used the same number of inputs. The average score for technical efficiency among the farmers under consideration is 89%. This indicates that potato farmers are able to utilise production inputs effectively. In addition, the results indicate that there is a likelihood that potato farmers will be able to increase their efficiency by 11% in the near future by making greater use of their current farm resources. The study’s technical efficiency scores reveal that smallholder potato producers in the Eastern Cape Province have performed equitably well on the levels of technical efficiency. This demonstrates the commitment of potato farmers to utilising the available resources very well knowing their scarcity for production. The average mean score of 0.89 (89%) is quite high and impressive for smallholder farmers as it shows that potato farmers are efficient in the way they use their production inputs. These findings align with Mezgebo et al. [26] and Rahman [35], emphasizing the potential for enhancing productivity by utilising the same inputs more efficiently among smallholder farmers.

The efficiency scores for each sampled respondent were estimated and categorized into four groups. The statistics reveal that the majority of potato farmers (46.57%) fell within the efficiency score range of 0.76 to 0.99, while 29.11% had a range of 0.51 to 0.75. Additionally, 22.05% had efficiency scores ranging from 0.26 to 0.50, whereas only 2.27% had scores ranging from 0.16 to 0.25 while there were zero scores of 0.01–0.015. The results of the study also indicate that smallholder farmers with technical efficiency scores of one are operating at the efficiency threshold and are deemed effective. Technically proficient potato farmers are unable to increase yields with the current technology set and inputs (smallholder farmers’ limited use of innovative agricultural practices). However, in order to increase their current output levels, these farmers may increase their current input levels and implement new technology.

The bias-corrected technical efficiency scores of the smallholder potato irrigation farmers in the Eastern Cape Province are shown as a Cumulative Probability Distribution Function (CDF) in Figure 1. Figure 1 is the graphical illustration of Table 5 above in which the mean technical efficiency of potato farmers under consideration is relatively high, at 89%. This implies that farmers are able to use their agricultural input efficiency and they are producing at a rational stage of production. This stage is later explained under the return to scale.

3.5. Profit Efficiency and Inefficiency Estimates of Potato Enterprise

The study utilised the stochastic profit frontier (SPF) method to estimate smallholder farmers’ technical efficiencies in potato production. Specifically, the research centred on potato production in Eastern Cape smallholder irrigation schemes. The maximum-likelihood estimates for potato production using SPF are presented in

Table 6. Maximum-likelihood estimates of the SPF model for the potato enterprise.

Profit Function	Parameter	Coefficient	S. Error	p > z
Constant	${\beta }_0$	6.738	1.260	0.009 ***
lnFarm Size	${\beta }_1$	0.278	0.122	0.000 ***
lnSeed cost	${\beta }_2$	0.184	0.126	0.000 ***
lnFertilizer cost	${\beta }_3$	0.152	0.098	0.002 ***
lnLabour	${\beta }_4$	−0.034	−2.257	0.041 **
lnPesticides cost	${\beta }_5$	0.013	0.105	0.067 **
lnHired tractor cost	${\beta }_6$	−0.029	−0.025	0.004 ***
Inefficiency regression
Age of the potato farmer	${\delta }_1$	−1.832	−0.321	0.018 **
Potato farm size	${\delta }_2$	0.618	0.244	0.48 **
Access to credit	${\delta }_3$	−0.546	−0.398	0.41 **
Years spent in school	${\delta }_4$	1.362	0.265	0.000 ***
Access to extension services	${\delta }_5$	0.920	0.127	0.006 ***
Family size	${\delta }_6$	0.468	0.097	0.014 **
Cold storage	${\delta }_7$	−0.353	−0.242	0.032 **
Non-farm Income	${\delta }_8$	0.269	0.135	0.012**
Variance parameters			LR test = 68.359 *** Return to scale = 0.56
Wald chi2(13) = 258.36	$\gamma =\frac{{\sigma }_u^2}{{\sigma }^2}$	1.56		0.000 ***
	${\sigma }_v^2$	0.70		0.162
	${\sigma }_u^2$	1.09		0.125
	Log-likelihood	−324.8550		Prob > chi2 = 0.0000

Note: ** and *** represent levels of significance of 5% and 1%, respectively.

which provides insights into profit efficiency and inefficiency outcomes.

To assess the technical efficiency of resources utilised by potato farmers, the study considered six input variables: farm area, seed costs, utilised costs, pesticide costs, labour utilised, and the use of hired tractors for mechanization. The modelling approach entailed a polynomial regression that incorporated both first-order and second-order (squared) variables, as well as interaction terms. This approach was adopted due to the inherent uncertainty surrounding the precise levels of input variables in potato farming. These results align with previous studies by Atamja and Yoo [4].

Using the gamma (γ) value, which was estimated using the generalized log-likelihood ratio test, the study also measured technical inefficiency in potato production. The results indicate that the gamma value is greater than zero, indicating that variations in profit efficiency are affected by both production inefficiency and external factors beyond the control of farmers, such as government policies, random shocks, and measurement errors. This finding is consistent with previous research. Overall, these results suggest that the variations observed in potato production within the province primarily stem from profit inefficiency among potato farmers.

Table 6 presents detailed information on the input parameters and technical inefficiencies associated with potato production.

Smallholder potato producers in the study utilised six input variables for potato production. The results indicate that, on average, the farmers produced 36.26 thousand kg of potatoes, with a minimum of 0.41 thousand kg and a maximum of 120 thousand kg. The stochastic profit frontier (SPF) analysis revealed that four variables had positive coefficients, which were statistically significant at the 1% and 5% levels, respectively, while two variables had negative coefficients, which were also significant at the 1% and 5% levels, respectively. This suggests that all six variables play a significant role in determining potato production.

Among the input variables, farm size (the area of land used for potato farming) exhibited the highest elasticity. Farm size was not only utilised for potato production but also for storage purposes. The positive and statistically significant effect of farm size at the 1% level implies that an additional hectare of farm size for potato production would result in a 0.575 unit increase in potato productivity. This highlights the importance of farm size in the potato enterprise and indicates that potato producers were operating at a very low level, consistent with smallholder environments. These findings align with previous studies by Tapera et al. [31], Dube et al. [36], and Kaka et al. [37] which also emphasized the role of increased farm size in enhancing smallholder farmers’ output and profitability. This additionally reduces the inefficiency of potato production.

The coefficient of seed cost was found to be positive and significant at the 1% level, making it the variable with the second-highest elasticity. This suggests that increasing expenditure on seed cost would result in a 0.439 unit increase in potato productivity. The high elasticity of seed cost implies that the quantity of seed used by potato farmers was a limiting factor in potato production, preventing them from reaching maximum productivity. The quality of potato seed used by farmers is determined by the cost of the seed. Using poor-quality potato seeds hampers production, while good-quality seeds are essential for optimal output. These findings align with previous studies by Sultana et al. [2], Tapera et al. [31], and Rahman [35], which emphasize the importance of seed cost in determining the type of potato seed used by farmers to enhance their output and profit.

The labour input in potato production encompasses family labour, draught power, and hired labour. The coefficient of labour was negative and statistically significant at the 5% level. This implies that a unit increase of farm labour used by potato producers would result in a 0.337 decrease in potato productivity. It may appear, based on the magnitude of the coefficient for the number of potato plots, that a 1% increase in the number of man-hours spent on maize production results in a decrease in the potato yield per hectare. This means that an increase in farm labour affected potato production and the profitability of farmers. These findings are consistent with Rahman [35], Kadakoğlua nd Karli [27], and Wassihun et al. [33], which highlight the adverse effects of increased labour expenditure on production output. However, these results contradict the findings of Dube et al. [36], who found a positive contribution of labour to potato production.

The fertiliser coefficient was found to be statistically and positive significant at the 1% level. This implies that a 1% increase in fertiliser use by potato producers would result in a 0.317 increase in potato productivity. Investing in fertiliser is crucial for potato farmers as it enhances their potato output and profit. This finding is not surprising, considering the importance of fertiliser in providing micronutrients like Nitrogen and Potassium, which are essential for healthy plant growth and soil conservation. These results align with previous studies by Sujan et al. [1], highlighting the significance of fertiliser use in improving soil quality and increasing potato output and profit margins for farmers.

In addition to having a positive coefficient, pesticide use was statistically significant at the 5% level. This implies that a 1% increase in pesticide use by potato farmers would result in a 0.126 increase in potato productivity. Farmers use pesticides to control diseases and pests that compete with potato output. These findings are consistent with the research conducted by Sujan et al. [1].

Given the effects of climate change, the use of mechanization has become increasingly important for farmers, particularly with the decline in livestock units available for land preparation. The coefficient for hired tractor cost was negative and statistically significant at the 1% level. This suggests that a 1% increase in the use of hired tractors would lead to a 0.287 unit decrease in potato productivity. This is probably because the use of hired tractors increases farmers’ expenditures, ultimately reducing potato production.

3.6. Technical Inefficiencies of Potato Enterprise

Table 6 above presents the profit inefficiencies of smallholder potato producers in the Eastern Cape Province, which are influenced by various farm characteristics, socioeconomic factors, and institutional factors. These variables play a crucial role in improving farmers’ technical efficiency and regulating the consistency and level of potato production. The LR test was calculated as 68.359 and showed an effect of non-random variables in terms of potato production in the enterprises. These results agree with Kadakoğlua and Karli [27]. Additionally, the lambda (λ) value is greater than one, indicating inefficiency. Furthermore, the value of gamma indicates that output varies by 70% due to technical inefficiency. This indicates that technical inefficiency is likely to play a significant role in explaining output among sampled potato producers. The coefficients in the table indicate the direction of the effects of these variables in the model. A negative sign on parameter inefficiencies implies that the variable reduces technical inefficiency while a positive sign increases technical inefficiency.

The coefficient for farmers’ age was found to be negative and statistically significant at the 5% level. The age of the household influenced inefficiency negatively. These results indicate that older farmers are more technically efficient than younger farmers. The negative coefficient suggests that higher age leads to a reduction in the inefficiency of potato-producing farmers. In other words, a 1% increase in farmers’ age leads to a 1.832% decrease in the technical inefficiency of the farmers. The reason for this is due to the mere fact that the farmers become more skillful as they grow older due to cumulative farming experiences. These results were in line with Belete [38] and Wassihun et al [33] but contradict the findings of Mezgebo et al. [26]. Age increases the farmer’s ability to evaluate the importance and complexities of good agricultural decision-making, including the efficient use of inputs and the promotion of technically efficient potato production.

The coefficient of potato farm size was found to be positive and statistically significant at the 5% level in Table 6, which means that larger farm sizes may not improve technical efficiency. Larger farms are more profitable because farmers are more adept at implementing modern technologies such as tractors and improved irrigation management. These results indicate that an increase in farm size by one additional hectare leads to decrease in the technical efficiency of farmers. Essentially, the findings suggest that potato farmers are utilising the available resources more efficiently. These results were in line with Sultana et al. [2] and Barasa et al. [39], who also emphasized the crucial role of farm size in increasing the technical inefficiency of smallholder farmers. However, it is worth noting that these results contradict the findings of Mengui et al. [32] who observed that farm sizes had a negative influence on technical efficiency.

The coefficient for years spent in school was found to be positive and statistically significant at the 1% level. This suggests that each additional year of education for potato producers increases their technical inefficiency. The findings suggest that years spent in school enhance farmers’ knowledge and management skills related to the resources used in potato production, hence increasing farmers’ efficiency. Educated farmers have the knowledge to employ higher-quality methods to their agricultural endeavours and, as a result, are more technically efficient. This variable allows potato farmers to better understand and interpret new agronomic information, as well as adopt innovative technologies aimed at improving production and profitability on their farms. According to Mezgebo et al. [26], farmers who spend more years in school are able to use resources more efficiently in potato production than their counterparts as they can optimize the input mix and use innovative technologies. When the household head is the main decision maker in the family, more educated farmers actively adopt new technologies (such as soil conservation and agronomic practices) which could positively influence the technical efficiency of potato production. This implied that there was an increased level of technical inefficiency as the level of education increased. These results are consistent with previous studies conducted by Mutenheri et al. [40], which could mean that an increase in education level, achieved through spending more years in school, enhances the probability of improving knowledge and, consequently, contributes to improving potato output and profit margins.

The extension services access coefficient was positive and statistically significant at the 1% level. level. This implies that an increase in access to extension services by one additional visit decreases the technical efficiency of potato farmers. Having access to extension services is associated with a higher technical efficiency of 0.920% compared to those who have no access to extension services. This implies that extension services are effectively disseminating information to farmers regarding improved farming practices and agricultural technologies. Potato producers who interact with extension workers more frequently are likely to be more productive. This implies that extension plays a significant role in improving technical efficiency in potato production.

Farmers with access to extension services were privy to more knowledge and had agronomic information about the use of resources and gained more technical knowledge about potato production and information about marketing, which are likely to lead to better technical efficiency. The provision of extension services supports farmers in bridging the gap between technology and formal education through training, field demonstrations, and farm visits [41,42].

The family size coefficient was positive and statistically significant at the 5% level. This implies that the technical inefficiency of potato production increases with each additional member added to a family. The family size parameter had positive and significant impacts on the technical inefficiency of potato production, indicating that a large family size does not constrain labour. This is due to the availability of family labour and the ease of allocating their duties, which results in enhanced farm output and returns. These findings are in line with Sultana et al. [2], Mengui et al. [32], Ojo et al. [42], and Nyam et al. [43], who found a positive relationship between family size and technical inefficiency. However, these findings contradict the findings of Barasa et al. [38] who showed that a large family size has more commitments, which diverts resources away from farming operations to household maintenance needs.

Access to credit had a negative coefficient that was statistically significant at the 5% level. This suggests that a greater availability of credit increases the technical efficiency of potato production. Consequently, agricultural credit improves technical efficiency. This suggests that the farmers who accessed formal credit would be more technically efficient than those with no access to credit. Access to credit is imperative for potato farmers as it allows them to purchase necessary agricultural inputs such as seeds, fertiliser, and pesticides, which ultimately enhances potato output and profit. The effect on credit access may reflect the low levels of access to credit among smallholder farmers. This is mainly due to the collateral requirements and high interest rates associated with seasonal agricultural loans. Credit can alleviate the liquidity constraints of farmers in order to improve their efficiency, which may impact their ability to timely acquire and apply inputs and implement farm management decisions. These findings are consistent with previous research by Mengui et al. [32] and Morais et al. [44], which emphasised the significance of credit access in enhancing the technical efficacy of farmers.

On the other hand, cold storage had a negative coefficient and was statistically significant at the 5% level. This implies that an increase in cold storage capacity among potato producers improves the technical efficiency of potato production. These findings align with the study by Sultana et al. [2], which could mean that cold storage negatively influences the technical inefficiency of potato producers as farmers lack facilities to store the produce and maintain its freshness.

In addition, the non-farm income coefficient was positive and statistically significant at the 5% level. This suggests that a unit increase in non-farm income by potato farmers increases profit efficiency, and also contributes to greater technical inefficiency in potato productivity. This is probably because farmers utilise their non-farm income as a means to supplement their farm expenditure, given their limited financial resources. This positive effect allows them to purchase necessary inputs and hire transportation for transporting their potato output to markets.

3.7. Return to Scale

Return to scale is very important to analyze, as it assists in terms of identifying the stages of production and whether farmers have made use of allocating resources in the stage of production. The results of the study imply that the total production coefficient (β_i) indicates a return to scale. The return to scale in the sample area was determined to be approximately 0.56, indicating a diminishing return to scale. This suggests that potato producers allocated their resources during the rational stage of production (Stage—II), in which a smaller quantity of return is added to the gross return for each additional unit of input to potato production. These results were in line with Bajracharya and Sapkota [11] who found that the return to scale of potato producers in Nepal was 0.84, while Sujan et al. [1] found the return to scale of potato farming to be 0.59 in Bangladesh. This simply means that potato production in the Eastern Cape Province under irrigation is using resources more efficiently and they allocate input resources in the rational stage of production. These results were in line with Mezgebo et al. [26]. This means that smallholder farmers and policymakers should encourage and put emphasis on the efficient use of agricultural inputs to enhance the productivity of potato.

3.8. Challenges Faced by Smallholder Potato Farmers

Potato production plays a significant role in households, providing both sustenance and farm returns. However, numerous constraints hinder potato production and farm returns, as depicted in Figure 2. The first major constraint faced by potato producers is the lack of quality seeds. This issue arises because farmers often opt for affordable potato seeds due to financial limitations, resulting in the purchase of lower-quality seeds that are priced more affordably. The second challenge revolves around the low price of potato output, which is predominantly driven by a lack of market information and low-value-added activities by small-scale potato farmers. Lack of market information is a challenge for farmers as it limits farmers from enjoying participation in high-value markets in order to generate a higher profit. This lack of market information led farmers not to follow handling practices for their produce or to set prices according to market value, resulting in their produce not being purchased as the pricing is higher. Also, lack of market information forces farmers to sell their produce informally at a cheaper price and thus reduces profitability. Natural disasters, accounting for 76% of cases, and pest and disease outbreaks, accounting for 74% of cases, pose significant challenges due to changing weather patterns, making farming vulnerable to various diseases and natural calamities. Potato farmers also encounter difficulties in securing sufficient operating capital, which is particularly prevalent among smallholder farmers in sub-Saharan Africa. This issue stems from the fact that many farmers do not view farming as a viable agribusiness, limiting investment in agriculture. This is because the lack of finance restricts smallholder farmers from adopting innovative technologies and implementing current agronomic techniques to enhance their output and profit. Storage and handling facilities present another challenge for potato producers, compelling them to sell their produce immediately after harvest and at lower prices due to the absence of proper storage facilities. Farmers often lack the crucial facilities necessary for effectively handling their produce. Lastly, farmers express concerns regarding the limited visibility of agricultural extension services. Some farmers reported only encountering extension personnel during the ploughing time, after which their presence diminishes. These challenges impede potato productivity and further restrict farmers’ abilities to employ up-to-date technologies to improve their profit efficiency.

4. Conclusions and Recommendations

4.1. Conclusions

This study analyzed the profitability of potato farming, evaluated farm-level efficiency, and identified factors influencing the efficiency levels of potato producers under irrigation farming in the Eastern Cape Province. The findings reveal important insights into the socio-economic characteristics of potato farmers, production functions, profitability, and technical efficiency of potato enterprises.

The socio-economic analysis of potato farmers showed that potato farming in the region is predominantly male-dominated, in line with cultural norms and patriarchal structures. The average age of farmers indicated that active and experienced individuals are engaged in potato farming, which is expected to contribute to productivity. Married farmers and larger family sizes were found to play important roles in farm decision-making and providing family labour for potato production.

The profitability analysis revealed that smallholder potato farmers in the Eastern Cape Province were generating sufficient profits, as indicated by positive gross margins and net farm income. This suggests that potato farming is a profitable venture for smallholder farmers in the region. The results align with previous studies highlighting the profitability of potato production.

The analysis of technical efficiency showed that there is room for improvement in potato production practices. The average scale of technical efficiency indicated that potato farmers could increase their average output by 11% without using additional inputs. This suggests that farmers are currently utilising their resources inefficiently, presenting opportunities for enhancing their technical efficiency. The distribution of technical efficiency scores revealed varying levels of efficiency among farmers, with a significant portion still operating below optimal levels.

The estimation of profit efficiency using a stochastic profit frontier model indicated that differences in profit efficiency among potato farmers were influenced by both production inefficiency and external factors beyond farmers’ control. The study identified several input variables that significantly affected profit efficiency, including farm size, seed cost, labour, fertiliser use, pesticides, and mechanization. These findings highlight the importance of managing these inputs effectively to improve profit efficiency in potato farming.

4.2. Recommendations

Based on the findings of this study, the following recommendations can be made:

Promote gender inclusivity: Efforts should be made to challenge cultural norms and patriarchal structures that limit female participation in potato farming. Providing equal opportunities and support for female farmers can contribute to increased productivity and overall farm efficiency.

Improve access to finance: Access to credit is crucial for smallholder farmers to overcome financial constraints and invest in quality inputs such as seeds, fertilisers, and machinery. Financial institutions and government agencies should develop tailored financial products and support schemes to facilitate access to finance for potato farmers.

Enhance technical knowledge and training: Continuous training and extension services are essential to improve farmers’ knowledge and skills in potato production. Training programs should focus on good agricultural practices, including optimal use of inputs, pest and disease management, and efficient use of machinery.

Promote cooperative farming and farm organisations: Encouraging farmers to form cooperatives and join farm organisations can provide them with collective bargaining power, access to information, and shared resources. This can lead to improved economies of scale, reduced input costs, and enhanced profitability.

Support research and innovation: Continued research and innovation in potato farming techniques, seed varieties, pest and disease management, and irrigation systems can contribute to increased productivity and efficiency. Research institutions, agricultural organisations, and government agencies should collaborate to facilitate knowledge transfer and adoption of innovative practices.

Improve infrastructure and access to markets: Investments in rural infrastructure, including irrigation systems, storage facilities, and transportation networks, can help reduce post-harvest losses, ensure quality control, and facilitate market access for potato farmers. Improving market linkages and value chain integration can also enhance profitability.

By implementing these recommendations, stakeholders in the potato farming sector can work towards improving the profitability, efficiency, and overall sustainability of potato production in the Eastern Cape Province.

4.3. Limitations

This study made use of a cross-sectional research design. As a result of the use of the cross-sectional nature of this study, the causal interpretation is not practicable. The sample of potato farmers studied may not be representative of all potato farmers in the Eastern Cape. There may be variations in practices, challenges, and outcomes across different districts and provinces. Future studies should consider using panel data or time series data. The study relied on self-reported data provided by the farmers. This can introduce biases and inaccuracies in the findings, as farmers’ perceptions and interpretations may differ. Due to the sample limitations and the specific context of Eastern Cape, the findings of this study cannot be broadly generalized to potato farmers in other districts or provinces. The sample size used in this study is small, and future studies should consider using a larger sample size and focus not only on irrigation farming.