Selection of Study Areas and the rationale In the present study, the researcher selects the study areas with great care so that real results are representative. In selecting the sample areas the researcher has to consider the limitation of his intellectual and financial capabilities and his time limitations. Thus, the present study was confined to Pabna district purposively. Then the researcher selects two unions randomly from Sujanagar and Santhia Upazila of the Pabna district. One is Tatibondo union taken from Sujanagar and the other Khatupara union from Santhia Upazila. Considering the constraints of time and fund, two villages were selected randomly from each union through the random sampling table. The selected villages are Ghoradha and Perghoradha from Tatibondo union and Joshomontodulia and Hoijor from Khatupara union. The rationale behind this selection is that the Pabna district is predominantly agro-based, onion is the second single dominant crop (first is jute). Farming is the principal occupation of the majority of the population and their livelihood almost completely depends on agricultural activities. They have also very little scope for complementary occupations during the crop seasons. The study areas are almost single and triple cropping areas and onion is grown extensively and there is sufficient scope to improve yield frontier through agronomic practices. All these features confirm to the typical characteristics of Bangladesh agriculture and these areas can be considered as area representative of the research objectives.
Sample selection A total of 100 onion farmers were randomly selected and twenty five were randomly selected from each of the four villages in the study area. The researcher has selected the sample of onion growers in such a way that can represent the whole onion growers in the study areas and provide effective results for the higher productivity of onion in future.
Sources of Data This research study has mainly based on primary data. Primary data has been collected from the selected sample villages in December 2015 using a well-prepared questionnaire. However, for this research some secondary data have also been collected. These secondary data has been collected from various government and non-government organizations such as Yearbook of Agriculture Statistics of Bangladesh (YASB), Bangladesh Bureau of statistics (BBS), Bangladesh economic review (BER), Food and agriculture organization (FAO), Ministry of agriculture (MOA), Union Parishad office, various website about agriculture etc.
Empirical Model Empirical model is used to determine the factors affecting the onion production and production function shows the purely technical relation between inputs and output of a given product. The most popular model, the Cobb – Douglas production function, has been chosen as an empirical model for the onion production function as follows: Y = A+ β1 X1+β2 X2+ β3 X3+ β4 X4+ β5 X5+ β6 X6 + β7 X7 + μi The log linear form of the Cobb- Douglas production function be: lnY = lnA+ β11n X1+β2 lnX2+ β3 lnX3+ β4 lnX4+ β5 lnX5+ β6 lnX6 + β7lnX7 + μi Where, Y = Total Return of onion production or gross return, A =constant, X1 = Seed cost per bigha (Tk), X2 = Cultivation cost per bigha (Tk), X3 = Fertilizer cost per bigha (Tk), X4 = Insecticide cost per bigha (Tk), X5 = labor cost (man/day) per bigha (Tk), X6= Irrigation cost per bigha (Tk) and X7=land rent (0.05% value of the bigha) Tk; μi = Error term. Assuming that μi is normally distributed having constant mean and zero variance. All variables are expressed in monetary terms. From this equation, the researcher has been derived the values of input coefficients, T-test, adjusted R2 , F- value, and Durbin- Watson value of autocorrelation.
Gross margin analysis: Gross margin analysis implicate the estimation of the costs and returns to production. The purpose of this analysis is to conclude the profitability of onion production per bigha. Subsequently, the fixed capital establishes an insignificant portion of the total costs of production. The implicit from is shown below. GM=TVO-TVC Where, GM= gross margin (tk), TVO=total variable output (mound) and TVC=total variable cost (tk)