Primary study area

The study was carried out in Ghana. Researchers collected primary data for this study from household surveys conducted in villages/communities selected from four regions (northern, Brong-Ahafo, eastern, and central regions) in Ghana from July to September 2019. These regions were purposively selected to cover all the agro-ecological zones and their maize production performance for the 2017-2018 farming seasons in Ghana.

The capital of the northern region is Tamale. In 2018, it had a population of about 3.576 million people and was ranked the fourth highest populous region in Ghana (^{EUROSTAT, 2018}). More than 75% of the economically active population work in agricultural and agricultural-related jobs in this region. Maize, rice, sorghum, and millet, are mostly grown in the northern region.

The Brong-Ahafo region is located in the southern part of Ghana. The capital of the Brong-Ahafo region in Sunyani. The Brong-Ahafo region has a total population of 2,310,983, with an average growth rate of 2.2% compared to the national average of 2.4%. The area is ranked sixth in terms of population with 9.33% (^{EUROSTAT, 2018}). Agriculture is the predominant activity, and many of the region's population are engaged in this sector. The main food crops are corn, yams, cassava, and some other root crops.

Koforidua is the capital of the eastern region. The eastern region has a population of about 2,633,154, and is ranked as the third most populous area of Ghana with 10.68% of the country's total population (^{EUROSTAT, 2018}). The eastern part covers 19,323 km², about 8.1% of Ghana's total land area. Crops produced in this region include grains, such as wheat, corn, and barley. Additionally, field crops, such as cotton and tobacco, vegetables, fruits and nuts, and horticultural specialties, such as flowers and ornamental plants, are grown in this region.

Cape Coast is the capital of the central region. The central area has a population of about 2,201,863, and it is ranked the eighth most populous region in Ghana, recording a 8.93% of the country's total population (^{EUROSTAT, 2018}). The main economic activity of the region is fishing and farming, and maize is the primary cereal grown here.

The central region contains many tourist attractions such as castles, forts, and beaches stretched along the region's coastline.

Sample size determination

This study used both primary and secondary data. The primary data was obtained through a cross-sectional survey conducted in Ghana's four regions (northern, Brong-Ahafo, eastern, and central regions) (Supplementary material 1). The study used the sample size formula (below) (^{Hashim, 2010}) to determine the appropriate sample size (Eq. 1).

where n is the sample size, t is the value for the selected alpha level of 0.025 in each tail, which is = 1.96, p is the proportion of the population engaged in maize production, g is the ratio of the people not involved in maize production, and d is the acceptable margin of error for the proportion being estimated = 0.05 (error researchers are willing to accept).

The Ghana Living Standard Survey reported that 49.1% of farmer households that cultivated staple and or cash crops were maize farmers (^{Ghana Statistical Service, 2018}). Assuming a 95% confidence level and 5% margin of error, the sample size was calculated as follows:

The study followed ^{Salkind and Rainwater (2003)} recommendation of oversampling by 40%-60% to account for a low response rate. Therefore, this study's sample was increased by 56.2%, resulting in a sample size of600 (^{Salkind & Rainwater, 2003}).

Sampling technique and size

A multi-stage sampling technique was used in this study. The first was to select four regions (northern, Brong-Ahafo, eastern and central regions) in Ghana to cover all the agro-ecological zones. After that, four districts/ municipalities were randomly selected from each of the four selected regions. In the next stage, three villages or communities were randomly selected from each of the four districts/municipalities. For the last step, a random selection was performed by picking every K ^th (sampling interval) farmer in a list, where k was obtained by dividing the population of smallholder maize farmers in the village by the sample size.

Method for estimating the efficiency of resource use in maize production

For maize farmers to be efficient in their use of production resources, these resources should be used in a manner such that their marginal value product (MVP) is equal to their marginal factor cost (MFC) under perfect competition, according to ^{Tambo and Gbemu (2010)}. Consequently, the resource use efficiency parameter was calculated using the ratio between the MVP of inputs and the MFC. According to ^{Fasasi (2006)} and ^{Goni et al. (2007)}, the efficiency of resource use can be calculated as follows:

where RE is the resource efficiency coefficient, MVP is the marginal value product, and MFC is the marginal factor cost of inputs.

where P _x is the unit price of the input, say X.

where y is the mean value of output, x is the mean value of input employed in the production of a product, MPP _x is the marginal physical product of input X, and P _y is the unit price of maize output.

Taking into consideration the translog production function (Eq. 5)

where MPP _x is the marginal physical product of input X and is a measure of input X's technical efficiency, and β _x is the output elasticity of input X.

Hence,

where Y represents the value of the output, X represents the value of the input and P _y represents the unit price of the output.

The MVP of a particular input resource is consequently computed by the product of output elasticity of that input, the ratio of mean output to mean input values, and the unit output price. The MFC of input was attained from the data composed on that input's unit price.

To decide whether or not an input is used efficiently, we used the following convention. If r=1, it implied the input was used efficiently, r>1 meant the input was underutilized, so the output would be increased if more of that input were employed. Finally, r<1 means that the input is over-utilized, so both the production and profit would be maximized if less input were utilized (^{Eze & Okorji, 2003}).

Socio-economic characteristics of farmers

Table 1 below shows that the pooled sample revealed that most maize farmers in the study area are males (449) representing 74.8%, compared to 151 females representing 25.2%. Male dominance in maize farming runs through all the four regions of the study. These results can be attributed to the fact that most Ghana people perceive farming to be an occupation for men and not women. This result was in agreement with the work of ^{Sadiq et al. (2013)}, who found a dominance of male maize farmers of 67% compared to 33% of female maize farmers in the studies of profitability and production efficiency of small-scale maize production in the Niger State of Nigeria. The result also showed the average age of 46 years with a minimum age of 18 and a maximum of 79 years (Tab. 1). The majority of the farmers were between 18 and 40 years, while very few farmers were above 60. This result means most maize farmers in Ghana are young, a fact that may affect productivity. This result was consistent with the studies by ^{Ojiako and Ogbukwa (2012)} who found a mean age of 44.8 years for farmers (Tab. 1).

TABLE 1 Descriptive statistics of the characteristics of the interviewed maize farmers. 

NGO_s - non-governmental organizations, Min - minimum, Max - maximum, M - mean, SD - standard deviation, Freq. - frequency.

Most of the maize farmers had a junior high school and senior high school education. The average number of schooling for maize farmers was five years. This result can be attributed to the fact that most educated youths wish to work in offices and see farming as a job for school dropouts in Ghana. This result agrees with the studies by ^{Oladejo and Adetunji (2012)} who also found that most maize farmers in the Oyo State of Nigeria (82.3%) had received formal education. The studies revealed that many maize farmers (56.9%) did not belong to farmer associations. This result was probably obtained because maize farmers in Ghana do not see the benefits of such farmer associations or because there are no farmer groups in the study areas.

The average household size of maize farmers in Ghana was seven people (Tab.1) with a range of 1 to 37 people. These results were consistent with the study of ^{Oladejo and Adetunji (2012)}, who found an average household size of 8 among maize farmers in the Oyo state of Nigeria. The average years of experience for maize farmers in the pooled sample was 14 years, meaning farmers interviewed in the study areas have spent much time in maize cultivation. The studies show that a slight majority of farmers had no access to extension with a percentage of 54.5% compared to 45.5% of farmers who had access to extension services, and an average number of visits of 3 (Tab. 1). Generally, there was poor extension contact with maize farmers, and this could affect their adoption of improved farming practices.

Our results revealed that smallholder maize farmers who were not beneficiaries of non-governmental organizations (NGOs) were slightly fewer compared to those who enjoyed some benefits: 48.2% for non-beneficiaries against 51.8% beneficiaries in Ghana. Also, our results revealed that very few maize farmers benefited from government subsidies with a percentage of 28.3% compared to 71.7% non-beneficiaries. For instance, the northern region recorded 63.9% of smallholder maize farmers enjoying government subsidies against 36.1% of the smallholder maize farmers who do not enjoy government subsidies. This result could be traced to the fact that the standard of living in the northern region of the country is low compared to other areas. For that matter, most smallholder maize farmers in this region are less able to afford to purchase improved production technologies to boost their productivity. Therefore, the government helps smallholder maize farmers in this region by subsiding enhanced production technologies. A meagre percentage recorded for maize farmers who had access (26.3%) as compared to 73.7% with no access to credit for the pooled sample. This trend runs through all the study regions. Low percentages of farmers have access to credit recording, 22.2%, 30.6%, 15.4%, and 37.2% for the northern region, Brong-Ahafo region, eastern region, and central region, respectively.

Resource use efficiency by maize farmers in Ghana

The return to scale parameters in Table 2, calculated as the sum of individual production input elasticity, showed an increase. This means that maize production in Ghana (northern, Brong-Ahafo, eastern and central regions) was a production function. The return to scale values for the pooled sample and the northern, Brong-Ahafo, eastern, and central regions were recorded as 3.268, 2.229, 7.594, 6.804, and 2.841, respectively (Tab. 2). These results suggest that smallholder maize farmers in the pooled sample (northern, Brong-Ahafo, eastern, and central regions) should enlarge their production scale by about 3.2%, 2.2%, 7.6%, 6.8%, and 2.8%, respectively, because of the scale elasticity recorded by them for maximizing productivity given their disposable resources (Tab. 2). The results revealed that smallholder maize farmers in Ghana could increase their maize output using more of the mentioned resources (fertilizer, pesticides, herbicides, improved seed, land, labor, and capital). This result agrees with ^{Saura-Calixto et al. (2007)}, who report that farmers could increase their output by increasing the quantity of fertilizer, seed, labor, and cultivated land size. The increasing returns to scale finding agree with those of ^{Uchegbu (2001)} and ^{Ajibefun (2002)}, even though they contradict the conclusions of ^{Obasi (2007)}.

TABLE 2. Input elasticity. 

Table 3 presents the marginal productivities that revealed that maize farmers in the pooled sample and all the regions (northern, Brong-Ahafo, eastern and central regions) used land more efficiently than other resources (fertilizer, herbicides, pesticides, improved seed, labor, capital). This result implied that if maize farmers had cultivated more land, it would have likely led to a rise in maize output by 1103 kg, 4369 kg, and 1408 kg among maize farmers in the pooled sample and the Brong-Ahafo and eastern regions, respectively (Tab. 3). Similarly, maize farmers in the northern region were more efficient in using herbicides to control weeds in their maize crops compared to the other regions. The results also revealed that maize farmers in the central region were more efficient in using labor in their maize production than the other regions. The results of the northern region suggest that if maize farmers had used more herbicides, the maize output would have increased by 157 kg (Tab. 3). The output of maize in the central region would have also increased by 40.3 kg if maize farmers had increased their use of labor in maize production (Tab. 3). The results revealed an inefficient use of capital in the pooled sample and all the four regions (northern, Brong-Ahafo, eastern, and central regions). It recorded the lowest MPP of 2.53, 0.69,1.99,1.04, and 0.34, respectively (Tab. 3). These results also corroborate the research work conducted by ^{Saura-Calixto et al. (2007)}.

TABLE 3 Marginal value product to marginal factor cost ratio across the various regions in Ghana. 

MPP - marginal physical product, MVP - marginal value product, MFC - marginal factor cost, R - efficiency coefficient.

Considering the technologies available to maize farmers and the inputs and output prices, resource use efficiency would be achieved at a level where the MVP is equal to the MFC. The resource can only be used efficiently if the compared MVP and the MFC are the same. The results revealed that the ratios of the MVP to the MFC for maize farmers in the pooled sample were greater than one for the use of fertilizer, herbicides, pesticides, seeds, and land with values of 2.7, 9.5, 7.0, 18.2, and 35.6, respectively (Tab. 3). The ratios for the use of labor and capital were found to be less than one with values of 0.8 and 0.2, respectively (Tab. 3). These results imply that maize farmers in Ghana were not efficient in allocating their resources (fertilizer, herbicides, pesticides, seed, land, labor, and capital). The above means that maize farmers in Ghana underutilized fertilizer, herbicide, pesticide, seed, and land, while labor and capital were over-utilized. In general, maize output could have been increased if more underutilized inputs like fertilizer, herbicides, pesticides, seed, and land were used.

In contrast, labor and capital could have been reduced. This result agrees with the work of ^{Chiedozie et al. (2010)}, who report similar results in their study that fertilizer, land, and pesticides were underutilized.

Table 4 shows MVPs adjustments for optimal resource utility (% divergence) by maize farmers in Ghana. The result from the pooled sample indicates that for resources to be efficiently utilized, there should be an increase of more than 70.4%, 89.7%, 86.3%, 94.6%, and 97.4% for fertilizer, herbicide, pesticide, seed, and land, respectively, to ensure a higher maize output (Tab. 4). However, labor and capital were over-utilized. Therefore, these inputs need to be decreased by 20.9% and 81.9%, respectively, for efficiency in maize productivity to be ensured (Tab. 4). In the northern region, for optimal resource utilization by farmers to be achieved, there should be an increase in fertilizer, herbicides, pesticides, labor, land, and capital of 21.8%, 91.9%, 99.4%, 66.5%, 84.7%, and 94.5%, respectively. In comparison, the quantity of seed would be expected to be reduced by 66.8% to ensure optimization (Tab. 4). The optimal resource use adjustment by maize farmers in the Brong-Ahafo region also revealed that for an optimal resource to be achieved, there should be an increase of 73.3% of fertilizer, 98.7% of herbicide, 99.6% of pesticide, 97.8% of seed, 33.4% labor, and 98.8% of land. In comparison, capital needs should be reduced by 85.9% for optimal output levels to be achieved (Tab. 4). For maize farmers in the eastern region, an increase of 90.5%, 95%, 99.8%, 68.9%, 52.4%, 99.3%, and 98.3% for fertilizer, herbicide, pesticide, seed, labor, and land, respectively, as well as a decrease in capital input of 90.8% would be required for optimal resource use to be achieved (Tab. 4). Optimal adjustment regarding optimal use of resources by maize farmers in the central region requires an increase of 91.9%, 3.9%, 99.3%, 91.8%, and 71.4% in fertilizer, herbicides, pesticides, seed, and labor, respectively. In comparison, land and capital need to be decreased by 33.8% and 98.4%, to ensure resource-use efficiency optimization for increasing maize production (Tab. 4). This result agrees with the studies of ^{Chiedozie et al. (2010)} and ^{Wongnaa et al. (2012)}, who obtain similar results in their studies on resource use efficiency. Our results suggest a significant divergence from the optimal levels of pesticides (underutilized) in all the agro-ecological zones compared to any other input resources. The divergence of pesticide use from the optimal levels was greater in the eastern region, whereas that of land was greater in the Brong-Ahafo region of Ghana (Fig. 1).

TABLE 4 Adjustments in marginal value products (MVP) for optimal resource use (% divergence). 

EG - efficiency gap, D - divergence from optimal level.

FIGURE 1 Adjustment in marginal value of products for optimal resource use. 

In the northern region, the results for the ratios of the MVP and MFC were greater than one for the use of fertilizer, herbicide, pesticide, labor, land, and capital with values of 1.2, 12.0, 86.2, 2.9, 6.5 and 13.8, respectively, while the use of seed was found to be less than one with a value of 0.3 (Tab. 3). This result means that fertilizer, herbicide, pesticide, labor, land, and capital were underutilized by maize farmers in this region, while seed was over-utilized. The maize output in the northern region could be increased if more underutilized inputs like fertilizer, herbicide, pesticide, labor, land, and capital were used. At the same time, the quantity of seed should be reduced.

In the Brong-Ahafo Region, the ratios of the MVP and MFC were greater than 1 for fertilizer, herbicide, pesticide, seed, labor, and land with values of 3.4, 70, 168, 45, 1.5, and 84, respectively, while the only input with a ratio less than one was capital 0.1 (Tab. 3). The implication of this is that fertilizer, herbicide, pesticide, seed, labor, and land were underutilized, while only capital was over-utilized. Therefore, maize farmers in the Brong-Ahafo region could have increased their outputs if inputs like fertilizer, herbicide, pesticide, seed, labor, and land were increased while capital was reduced.

In the eastern region, the MVP and MFC ratio was greater than one for fertilizer, herbicides, pesticides, seed, labor, and land with values of 10.5, 19.6, 559, 3.1, 2.1, and 59.0, respectively. The capital ratio of MVP and MFC was less than one (0.08) (Tab. 3). This means capital was over-utilized while fertilizer, herbicides, pesticides, seed, labor, and land were underutilized by maize farmers in this region. Therefore, if maize farmers had increased their use of fertilizer, herbicides, pesticides, seed, labor, and land and decreased the amount of capital, then it is likely that their maize output would have increased.

The MVP and MFC ratios calculated for maize farmers in the central region were greater than one for fertilizer, herbicide, pesticide, seed, and labor, recording 12.2, 1.04, 35.3, 11.1, 3.5, respectively. Simultaneously, land and capital were found to be less than one, recording 0.66 and 0.02, respectively (Tab. 3). This result indicates that fertilizer, herbicide, pesticide, seed, and labor were underutilized, while land and capital were over-utilized. Maize farmers in the central region of Ghana could have increased their outputs if more of such inputs like fertilizer, herbicide, pesticide, seed, and labor were used while land and capital were reduced. The studies of ^{Chiedozie et al. (2010)} also reported similar results.