Introduction

The issue of food and its provision for the growing global population, especially in developing countries, has become a concern due to the high population growth rate (Vishnoi and Goel 2024). The optimal utilisation of agricultural resources and facilities, along with increasing the efficiency of strategic agricultural production, is the best approach to ensure food security for the expanding world population (Bazargani and Deemyad 2024). Part of the low income of farmers is attributed to external factors such as the prices of inputs and the market prices of agricultural products. However, another factor contributing to the reduction of profits from agricultural products is related to internal factors, such as the inefficiency of farmers (Mizik 2023).

Efficiency assessment in agricultural production is crucial to implementing agricultural development processes in developing countries (Tenaye 2020). Efficiency is essential to ensuring the long-term sustainability of organisations in critical economic sectors across different societies. Optimisation of resource consumption through improving economic units’ efficiency is important. Efficient units prevent resource wastage and ensure the proper allocation of resources (Adom and Adams 2020).

The efficiency of a production company is derived from its performance in utilising available resources (Jiang et al. 2024). The existence of inefficiency in production indicates that there is potential for increasing production without additional inputs and new technologies (Amirteimoori et al. 2023).

In many developing nations, agricultural output falls notably behind that of developed countries due to inadequate utilisation of production resources and low efficiency. A key issue in these countries’ agricultural sectors lies in the weak management and technical inefficiencies of farms (Khatri-Chhetri et al. 2023). Hence, acknowledging the resources and constraints within the agricultural domain, the optimal solution for enhancing production, income generation, and reducing costs revolves around efficiently allocating available production resources and enhancing efficiency (Yang et al. 2023).

Potatoes rank among the foremost tuber crops cultivated globally, particularly thriving in semi-tropical and temperate climates (Wang et al. 2020). This strategic crop plays a crucial role in income generation, employment, livelihood opportunities, food security, and nutrition. Following wheat, rice, and corn, potatoes rank fourth globally as a consumable and food-producing crop (Zhang 2023).

According to the 2021 FAO statistics, the global cultivated area of potatoes is approximately 18.13 million hectares, with a production exceeding 376 million tons per year. Most potato production occurs in industrialised countries, with China, Russia, Ukraine, and Poland as major global producers. Potatoes are a significant worldwide crop and a major agricultural product in Afghanistan, ranking third after wheat and rice (WFP 2023). FAO studies indicate that potato yields in Afghanistan are two to seven times higher than wheat. Consequently, potatoes are recognised for their higher productivity and economic value compared to grains, which is crucial in addressing food insecurity in Afghanistan (Hashemi et al. 2019).

In Afghanistan, the potato cultivation area in 2021 was 53,494 hectares, yielding 879,372 tons, with an average yield of 16 tons per hectare (FAO et al. 2022). The strategic province of Baghlan in central Afghanistan has a long history as a vital centre for agricultural activities. This province’s cultivated potato area is 2326 ha, producing 37,216 tons, with an average yield of 16 tons per hectare (Agriculture Department of Khinjan County 2022).

Within Baghlan province, Khinjan district stands out as a central point, particularly due to its role as the epicentre of potato cultivation. The geographical complexities of Khinjan district, along with favourable climatic conditions, provide an ideal location for potato cultivation. The diverse landscapes and variations in environmental climate create conducive conditions for cultivating this primary crop, underscoring Khinjan’s importance in agricultural production in Afghanistan. Of the acreage of cultivable land in this district, 310 ha are dedicated to potato cultivation (Muradi and Boz 2018).

With the increasing demand for potatoes in local markets and the global trade scene, understanding production efficiency in the Khinjan district becomes highly significant. As a staple in the Afghan diet and a commodity in growing demand internationally, potatoes play a crucial role in regional economic development (Agriculture Department of Khinjan County 2022). Increasing potato production is possible through two avenues: expanding cultivated area and enhancing yield per unit area (Devaux et al. 2021). This can be achieved by using modern and appropriate technology and establishing coordination among production factors in an efficient management system. Weak management and economic inefficiency of production units are among the main obstacles to improving productivity (Rashid et al. 2024).

The existing challenges in potato cultivation have led to Afghanistan’s production capacity having lower performance per unit area compared to most countries worldwide, indicating the lower efficiency of this crop in the country (Radmand et al. 2023). Agricultural efficiency encompasses numerous dimensions, each integral to the success of agricultural endeavours, making it a multifaceted concept (Rezaei et al. 2024).

This study employs four key criteria to explore efficiency (technical, managerial, scale and economic). Technical efficiency (TE) serves as a comprehensive gauge, assessing the overall utilisation of resources in the potato production process. TE provides a holistic picture of how resources are effectively employed in potato production, from land allocation to workforce management and capital utilisation. Delving deeper into the intricacies of production (Rashid et al. 2024), pure technical efficiency (managerial efficiency) (PTE) scrutinises the effectiveness of management practices (Cong 2022). Scale efficiency (SE), focusing on optimal production scale (Alam et al. 2020), provides insights into whether potato farms in Khinjan operate at their maximum potential. In economic efficiency (EE), understanding the subtle relationship between efficiency and scale is beneficial for optimising resource utilisation and ensuring the long-term sustainability of agricultural practices. Despite agriculture’s crucial role in Afghanistan, more comprehensive studies need to quantify the efficiency of specific crops (Chen et al. 2023).

This research focuses on potato producers and aims to address the gap in potato production in the Khinjan district. Through a meticulous examination of TE, PTE, SE, and EE, our study seeks to uncover the complexities of potato production. The lack of detailed empirical studies challenges informed decision-making among policymakers, farmers, and other stakeholders. By conducting this research, we aspire to contribute valuable knowledge that can inform policies, guide best practices, and ultimately enhance the efficiency and sustainability of potato cultivation in the Baghlan province.

Many research endeavours have evaluated the efficiency of agriculture, focusing on TE, PTE, SE and EE. For example, Tung (2013) examined the TE and SE of rice producers in Vietnam’s Mekong Delta using data envelopment analysis (DEA). The findings revealed a notable shift in TE between 2002 and 2010, displaying an upward trajectory. However, the surge in efficiency was primarily driven by scale, highlighting the necessity for overall expansion in rice production scale and land utilisation, especially in targeted regions.

Tung (2013) investigated the TE and SE of rice producers in the Mekong Delta of Vietnam using data envelopment analysis (DEA). The correct data includes sample production sets from 1998, with biennial updates from 2002 to 2010.. On the other hand, the increase in efficiency was dominated by the scale, indicating the need for an overall increased scale of rice production and land use expansion, particularly in specific areas.

Karimov et al. (2014) investigated the SE of maize farmers in the northwest area of Nigeria employing DEA. The outcomes revealed inefficiencies in both production and scale within maize farming. The research concluded that opportunities for enhancing efficiency remain within the existing maize production methods. Moreover, various socio-economic factors such as off-farm jobs, education, support services, and access to credit were identified as positively influencing the technical efficiency of agricultural households.

Dashti et al. (2019) conducted a study using a production function to investigate the relationship between efficiency and sustainability of potato cultivation in the Kabudarahang district of Iran. The Stochastic Frontier Analysis (SFA) approach was employed to determine sustainability, and the random frontier production function approach was utilised for efficiency determination. The results indicate that the TE of farmers in this product ranges from 53 to 96%, with an average efficiency of 84%. Regression model estimation results showed a significant relationship between agricultural sustainability and efficiency.

Anang (2021), using the Data Envelopment Analysis (DEA) method, examined the technical, allocative, cost, and profit efficiencies of potato cultivation and input usage in 23 provinces of Iran. The results indicated average technical, allocative, and cost efficiencies of 0.917, 0.643, and 0.742, respectively. The average profit per hectare of irrigated potatoes can be increased to 17.01 million Iranian Rials. Among the studied provinces, Zanjan, West Azerbaijan, and Semnan had the lowest efficiency rankings in profitability, scoring 0.160, 0.240, and 0.260, respectively.

Anang (2021) investigated the TE and SE of groundnut producers in Ghana using DEA. The findings indicated that farmers operated at 70% technical efficiency under variable returns to scale and achieved 73% efficiency in terms of scale. Factors influencing TE included farmers’ gender, farming experience, household size, exposure to extension services, and participation in off-farm activities, as well as the presence of pests and diseases. SE was affected by educational attainment, household size, membership in farmers’ groups, and the size of the farm.

Hassan (2021) examined the efficiency, economic performance, and scale of broiler production units using DEA. The findings revealed an average TE of 0.915 under Constant Return to Scale (CRTS) and 0.985 under Variable Return to Scale (VRTS). The average allocative and economic efficiencies were assessed at 0.941 and 0.918, respectively, with only 2% of farms achieving complete allocative and economic efficiency. Furthermore, the average scale efficiency (SE) was 0.929, with the majority of broiler farms (82%) operating with increasing returns to scale.

Aprilia and Prihtanti (2023) analysed potato production efficiency in Ngaduman, Getasan district, Semarang subdivision, India, using a production function. The research involved interviews with 30 potato farmers through purposive sampling. Results showed that land area and labour positively and significantly affected potato productivity. However, seeds, fertilisers, and pesticides did not significantly impact potato productivity. Seed and labour inputs were not specifically efficient, while fertiliser and pesticide inputs could have been more efficient.

Marcomini et al. (2023) employed a random frontier approach to analyse the factors influencing potato production’s technical and economic efficiency in Brazil. The results revealed an average technical efficiency of 82%, cost efficiency of 83%, and profit efficiency of 40%. Harvesting, processing, and utilising systems and skills for farm management were identified as the primary determinants of potato production efficiency in the studied region.

Using DEA, Putri et al. (2023) evaluated the TE and influencing factors in potato production in the Karangjaya region of Purwalingga, Indonesia. The results revealed that, according to the CRTS method, 71.45% of potato farming operations were efficient, whereas the VRTS approach indicated 51.43% efficiency. On average, TE stood at 88.30% under CRTS and 91.90% under VRTS. Farms achieving CRTS conditions represented 51.43% of the total.

Radmand et al. (2023) investigated the efficiency of wheat producers in the Dihdadi district using the DEA approach. These results suggest that enhancing the efficiency of wheat producers in this district could lead to improvements of 14.2%, 36.8%, 45.9%, 3.6%, and 43.6% in technical, allocative, economic, management, and scale efficiencies, respectively. Furthermore, the analysis reveals that 16.95% of wheat producers operate with decreasing returns to scale, 72.2% with increasing returns, and only 10.85% operate at constant returns to scale.

Sultana et al. (2023) assessed the efficiency of potato production in Bangladesh using random frontier analysis and DEA. The findings highlighted notable inefficiencies in the economic, technical, and allocative dimensions of potato farming, implying the potential for enhanced potato production through efficiency enhancements. Additionally, the analysis of inefficiency indicated that infrastructural and socio-economic factors collectively shape the diversity of potato production.

This study delves into the efficiency of potato producers in the Khinjan district, focusing on TE, PTE, SE and EE. By identifying specific areas where efficiency can be improved, the study provides actionable insights for both policymakers and farmers to boost productivity and sustainability. The findings not only enhance our understanding of agricultural efficiency in developing countries but also offer practical strategies to strengthen food security and economic stability in the region. The research assumes that the surveyed 252 potato farmers accurately represent the broader population and that the data collected are precise and reliable. Furthermore, the study employs the DEA model, chosen for its suitability in evaluating agricultural efficiency due to its ability to manage multiple inputs and outputs without a predefined functional form. The input-oriented DEA model is particularly appropriate for this study, as it emphasises reducing input usage while maintaining production levels, which is crucial given the resource limitations faced by local farmers.

Methodology

Research Area

The study area is the Khinjan district in the Baghlan province of Afghanistan. Baghlan is among the agricultural and industrial provinces in northeast Afghanistan. Covering an area of approximately 21,118 km2, the province is geographically positioned at 29° and 31′ north latitude and 58° and 48′ east longitude. Baghlan is administratively divided into one central district and 14 other districts (Fig. 1), with its central district being Pol-e Khumri. As of 2020, the population of Baghlan province is estimated to be around 1,770,000 people, according to statistics provided by the Afghan government (WPR 2023). The climate of Baghlan is characterised as temperate, experiencing cold winters and warm summers. Winter temperatures range from minus 22 to 32 °C, while summer temperatures can reach 40 to 48 °C. The average annual precipitation in this region is estimated to be 2698 mm (NSIA 2020).

Fig. 1
figure 1

Geographic location of Khinjan district in Baghlan province, Afghanistan

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Khinjan district is one of the districts within Baghlan province, Afghanistan, covering an area of 11,894 km2. It ranks as the seventh largest district in Baghlan province. As of 2020, the population of this district is approximately 45,411 people, according to the statistics provided by the Central Statistical Office. Khinjan district possesses 20,061 ha of cultivable land, with 1803 ha designated as irrigated land and 258 ha as rain-fed land. According to the available data for 2021, the cultivated area for potatoes in this district is reported to be 310 ha (NSIA 2021).

Khinjan district plays a pivotal role in the potato production landscape of Baghlan province, Afghanistan. As a major agricultural hub within the province, Khinjan significantly contributes to the overall potato yield of Baghlan. The district’s favourable climatic conditions, characterised by an altitude ranging from 1200 to 2500 m above sea level, and its diverse topography provide an ideal environment for potato cultivation. Moreover, Khinjan district benefits from seasonal streams and rivers fed by mountain snowmelt. These water resources are vital for irrigation, ensuring that potato crops receive sufficient moisture, especially during critical growth periods.

In Baghlan province, approximately 2326 ha are dedicated to potato farming, producing around 37,216 tons of potatoes annually. Khinjan district, with its 310 ha of potato fields, is a leading contributor within the province. This district alone accounts for a substantial portion of Baghlan’s total potato output, underlining its importance in the region’s agricultural economy. The prominence of Khinjan in potato production is attributed to its strategic location, which offers optimal growing conditions, and the dedicated efforts of local farmers. This district’s significant share in the province’s potato production not only supports local food security but also contributes to the economic stability of the region, reinforcing its role as a key player in Baghlan’s agricultural sector (MAIL 2019).

Empirical Model

Stochastic frontier analysis (SFA) and data envelopment analysis (DEA) are key methodologies for assessing production efficiency. SFA, a parametric approach, estimates the production frontier—the maximum attainable output given specific inputs—assuming a functional form like the Cobb–Douglas or Translog production function. By incorporating a stochastic error term, SFA accounts for random fluctuations and measurement errors, allowing for the identification of inefficiency. This enables the derivation of technical efficiency scores for individual units, facilitating comparisons and pinpointing inefficiency factors.

DEA, in contrast, is a non-parametric method that constructs the production frontier from the best-performing units in the dataset, without assuming a specific functional form. This flexibility makes DEA suitable for complex production systems without detailed functional knowledge. DEA assesses the relative efficiency of decision-making units (DMUs) by comparing their performance to the constructed frontier, considering both input minimisation and output maximisation. It handles multiple inputs and outputs simultaneously, making it ideal for intricate production processes or data constraints.

While SFA relies on specified functional forms and stochastic error, DEA uses observed data to construct the frontier. The choice between SFA and DEA depends on data availability, production system complexity, and modelling preferences. Both methods offer valuable insights into production efficiency, guiding decisions to enhance productivity.

The study utilised two variations of the DEA model, namely the input-oriented Banker, Charnes and Cooper (BCC) model and Charnes, Cooper, and Rhodes (CCR) model. The CCR model operates under the CRTS assumption (Kohl and Brunner 2020). On the other hand, the BCC model is based on the VRTS assumption. Efficiency estimates were computed using the DEA solver software, version 2.1 (Zarrin and Brunner 2023). The assessment of efficiency considered three distinct aspects, as defined by Diacon et al. (2002):

  • Technical efficiency (TE) describes the degree to which a firm optimally utilises its resources in the production process to achieve the highest possible output level. Simply put, it evaluates how efficiently a business transforms inputs like labour, capital, and resources into outputs, such as goods and services (Li and Ito 2023).

  • Pure technical efficiency (PTE) evaluates the effectiveness with which a firm can decrease its inputs (in a fixed ratio) while remaining within the variable returns to scale (VRS) frontier. Essentially, TE measures the overall efficiency of a decision-making unit (DMU) in utilising its inputs.

  • Scale efficiency (SE) indicates the extent to which a company, projected to the VRS efficiency frontier, can further decrease its inputs (in fixed proportions) while operating within the constant returns to scale (CRTS) frontier. SE assesses how efficiently a company can reduce inputs by moving to a frontier segment with more favourable returns to scale characteristics (Alam et al. 2020).

  • Economic efficiency (EE), a concept often used in microeconomics, refers to the optimal functioning of a product or service market. It involves producing goods or services at the lowest possible cost, achieving maximum output, and generating the highest possible surplus from market operations (Petrou 2014).

The input-oriented DEA model was selected because the primary focus of this study is on minimising input usage while maintaining the current level of potato production. This approach is appropriate given the context of resource constraints faced by farmers in Khinjan district.

The selection of DEA is motivated by three key factors: (1) its non-parametric nature, eliminating the need for a predetermined functional form; (2) its capability to handle small sample sizes; and (3) its ability to decompose TE into PTE and SE, with TE being the product of PTE and SE (Xu et al. 2020). Achieving PTE requires a firm to shift to the variable return to scale (VRTS) frontier established by the BCC model. On this frontier, a firm can demonstrate increasing returns to scale (IRTS), constant returns to scale (CRTS), or decreasing returns to scale (DRTS). If a firm operates with either IRTS or DRTS, improving technical efficiency is feasible by transitioning to CRTS. When PTE equals TE for a firm, it operates with CRTS and is deemed scale efficient, indicating SE equals 1. Another approach to determining scale efficiency is expressed as \(SE=\frac{\theta CRS}{\theta VRS}\), where \(\theta CRS\) and \(\theta VRS\) represent efficiency scores under Constant Return to Scale (CRS) and Variable Return to Scale (VRS), respectively (Blas-Cortés et al. 2023).

CCR Model

Designate the entity to be evaluated, DMUj, as DMUo, where o spans from 1 to n. We address the ensuing fractional programming problem to derive values for the input “weights” (vi) (i = 1,…,m) and the output “weights” (ur) (r = 1,…,s) as variables.

$$(F,Po){}_{u,v}^{Max\theta}=\frac{V_1Y_{10}+V_2Y_{20}+\cdots+V_sY_{SO}}{V_1Y_{10}+V_2X_{20}+\cdots+V_sY_{SO}}$$
$$\begin{array}{ll}\text{Subject to}& \frac{{V}_{1}{Y}_{1j}+\dots +{V}_{S}{Y}_{sj}}{{V}_{1}{X}_{1j}+\dots +{V}_{s}{X}_{sj}}\le 1\left(j=1,\dots ,n\right)\\ & {V}_{1},{v}_{2},\dots ,{v}_{m}\ge 0.\\ & {V}_{1},{V}_{2},\dots ,{V}_{s}\ge 0.\end{array}$$

The aforementioned fractional program (FPo) can be substituted with the subsequent linear program (LPo).

$$\begin{array}{cc}\left(F, {P}_{o}\right)& {}_{u,v }{}^{\text{Max}\theta }={V}_{1}{Y}_{10}+\dots +{u}_{s}{Y}_{so}\end{array}$$
$$\begin{array}{ll}\text{Subject to}& {V}_{1}{X}_{10}+\dots +{v}_{s}{x}_{mo}=1\\ & {\mu }_{1}{y}_{1j}+\dots +{\mu }_{s}{y}_{sj}\le {v}_{1}{x}_{1j}+\dots +{v}_{m}{x}_{mj}\\ & (j=1,\dots ,n)\\ & {v}_{1},{v}_{2},\dots ,{v}_{n}\ge 0\\ &{\mu }_{1},{\mu }_{2},\dots ,{\mu }_{s}\ge 0\end{array}$$

DMUo achieves CCR efficiency when θ* equals one and at least one optimal solution (v*,u*) with v* and u* both greater than 0. Otherwise, DMUo is considered CCR-inefficient. Organising the datasets into matrices X = (xj) and Y = (yj), the production possibility set P can be defined as follows:

$$P=\{\frac{x,y}{x}\ge X\lambda ,y\le Y\lambda ,\lambda \ge 0\}$$

Here, λ represents a non-negative vector in real numbers Rn. The linear program in multiplier form can now be expressed as

$$\left({LP}_{0}\right){}_{v,u}{}^{\text{max}} {uy}_{0}$$
$$\begin{array}{cc}\text{subject to}& {vx}_{0}=1\\ & -vX+vY\le 0\\ &v\ge 0, u\ge 0\\ &\left({DLP}_{0}\right){}_{\theta ,\lambda }{}^{\text{min}} 0\end{array}$$
$$\begin{array}{cc}\text{Subject}& \theta {x}_{0}X\lambda -\ge 0\\ & Y\lambda \ge {y}_{0}\\ & \lambda \ge 0\end{array}$$

The dual problem corresponding to (LPo) is formulated using a real variable θ and a set of non-negative variables represented by the vector λ = (λ1, λ2, …, λn) in the form of envelopment, outlined as follows:

$$({DLP}_{0}){}_{\theta ,\lambda }{}^{\text{min}} 0$$
$$\begin{array}{cc}\text{Subject to}& \theta {x}_{0}-X\lambda \ge 0\\ & Y\lambda \ge {Y}_{0}\\ & \lambda \ge 0\end{array}$$

DLPo exhibits a workable solution with θ = 1, λo = 1, and λj = 0 (for j ≠ 0). We characterise the input excesses as s-ε Rm and the output shortfalls as s + ε Rs, labelling them as “slack” vectors, expressed as

$${s}^{-}=\theta {x}_{0}-X\lambda ,{S}^{+}=Y\lambda -{y}_{0},$$

with \({s}^{-}\ge 0\), \({s}^{+}\ge 0\) for any feasible solution (θ,λ) of (DLPo).

Now a DMUo is called CCR if its θ* = 1 and all slacks are zero (\({s}^{-}\)* = 0, \({s}^{+}\)* = 0).

BCC Model

The BCC model in the input-oriented form assesses the efficiency of DMUo (o = 1,2,…,n) through the resolution of the subsequent linear program in envelopment form:

$${(\text{BCC}}_{0}) {}_{\theta B,\lambda }{}^{\text{min}} {\theta }_{B}$$
$$\begin{array}{ll}\text{Subject to}& {\theta }_{B}{X}_{0}-X\lambda \ge 0\\ & Y\lambda \ge {y}_{0}\\ & e\lambda =1\\ & \lambda \ge 0\end{array}$$

where \({\theta }_{B}\) is a scalar.

The dual form of multipliers corresponding to this linear program (BCCo) is articulated as follows:

$$\begin{array}{cc}\overset{max}{v,u,u_0}&z={uy}_0-u_0\end{array}\\$$
$$\begin{array}{cc}\text{Subject to}&{vx}_0=1\\&-vX+uY-u_0e\leq0\\ & v\geq0,u\geq0,u_0\text{ free in sign,}\end{array}$$

In this context, v and u represent vectors, while z and uo are scalars. The latter, described as “free in sign,” can be positive, negative, or zero. The corresponding BCC fractional program is derived from the dual program as follows:

$$\text{max}\frac{{uy}_{0}-{u}_{0}}{{vx}_{0}}$$
$$\begin{array}{cc}\text{Subject to}& \frac{{uy}_{j}-{v}_{0}}{{vx}_{j}}\le 1 \left(j=1,\dots ,n\right)\\ & v\ge 0, u\ge 0,{u}_{0} \text{free}\end{array}$$

If the optimal solution (θ*B, λ*, s−*, s+*) achieved through this two-phase procedure for (BCCo) meets the conditions θ* = 1 and has no slacks (s−* = 0, s+* = 0), the DMUo is classified as BCC-efficient; otherwise, it is considered BCC-inefficient (Kohl and Brunner 2020).

Results

The results of the descriptive analysis of potato farmers in the Khinjan district of Baghlan province, Afghanistan, are presented in Table 1. The data analysis indicates that potato farmers varied in age from 19 to 78 years, with an average age of 43.6 years. Therefore, it is evident that the farmers in the region are, on average, middle-aged. The educational attainment of the farmers averages 7 years, suggesting that the studied population has a moderate literacy level. On average, these farmers have six dependents. The operators’ experience ranges from 2 to 40 years, with an average operational experience of 20. The maximum cultivated area for this crop is 0.60 ha, the minimum is 0.10 ha, and the average cultivated area per operator is 0.32 ha.

Table 1 Descriptive statistics of potato producers of Khinjan district
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Furthermore, the analysis of central tendencies and dispersion of economic variables for the potato crop are presented in Table 2. It indicates that the production performance of potatoes varied from 3040 to 12,981 kg per hectare, with an average yield of 8844.9 kg per hectare. The average income obtained from 1 ha of this crop is 118,2267.8 Afghanis, with the minimum income being 60,800 Afghanis and the maximum income equivalent to 298,541 Afghanis. The average production costs per hectare are estimated at approximately 68,219 Afghanis, with the minimum and maximum costs being 39,423 and 139,172 Afghanis, respectively. Additionally, the average selling price of the product in 2023 the local market is 20.55 Afghanis. Moreover, the average profit per hectare from potato production, according to questionnaire results, is estimated at 114,058.8 Afghanis. In the data collection process, labour costs were calculated on a daily wage basis, while land costs and other fixed expenses, such as machinery and tools, were computed as rentals.

Table 2 Income, cost, price, and benefit of potato producers of Khinjan district
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Table 3 presents the results of the descriptive statistics of variables considered in the data envelopment analysis (DEA) model. In this table, the averages, minimum and maximum input consumption, standard deviations, average prices per unit, average costs per input, and average share of each factor in potato production in the Khinjan district are shown for inputs such as land, phosphate fertiliser, nitrogen fertiliser, seed, labour, water, and machinery. Accordingly, the highest cost shares in production are attributed to seed, land rental, and labour, accounting for 22.9%, 21.4%, and 20.5%, respectively. Subsequently, phosphorus fertiliser and machinery costs are in the next tiers. The lowest cost share is associated with the fungicide input, which is equivalent to 1.0%. The cost shares of herbicide and insecticide inputs follow in the subsequent ranks. The study area boasts abundant water resources, leading to potato farmers incurring no costs for water usage.

Table 3 Descriptive statistics of variables used in the DEA model
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Table 4 presents the statistical description of potato producers’ performance results in TE, PTE, and SE in Khinjan district. The average TE, PTE, and SE are 0.8129, 0.9668, and 0.8377, respectively. The lowest efficiencies in each category are 0.4450, 0.6710, and 0.447, while the highest are all at 1. This indicates a significant disparity between the best and worst potato producers in the studied region.

Table 4 Frequency distribution of TE, PTE, SE, and EE of potato producers
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From an institutional perspective, this difference implies that potato producers can achieve similar output levels by utilising fewer production inputs, as they need to utilise their production inputs optimally. The examined units can potentially increase their TE by reducing the use of inputs without compromising their output, thus preventing the wastage of production inputs and improving overall production efficiency.

The results reveal a 55.5% and 32.9% gap in TE and PTE between the best and worst producers among the investigated units. Additionally, the average potato producer in the study area can reduce input consumption by 18.71% and 3.32%, respectively, without altering production levels, thereby enhancing efficiency. Furthermore, technical, pure technical, scale and economic inefficiencies for potato producers in Khinjan district are 18.71%, 3.32%, 16.32%, and 0.478, respectively.

Eliminating scale inefficiency will increase the average TE of farms from 0.8129 to 0.9668. Addressing SE involves considering units with IRTS, allowing them to improve efficiency by increasing production inputs. Similarly, units with DRTS should avoid adding inputs to their production process to enhance efficiency.

The research findings indicate that agriculture in the studied region is primarily subsistence-oriented and operates on a small scale. The primary objective of farmers is to reduce production costs, a goal supported by the study results presented in Table 5. It has been observed that 68.25% of farmers operate with IRTS, 2.38% with DRTS, and only 29.13% at an optimal scale (CRTS). Consequently, increasing the use of inputs and expanding the production scale align with the region’s goal of increasing production levels and farmers’ income.

Table 5 Return to scale of potato producers of Khinjan district
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The economic logic driving this choice lies in the fact that, with IRTS, the output ratio surpasses the input increment, leading to greater potato yields per additional input unit. Assuming constant prices for all production factors, this occurrence results in movement along the average cost curve. As production scale and size grow, unit production costs decline. The allocation, division of labour, and technological factors enable producers to lower unit costs by expanding production scale.

Discussion

The study sheds light on key insights into potato production efficiency, economic performance, and scale considerations in Khinjan district, Baghlan province, Afghanistan. The analysis uncovers significant variations in potato yield, income, production costs, and selling prices among farmers, mirroring the diverse economic landscape of the region. Despite the predominantly subsistence and small-scale nature of agriculture in this area, there is considerable potential for improving efficiency and increasing productivity.

The analysis of TE reveals that while many potato producers exhibit commendable performance, there is room for improvement, especially among those with lower efficiency scores. Closing the gap between the most and least efficient operators could yield substantial gains in technical efficiency, optimising resource utilisation without sacrificing output levels. Additionally, the assessment of managerial efficiency indicates a high level of proficiency among potato farmers in the Khinjan district, demonstrating effective resource utilisation to maximise yield. However, focusing on managerial practices could further enhance efficiency and productivity across the sector.

The analysis of composite image scale efficiency reveals that a significant portion of farmers operates optimally under scale conditions. Addressing scale inefficiencies presents an opportunity to enhance overall productivity by aligning input usage more effectively with production requirements. The analysis of economic efficiency among potato producers in Khinjan County reveals significant disparities in performance, with a wide range between the least and most efficient producers. The average efficiency level indicates room for improvement, and a substantial portion of producers is operating inefficiently. Overall, these findings underscore the importance of improving efficiency, expanding scale, and enhancing management practices to unlock the full potential of potato production in Khinjan district. By seizing these opportunities, farmers can not only improve their economic well-being but also contribute to agricultural development goals and regional food security.

The economic rationale behind the observed trends in potato production yields and scale considerations fundamentally relates to increasing returns to scale. As farmers expand their production scale, they experience a proportionate increase in output relative to the increase in inputs, leading to higher potato yields per additional unit of input. This phenomenon, combined with fixed prices for production factors, guides movement along the average cost curve, consequently reducing production costs with increased production size.

Resource allocation, division of labour, and the adoption of technological advancements play pivotal roles in empowering producers to achieve scale efficiencies and reduce unit costs. By strategically expanding production scale and optimising resource allocation, farmers can enhance their profitability and competitiveness in the market. Moreover, the observed shift towards efficiency improvement and scale expansion among potato farmers indicates a strategic response to economic incentives and market dynamics. By aligning production strategies with market demand and utilising available resources effectively, farmers can capitalise on income-generating opportunities and drive agricultural growth.

As a result, these findings underscore the importance of adopting efficient production methods, optimising scale, and embracing technological innovations to advance sustainable agricultural development in Khinjan and similar agricultural regions. By fostering an enabling environment for agricultural entrepreneurship and innovation, policymakers and stakeholders can support the growth and prosperity of the potato agricultural sector while contributing to broader socio-economic development goals.

To enhance the efficiency of potato producers in this region, targeted capacity-building initiatives should be implemented to strengthen technical and management skills among farmers. Training programs focusing on best practices in crop management, resource utilisation, and farm management can empower farmers to optimise their production processes and improve efficiency. Additionally, expanding access to extension services and technical assistance can provide timely guidance and support to farmers in adopting innovative technologies and sustainable agricultural practices.

Measures to promote joint efforts and collective action among farmers should also be encouraged. The establishment of farmer cooperatives or producer groups can facilitate resource pooling, knowledge sharing, and collective bargaining, thereby enhancing farmers’ access to inputs, markets, and support services. Through collective action, farmers can leverage economies of scale, negotiate better prices for inputs and outputs, and strengthen their bargaining power in the market. This ultimately leads to improved profitability and resilience in the face of market uncertainties and challenges.