The Agro-climatic conditions of Himachal Pradesh make it ideal for cultivating temperate to sub-tropical fruits. As a result, there has been a shift in cultivation patterns from Agriculture to Horticulture crops over the past few decades. The area devoted to fruit cultivation in Himachal Pradesh has grown significantly, from 792 hectares in 1950-51, yielding 1,200 tonnes, to 2,33,300 hectares in 2019-20, with total production reaching 8.45 lakh tonnes. Apple remains the most significant fruit crop contributing around 85% of total fruit production with 49% of the total area under fruit crop in the region. There has been a significant rise in area under apple cultivation from 400 hectares in 1950-51 to 3,025 hectares in 1960-61 and reached 1,14,144 hectares by 2019-20. The shift towards fruit cultivation especially Apple due to the commercialization of the same in Himachal Pradesh requires proper study to find out whether the farmers are making the best use of the resources. (Economic Survey Report 2018-19).
       
Several studies were conducted by Bhat and Dhar (1989); Singh and Vashist (1994); Haque (2006); Kumar and Sharma (2011); Kireeti (2013); Singh (2013); Ravi et al. (2017); Kumari et al. (2018); Venkatraman et al. (2019); Bey et al. (2022); Sindhu et al. (2023); Chotaliya et al. (2024); Adaik et al. (2024) and Ishita et al. (2025) to understand the input-output relationship in agriculture production and all the given studies identify that factor inputs like fertilizers, human labour, manures etc influence the agriculture production but misuse of the same can make the crop production inefficient therefore considering this aspect, a study was conducted at two different Tehsils (Kotkhai and Jubbal) of District Shimla of Himachal Pradesh to understand the resource and allocative efficiency on Apple crop production of different farm sizes and to find whether the farmers are making the best utilisation of resources or if there are possibilities for improvement.
               
Jubbal and Kotkhai play a significant role in apple cultivation in the Shimla district, with most of the local population dependent on this activity for their livelihood. Therefore, this study contributes to understanding the key factors influencing apple production and highlights the issue of resource overutilization. By identifying these factors, the study can help farmers minimise resource wastage through better allocation, ultimately enhancing resource efficiency and profitability across all farm sizes in apple cultivation.

The present study was conducted in the Jubbal and Kotkhai Tehsils of the district Shimla, where the field survey was conducted on 200 farming households of different farm sizes with the help of a questionnaire. The stratified random sampling method has been used, where the study area was divided into 10 different panchayats, with an equal distribution across both Tehsils. From each panchayat, two villages were selected and 10 farming households from each village-representing different categories (Marginal, Small and Medium)-were randomly chosen. The Study primarily relies on primary data, collected through personal interviews, face-to-face interactions with farmer respondents and observational methods to gather relevant information.
 
Resource use efficiency
 
Land, labour, manure and other resources are vital in agricultural production. To assess resource use efficiency, it is essential to understand the marginal productivity of each factor, which can only be determined if the full technical relationship between output and input is known. Therefore, in this study, the Cobb-Douglas production function has been employed to analyse resource use efficiency across Marginal, Medium and Small farms. The specification of the model for Apple production in Marginal, small and medium farms is given as:
 

Y=    Ax₁^b1 x₂^b2 x₃^b3 x₄^b4 x₅^b5 e^u

 
Were
Dependent variable, Y= Gross returns (Rs/farm).
Independent variables,
X₁ = Land (hectares/farm).
X₂ = Human labour (Mandays/farm).
X₃ = Manures and fertilisers (Rs/farm).
X₄ = Seed (Rs/farm).
X₅ = Others (Rs/farm).
a = Constant (Intercept term).
u = Random variable.
       
b₁ to b₅ indicate the regression coefficient of respective inputs and implicitly represent the elasticities of the production of factor inputs. A positive elasticity of less than one indicates decreasing marginal productivity of factor inputs. The larger the elasticity of factor input, the larger the increase in output in response to a given proportionate increase in that factor input, with other inputs held constant. Negative production elasticities of factors indicate their inefficient and excessive use.
       
Such a type of function can be transformed into the logarithmic form so that it can be solved by the methods of least squares.
 

Log Y = log A + b₁LogX₁ + b₂LogX₂ + b₃LogX₃ + b₄LogX₄ + b₅LogX₅

 
The statistical significance levels of regression coefficients were worked out to determine the goodness of fit. It was carried out by calculating the ‘t’ statistics by following the formula for regression coefficients.

The sum of these production elasticities indicates returns to scale, which indicates the proportionate increase in output when all the inputs are increased by the same proportion. If this sum is less than, equal to or greater than unity, it indicates decreasing, constant or increasing returns to scale, respectively.
       
The resources are said to be efficiently allocated if their MVP is equal to its acquisition unit price therefore for efficient resource utilisation in crop production, the marginal value product (MVP) must be equal to the marginal factor cost (MFC), It was calculated by using the formula shown below:

 
The marginal value productivity of inputs is calculated as:

 
Where,
MVP = Marginal value productivity of i^th input.
β_i = Regression coefficient associated with i^th input.
Y = Geometric mean of output.
X_i = Geometric mean of i^th input.

Where,
AE = Allocative efficiency.
MVP = Marginal value product.
MFC = Marginal factor cost.
AE = 1, it indicates efficient use of resources.
       
AE < 1 indicates a particular resource is over-utilised, i.e., the profit level can be increased by decreasing the quantity of a particular input used.
               
AE > 1 indicates a particular resource is being under-utilised, i.e., the profit level can be increased by increasing the quantity/rate of input particular used.

Production involves the process where resources are used to produce some product therefore farmers also make use of various resources such as human labour, bullock power, mechanical power, water for irrigation, seeds, manures and fertilizers, insecticides and pesticides to produce the different crop but the output of the crop depends upon the productive and allocative efficiency of the resources. The Cobb-Douglas production function shows the relationship between various inputs and crop yield of different farm sizes of different Tehsils and therefore reveals the efficiency.
 
Resource utilization and efficiency of marginal farms in Jubbal and Kotkhai Tehsil
 
In apple production, critical resources include land, labour, fertilisers, seeds and other inputs. Table 1.1 highlights the comparative analysis of two tehsils marginal farmers resource utilisation patterns. The Tehsil Kotkhai farmers use on average: Labour: 3,105 mandays/ha, Fertilizer: ₹ 368,311/ha, Seeds: ₹6,613/ha, other inputs: ₹359,932/ha and Tehsil Jubbal farmers use: Labour: 3,206 mandays/ha, Fertilizer: ₹342,879/ha, Seeds: ₹5,625/ha, other inputs: ₹334,205/ha. In terms of gross output, Kotkhai yields ₹5,155,181 per hectare and ₹1,660 per manday of labour and Jubbal yields ₹6,652,900 per hectare and ₹2,074 per manday of labour. As far as evaluating productivity per rupee invested in inputs, Kotkhai achieves: ₹13.99 per ₹1 of fertilizer, ₹7.79 per ₹1 of seeds, ₹14.30 per ₹1 of other inputs however Jubbal achieves: ₹19.40 per ₹1 of fertilizer, ₹11.82 per ₹1 of seeds and ₹19.90 per ₹1 of other inputs. The analysis reveals that Jubbal farmers utilise slightly more labour per hectare than Kotkhai farmers, whereas Kotkhai incurs higher costs in fertilizer, seeds and other inputs. However, Jubbal outperforms Kotkhai in output efficiency across all these input categories, resulting in higher returns both per hectare and per unit of input.


       
However, to reveal more understanding about the Input-Output, we have to go with more statistical analysis, which will explain the relative picture of resource efficiency.

Table 1.2 presents the regression coefficients for Apple crop production. The regression model includes several independent variables: land, human labour, manures and fertilizers, seeds and other inputs. For marginal farms in Kotkhai Tehsil, the variables land, labour and manures  and fertilizers are statistically significant at the 5% and 10% levels. This indicates that a 1% increase in the use of land, labour and manures and fertilizers results in an average increase in gross output of 0.86%, 0.78% and 0.52% respectively, demonstrating a positive relationship between these inputs and apple production. In contrast, the elasticity coefficient for seeds is -0.42%, which is statistically significant and suggests a negative impact on output. For marginal farms in Jubbal Tehsil, land and manures  and fertilizers show positive elasticity coefficients, while labour and seeds have negative coefficients; however, these are not statistically significant. The coefficient of multiple determination (R²) is relatively high for Kotkhai Tehsil at 0.81, indicating that the independent variables explain a substantial portion of the variation in apple output. In comparison, the R² value for Jubbal Tehsil marginal farms is lower, at 0.316, suggesting a weaker explanatory power of the model in that region.


       
The sum of the regression coefficients, or output elasticities, derived from the Cobb-Douglas production function for Marginal farmers in Kotkhai Tehsil was 1.99, while for Marginal farms in Jubbal Tehsil, it was 1.37. This indicates that if all factors of production were to increase simultaneously by 1.00 per cent, the output would increase by 1.99 per cent in Kotkhai Tehsil and by 1.37 per cent in Jubbal Tehsil’s marginal farms.
 
Allocative efficiency of marginal farms in Jubbal and Kotkhai Tehsil
 
Determining resource use efficiency involves estimating the marginal value products (MVP) of various resources. The MVP of each input is then compared to its corresponding factor price or marginal factor cost (MFC). This comparison provides a valid assessment of the efficiency with which inputs are allocated in the production process. Table 1.3 reveals the resource allocation picture for the Kotkhai and Jubbal tehsil marginal farms. In Kotkhai Tehsil, the marginal farms show the following ratios for the marginal value product (MVP): Land (0.00), Labour (0.00), Manures and Fertilizers (0.66) and Others (0.16). All of these are statistically less than unity, indicating that farmers are using these resources in excess. Additionally, the significantly low MVP ratio for Seeds (X4) at -0.91 suggests that their usage should be reduced to achieve higher returns.


       
In Jubbal Tehsil, the marginal farms exhibit MVP ratios of Land (0.00), Labour (0.00), Manures  and Fertilizers (0.28) and Others (0.39), all of which are also less than unity, pointing to the overutilization of these resources. Furthermore, the MVP ratio for Seeds at -1.33 indicates their overuse, suggesting that reducing seed usage would lead to higher returns.
 
Resource utilisation and efficiency of small farms in Jubbal and Kotkhai Tehsil
       
Resource utilisation and allocation give us understanding about the farm’s performance; therefore, in the current study, we have taken Land, Labour, fertilizers, seeds and other Inputs as the key resources in Apple cultivation. Table 2.1 reveals the utilisation pattern of different inputs for small farmers concerning the land (per hectare) and Gross Output (Rs). From the study, it is noticed that the Average labour Mandays, Fertilizers, seeds and other Inputs for Tehsil Kotkhai farmers are 3252 (Mandays per hectare), Rs 419296 (per hectare), Rs. 6672 (per hectare) and Rs. 404959 (per hectare) respectively in comparison to the Tehsil Jubbal farmers 2892 Mandays (per hectare), Rs. 297484 (per hectare), Rs. 4788 (per hectare) and Rs. 324346 (per hectare). As far as Gross output is concerned, for Land and Labour it is estimated to be Rs. 5155181(per hectare), Rs. 1660 (per man day) for Tehsil Kotkhai farmers and Rs. 6652900 (per hectare), Rs. 2074 (per man day) for Tehsil Jubbal farmers. However, Gross output per Rs. of Fertilizers, seeds and other inputs is concern, it is estimated to be Rs. 18, Rs 1112 and Rs. 148 for Tehsil Kotkhai farmers and Rs. 27, Rs. 1647 and Rs. 24 for Tehsil Jubbal farmers.



The study reveals that the per-hectare use of all the input resources for Kotkhai Farmers is more than compared of the Jubbal farmers. When one looks towards the Gross output, it looks that Jubbal has more Per Hectare Output in all the Inputs as compared to the Kotkhai farmers.
       
However, to reveal more understanding about the input-output, we have to go with more statistical analysis, which will explain the relative picture of resource efficiency.
       
Table 2.2 presents the regression coefficients for apple crop production on small farms in Jubbal and Kotkhai Tehsils. The independent variables in the regression model include Land, Human Labour, Manures and Fertilizers, Seeds and other inputs. Labour emerged as a statistically significant factor at both the 5% and 10% probability levels in both the Tehsils. Notably, the labour coefficient is higher for small farms in Jubbal Tehsil (1.38%) than in Kotkhai Tehsil (1.23%), indicating that a 1% increase in labour input would lead to a 1.38% and 1.23% increase in total returns, respectively. The coefficient for land is positive but not statistically significant in either Tehsils. Similarly, the coefficients for manures and fertilizers are negative and non-significant in both regions. In terms of seed input, the coefficient is positive (0.08%) for small farms in Jubbal Tehsil and negative (-0.22%) for those in Kotkhai Tehsil, though neither is statistically significant. The “Others” variable (X…) shows a positive but non-significant coefficient in Kotkhai and a negative, non-significant coefficient in Jubbal. The coefficient of multiple determination (R²) is relatively high-82.00% for small farms in Jubbal and 57.00% for those in Kotkhai-indicating that the included variables explain a substantial portion of the variation in output, with minimal influence from unaccounted factors.


       
The sum of the regression coefficients or output elasticities, derived from the Cobb-Douglas production function for small farmers in Kotkhai Tehsil was 1.03, while for small farms in Jubbal Tehsil, it was 1.19. This suggests that a simultaneous 1.00% increase in all factors of production would result in a 1.03% increase in output in Kotkhai Tehsil’s small farms and a 1.19% increase in output in Jubbal Tehsil’s small farms.

Allocative efficiency of small farms in Jubbal and Kotkhai Tehsil
 
Small farms resource allocation picture for Kotkhai and Jubbal tehsil had been revealed in Table 2.3. In Kotkhai Tehsil, the MVP ratios for Small farms in Land (0.00), Labour (0.00) and Others (0.10) are all statistically less than unity, indicating that these resources are being used in excess. Additionally, the significantly low MVP ratios for Seeds (X4) and Manures and Fertilizers, at -0.47 and -0.19, suggest that their usage should be reduced to achieve higher returns.


       
In Jubbal Tehsil, the MVP ratios for Small farms in Land (0.00), Labour (0.00) and Seeds (0.19) are also statistically less than unity, signalling overutilization of these resources. Furthermore, the negative MVP ratios for Seeds (-0.42) and Manures and Fertilizers (-0.62) indicate their overuse, suggesting that reducing their usage would lead to higher returns.
 
Resource utilization and efficiency of Medium Farms in Jubbal and Kotkhai Tehsil
 
Land, Labour, fertilizers, seeds and other Inputs are the key resources in Apple cultivation; therefore, Table 3.1 reveals the utilisation pattern of medium farmers for different inputs. Medium-scale apple farmers in Tehsil/ Kotkhai apply more inputs per hectare-3,217 labour mandays, ₹349,706 on fertilizer, ₹6,036 on seeds and ₹358,699 on other inputs-compared to those in Tehsil/Jubbal, who use 3,163 mandays, ₹260,012 on fertilizer, ₹4,585 on seeds and ₹349,213 on other inputs. Despite their lower input usage, Jubbal farmers outperform Kotkhai farmers in gross output per hectare- ₹8,066,966 versus ₹6,764,974-and deliver higher returns per unit of input: ₹2,551 per labour manday (vs. ₹2,103), ₹31 per rupee of fertilizer (vs. ₹19), ₹1,760 per rupee of seed (vs. ₹1,121) and ₹23 per rupee of other inputs (vs. ₹19).


       
However, to reveal more understanding about the Input-Output, we have to go with more statistical analysis, which will explain the relative picture of resource efficiency.
       
Table 3.2 presents the regression coefficients for apple crop production, incorporating the independent variables: Land, Human Labour, Manures  and Fertilizers, Seeds and Others. The labour input was found to be statistically significant at the 5% and 10% probability levels on small farms in both Jubbal and Kotkhai Tehsils. Notably, the regression coefficient for labour is higher on medium-sized farms in Jubbal Tehsil (1.03%) compared to Kotkhai Tehsil (0.65%), indicating that a 1% increase in labour input would lead to an increase in total returns of 1.03% and 0.65%, respectively. For the “Others” category of inputs, the coefficient on medium farms in Kotkhai Tehsil is both positive and statistically significant at the 5% and 10% levels, with a value of 0.53. This suggests that a 1% increase in these inputs would increase total returns by 0.53%. The coefficient for seeds (X₄) on medium farms in both Tehsils is positive but not statistically significant. Inputs such as Manures  and Fertilizers and Land show negative coefficients on medium farms in both Jubbal and Kotkhai Tehsils, though these relationships are not statistically significant. The coefficient of multiple determination (R²) is 0.90 for medium farms in Jubbal Tehsil and 0.63 for those in Kotkhai Tehsil, indicating that the model explains a substantial portion of the variation in output, particularly in Jubbal Tehsil.


       
The sum of regression coefficients is derived from the Cobb-Douglas production function. The sum of regression coefficients, i.e., output elasticities of Medium farmers of Kotkhai Tehsil was 1.15 and Tehsil Jubbal Medium farms was 0.84. It implies that if all the factors of production increased simultaneously by 1.00 per cent, then it will increase output by 1.15 and 0.84 per cent in medium farms.
 
Allocative efficiency of medium farms in Jubbal and Kotkhai Tehsil
 
Table 3.3 indicates the medium farms resource allocation for Kotkhai and Jubbal tehsil. In Kotkhai Tehsil, the MVP ratios for Small farms in Land (0.00), Labour (0.00), Seeds (0.04) and Others (0.66) are all statistically less than unity, indicating that these resources are being used in excess. Additionally, the significantly low MVP ratio for Manures  and Fertilizers (-0.02) suggests that their usage should be reduced to achieve higher returns.


       
In Jubbal Tehsil, the MVP ratios for Small farms in Land (0.00), Labour (0.00), Seeds (0.01) and Others (0.03) are also statistically less than unity, signalling overutilization of these resources. Furthermore, the negative MVP ratio for Manures  and Fertilizers (-0.06) indicates their overuse, suggesting that reducing their usage would lead to higher returns.

The study found that, in Kotkhai Tehsil, the elasticity of marginal farm production with respect to land, labor and manure  and fertilizers was statistically significant at the 5% and 10% levels. In contrast, in Jubbal Tehsil, while land and manure and fertilizers had positive elasticities for marginal farms, the elasticities for labor and seeds were negative-though these were not statistically significant. Moreover, the labor coefficient for small farms in Jubbal (1.38%) exceeded that in Kotkhai (1.23%), indicating that a 1% increase in labor yields a 1.38% increase in output in Jubbal, compared to 1.23% in Kotkhai. For medium-sized farms, the labor coefficient in Jubbal (1.03%) was also higher and statistically significant, compared to 0.65% in Kotkhai-suggesting that a 1% increase in labor input results in a 1.03% return increase in Jubbal and just 0.65% in Kotkhai.
       
In terms of allocative efficiency, the MVPs of Land, Labour, Seeds and Others are statistically less than unity for small, marginal and medium farms in both Kotkhai and Jubbal Tehsils. This indicates that farmers are using these resources in excess. Additionally, the MVP of Manures and Fertilizers is negative for small and medium farms in both tehsils, suggesting that their usage should be reduced to achieve higher returns.
 
Disclaimers
 
The views and conclusions expressed in this article are solely those of the authors and do not necessarily represent the views of their affiliated institutions. The authors are responsible for the accuracy and completeness of the information provided but do not accept any liability for any direct or indirect losses resulting from the use of this content.
 
Informed consent
 
All animal procedures for experiments were approved by the Committee of Experimental Animal Care and handling techniques were approved by the University of Animal Care Committee.

The authors declare that there are no conflicts of interest regarding the publication of this article. No funding or sponsorship influenced the design of the study, data collection, analysis, decision to publish or preparation of the manuscript.