Basic Theoretical Concepts of Production Functions
The MPP is the additional output for one unit increase in input, i.e. the addition to the total product resulting from the addition of an additional unit of input. This is the minimum amount of variable input to use, and occurs when the efficiency of the variable input is at its maximum.
The Cobb - Douglas Production Function
- Multiple regression analysis with linear parameters ................................................ 1 0
Table 5.1 shows that the VMPs for purchased concentrates for the three categories of sample farmers are lower than the unit price of the input. Similarly, the cost function showed that the sum of average total variable costs for the bottom third of dairy farmers is greater than the unit price of production.
Calculations of Economic Terms from Production Functions
- Returns to scale and elasticity of production
- Marginal product and value of marginal product
- Marginal rate of input substitution
- Leastcost combination of inputs
- The cost function
Problems Encountered in the Analysis of Production Functions Based on Farm Cross-
- Choice of function (algebraic form)
- Choice of variables
- Aggregation of variables
- Multicollinearity
- Omission of variables
- Zero input levels
- Inter-farm versus intra-farm interpretation
- Error of measurement in farm inputs
- Dummy variables
Due to the complexity of the agricultural process, the true mathematical forms of production functions are not known. Various approaches or bases for selecting the 'best fit' algebraic form are discussed by Heady and Dillon (1961, p. 203). A forward inflation factor is a measure of the strength of the relationship between each explanatory variable and all other explanatory variables in the regression.
Heady and Dillon (1961, p. 136) stated that if the absolute correlation coefficient of the input variables is close to or greater than 0.8, regression analysis should be performed with highly correlated variables omitted. However, a commonly used method for determining the value of c is based on the crest trace and the VIF value of the explanatory variables. When the independent variables in regression analysis are subject to measurement error, it follows that there is a systematic downward bias in the magnitude of the regression coefficients.
Gujarati (1978, p.324) showed that measurement errors present a serious problem when they are present in the explanatory variable(s) because they make consistent parameter estimation impossible. The next chapter deals with the research method used in this study and a description of the study areas.
Research Methodology
- Objectives
- Data collection method
- Methods of data analysis
The amount of concentrate supplied to each faffi1 is based on the number of registered dairy animals in the herd and on the amount of milk produced by the faffi1, since the prices of inputs are lower than they are sold in the free market. Faffi1ers were regionally stratified to avoid qualitative differences (farming practice, biodiversity and management skills) due to location. Farmers were sorted according to the amount of annual milk production in liters obtained from the milk collection and cooling centers in each study area.
Thus, farmers producing at least 12500 liters/year in the central zone and farmers producing more than 4300 liters/year in both study areas of the southern zone were selected. Finally, based on the above criteria, 48 farmers from the central zone of "Asmara and its surroundings" and 72 farmers from the southern zone (42 and 30 farmers from Mendefera and Dekemhara, respectively) were randomly selected to avoid sampling bias. Based on a prepared questionnaire (see Appendix A), the target farmers were interviewed about their land utilization, herd structure, annual income and annual expenditure on variable inputs and fixed assets for the year 2002.
For example, regression coefficients are direct elasticities of output with respect to factors of production, but elasticities are independent of the unit of measurement. Other strengths were discussed in Chapter L. However, strong intercorrelations between the explanatory variables were encountered during the analysis using ordinary least squares (OLS) multiple regressions of the Cobb-Douglas fOIm.
Description of the Study Areas
- Land utilization
- Capital investment
- Annual fann incomes and expenses
In Eritrea, most dairy farms are concentrated in and/or very close to cities and towns and over half of dairy farmers do not have irrigated land for fodder and pasture production. The remainder have no irrigable land at all or tentatively leased land, but are not secured as: (1) the owner may take the land at the end of the lease (ie termination of the lease), (2) there is no official land market, since the land belongs to the state. Based on sample data, 69% of available irrigated land is used for horticulture and horticulture cultivation and only 31% is used for green food production.
An inventory of the size, quantity and cash value of each physical asset (land, fixed improvements, machinery, livestock, stock, supplies, etc.) should be taken to estimate the capital investment of dairy producers, which is prepared at the end. of each successive financial year. Annual income: The main source of income for dairy farmers includes: fresh milk sales (annual formal and estimated informal milk sales), cattle sales (including calves and culls) and other items such as manure sales. The average shares of the costs listed above for each field of study are given in table 2.2.
From Table 2.2, the expenditure ratio on purchased concentrate including leaks is the highest, followed by labor and purchased feed. Especially for the Mendefera study area, purchased concentrates including licks are the highest, not because farmers use more of the specified input but because they pay a higher price for the item due to transport distance from the source of the input.
Therefore, a separate production function analysis was performed for each study area, as long as there were sufficient degrees of freedom for the data from each area. Therefore, the production function analysis carried out for each study area (Chapters 4, 5 and 6) would be preferred and recommended in order to draw conclusions on the production function and make future planning decisions on dairy farming in the three study areas of the Highlands of Eritrea.
Results and Discussion
- Marginal rates of substitution and least cost combination of inputs
- Profit maximizing combination of inputs
- Cost function
The margin increase among the top third of sampled farmers is much less compared to the overall average and bottom third of sampled farmers. The total costs for the bottom third and top third of the sampled dairy farms at their respective geometric means of annual milk yield (25859 and 78810 liters) were Nfa 71665 and 163024 respectively. The MC for the bottom third is greater than the MC of the overall average and the top third of the farmers in the sample, and this coincides with the results obtained from the MP and VMP analysis presented in the previous paragraphs has been carried out.
The margins of the lowest cost combinations were cost reductions of 6757 and 5811 Nfa for the bottom and top third of the sampled dairy farmers, respectively (see Table 5.2). From Table 5.5, the MC for concentrates for the entire sample, the lower and upper third of the dairy farms is greater than the selling price of fresh milk (5.00 Nfa). The addition of a dairy cow resulted in an increase in annual milk yield of 819 litres/year for all dairy farmers in the sample, and 656 and 1030 litres/year for the bottom and top thirds of the sample of dairy farmers, respectively. respectively. .
The cost function for the Dekemhare area dairy farmers shows that for the bottom third of the sampled dairy farmers, the sum of the average variable costs is greater than the unit price of fresh milk. Furthermore, the bottom third of milk producers in the southern zone did not cover short-term costs during the study period.
Results and Discussion
- Marginal product and value of marginal product
- Profit maximizing combination of inputs
- Cost function
The change in milk yield after a 1 % change in dairy cows is also calculated for the bottom third and top one third of sample farmers at their respective geometric mean milk yield, so that the estimates will not be unrealistic. Similarly, the VMPs for the annual operating and mechanical expenses are less than their unit costs for the entire sample and bottom one-third category at their respective geometric means. Therefore, by substituting the above expressions in the estimated model, the least cost combination of concentrate and feed is calculated for the entire sample and the bottom and top one third of sample farmers at their respective average milk yields (Table 5.2).
The profit-maximizing level of concentrates and roughages is calculated for the entire sample, as well as for the bottom and top thirds of farmers in the sample, based on their respective geometric means for milk yield. A similar analysis for the bottom third of farmers could improve milk yield by 39% (cost). For the top third of farmers in the sample, milk yield and margin improved by 72.6% and 129.9% respectively, while costs increased by 42.6%.
For the bottom category of sample farmers, the margin was negative at the actual level. Similarly, the MC of operating and mechanical costs for the entire sample and the bottom third of dairy fans is greater than the unit production cost.
Results and Discussion
- Marginal product and value of marginal product
- Marginal rate of substitution and least-cost combination of inputs
- Profit maximizing combination of inputs
- Cost function
The marginal substitution rate (MRS) of concentrate for feed is calculated for the entire sample and the bottom and top one-third of sample farmers at their respective geometric mean milk yield. However, for the bottom one-third of sampled dairy farmers, the A VC > Py does not cover the total variable costs of production. Similarly, the MK of labor for the bottom one-third of sampled dairy farmers is greater than the unit price of output.
However, for the top third of the dairy farmers in the sample, the highest return comes from a unit addition of roughage (3,606 Nfa), followed by concentrate, labor and dairy cow. However, an analysis of the cheapest combination of the two measures, ceteris paribus, showed that none of the categories of dairy farmers in the sample applied it optimally. The marginal replacement rate of concentrate with roughage and -0.198) for the entire sample, the bottom and top third of sampled dairy farmers respectively, indicated that farmers use more concentrates than roughage.
In terms of profitability, the maximum use of concentrates and forage milk improved by 72.6% for the entire sample, and the bottom and top thirds of sampled dairy farmers, respectively. Thus, under perfect knowledge, risk-free, and unlimited capital assumptions, the sample of dairy farmers could improve their gross margins by and 129.9% for the entire sample, the bottom and top thirds of dairy farmers, respectively. sample. The production function of fresh milk production of the sampled dairy farmers of the Dekemhare area is similar to that of the Mendefera area.
As for the Mendefera dairy farmers, the sample of dairy farmers from the Dekemhare area also overuse concentrate and underutilize feed.
