Determining the lower limits of irrigation capacity use

The objective of the study was to determine the limits of economic justification for irrigation system capacity use. The first step was focused on determining the lower limit of capacity use by comparing the economic effects of irrigation with the costs of the irrigation system use. In addition, while determining these limits the need was stressed to consider the economic effects of irrigation by optimizing the production structure and the modes for limit determination under irrigation and non-irrigation conditions. Eventually, the empirically verified possibility stating that this limit may be determined by comparing the water processing prices with its cost price is given. The limit was found to be the point at which these two prices equalize.


I n t r o d u c t i o n
Over the past decades a comparative decline of the available agricultural land has been recorded all over the world.According to the FAO agricultural land for the intensification of farming (cultivable land, orchards, vineyards) was approx.0.43 ha and 0.25 ha in 1965 and 1995 respectively (1).The decline has been provoked by the decreasing possibility to change uncultivated to cultivable land, limited land area, occupation of agricultural land by buildings, roads, channels for irrigation and drainage, factories on one hand and the ever-growing population on the other.
The issue raising major concern focuses on how to increase food production in the future considering the constrained agricultural land area.
Increasing crop production output has been considered one of the alternatives contributing to food production increase due to the necessary bioenergy obtained.
Until recently crop yield increase used to refer to the reliance on modern agricultural practices (high levels of use of mineral fertilizers, plant protection products, efficient systems of soil cultivation), new resistant, high-yielding cultivars, etc.However, irrigation needs to be implemented in order to raise production output, i.e. the installation of new and the rational use of the existing irrigation systems is advisable and justifiable.
Therefore, the future development of agriculture production refers to the reliance on the intensification of production meaning thereby not only the application of agricultural practices mentioned above but the changed structure of both crop and livestock production as well, i.e. higher investments may be expected to encourage future development.Inadequate investments in agricultural production may be expected to slow down the development of both industry and economy on the whole.
Considerable investments are needed for the preparation and implementation of an irrigation project.Therefore, economic arguments with regard to the advisibility and justification of the irrigation capacity utilization level need to be taken into account in the design of the irrigation system.The objective of this study was to discuss and contribute to the implementation of the procedure with regard to the determination of the lower level of irrigation capacity use.

Materials and Methods
An agricultural enterprise involved in the field crop/livestock production system was used as a model for determining the lower level of irrigation capacity use.The enterprise comprised 960 ha of cultivable land, uniform in quality having successfully solved the problem with regard to excessive waters on 400 ha by excavating a network of open channels.Livestock production focused on bullock fattening amounting annually to 1260 animals up to 250 kg and 740 animals up to 450 kg.
The enterprise was located in the region with low precipitation, unevenly distributed over the year.During the vegetation growth period average annual precipitation amounted to 300 mm/m 2 .Due to water deficiency yields were far below the anticipated.
The installation of the system for irrigation on a net area of 316 ha on which an open channel network for excessive water drainage had previously been installed was hypothesized.The water required shall be obtained from wells of the uppermost water horizons.However, the maximal water amounts required from the standpoint of some field crop needs (soybean, sugar beet and alfalfa) in July and August shall not be met because during that period soil horizons are usually deficient of water.Namely, during these months approx.110 000 m 3 of water may be expected to be provided.
The installation of an irrigation system may be expected to enhance agricultural production, increase yields and by changing the production structure raise the financial results of the enterprise.However, it is of major importance to know the economic effects of production under the conditions prior to and following the installation of an irrigation system in order to contribute to increased financial results.
In our case the economic effects of production under the conditions prior to and following the installation of an irrigation system shall be given by the net income as the difference between the final value and the external production costs without irrigation system costs and its maximal value shall be obtained by maximazing production.The optimal production structure under the given conditions may be projected using different methodological procedures including linear programming, the results of which shall be used in the study.
Using the linear programming method the economic effects under irrigated and non-irrigated conditions shall be obtained by determining the unknown xi, the function of which along with the constraints and under the condition xi ≥ 0, shall maximize net income, where: F(xi) -equals the objective funcion value, i.e. in our case the economic effect of production (net income); xi -unknown value (production activities); ci, ai, bi -permanent numbers.
Using the linear programming method the problem may be solved by applying some of the general methods.In our case the simplex method shall be used whereby the previously hypothesized problem of the mathematical linear programming model shall be of help in converting the system of unequations to the system of equations.
Considering the objective of the installation of the irrigation system, namely to increase the financial result of the enterprise, it is of major importance while planning its installation to determine the amount of water it can provide during July and August, i.e. the degree of capacity use required to raise the financial result.The degree of irrigation capacity use needed for financial result increase may be determined by comparing the change of net income with irrigation system costs.A loss shall be registered provided utilization costs are greater than net income increase.The degree of irrigation capacity use at which the change of net income equals costs represents the lower level of economic justification (usefulness threshold) of capacity use.
However, the economic effect of the water used for irrigation may be obtained by computing its processing price, i.e. by dividing the change of net income after irrigation with the amount of the water used: where: pc -processing price of water NP 1 -net income under the conditions of irrigation NP 0 -net income under the conditions of non-irrigation Q -amount of water used for irrigation.
The lower limit of economic justification of the degree of irrigation capacity use may be obtained by comparing the processing price with the cost price using the following formula: where: ck -cost price of water vt -amount of variable cost per m 3 of water PT -total amount of fixed costs of the irrigation system.
As long as the processing price of water is lower than its cost price, the use of the irrigation system does not contribute to the increase of the financial result.The lower level of capacity use may be expected to be achieved when these two prices equalize and the financial result starts increasing when the capacity use rises above this level.

Results and Discussion
The economic effect of production given as the net income under nonirrigated conditions was determined using the optimization of the simplex method and shown in Table 1.
T a b .The economic effects of production under the conditions of irrigation and different water availability in July and August were determined using the optimization simplex method and shown in Table 2.
Total fixed costs and variable costs per m 3 of this irrigation system amounted to 174 494 Dinars and variable costs per m 3 0.0084 Dinars.The changing amounts of net income and the financial result for the variously assumed possibilities of water supply intended for irrigation in July and August are given in Table 3 Both the processing and cost price of water as well as their differences for different degres of irrigation use are given in Table   The determination of the lower limit of the degree of irrigation capacity use comparing processing prices with cost prices of water is presented in Fig. 1.In our case the lower limit of the degree of irrigation capacity use was determined graphically, i.e. by lowering the ordinates of the cutting points, the lines of the cost price and the processing price (point P) on the abscissa.Thus the lower limit of the irrigation system use was approx.68 000 m 3 of water in July and August or a total of approx.528 000 m 3 .
Ensuring water above this limit tends to increase the difference between the processing and cost price of water.Providing 100 000 m 3 of water in July as well as in August the difference was the biggest.Knowing that the difference between the processing and cost price represents the average increase of the financial result per m 3 of water, a maximal amount would thus be achieved at the amount of water provided.Increasing the degree of capacity utilization tends to decrease the differences because total costs would rise rapidly compared with the net income due to the restricted production capacities and conditions.
At the low level of irrigation capacity use, i.e. water availability up to 68 000 m 3 in July and August the loss would be provoked by fixed costs due to the fact that in the total amount they would be higher in relation to the change of the net income.
Considering the dynamics of the financial result, i.e. comparing changes of net income with the costs of irrigation use (Tables 3 and 4), the procedure for determining the lower limit of the degree of irrigation capacity use gains in importance.The dynamics of financial results is shown in Fig. 2. Based on the data shown (Fig. 2), the lower limit of irrigation system use amounts to approx.68 000 m 3 of water available in July and August.
Based on the dynamics of the financial result in relation to the degree of irrigation capacity use (Tables 3 and 4 and Fig. 2), it can be concluded that the dynamics of the total financial result differs as does the dynamics of the average financial result.An average financial result may be achieved by providing July and August with 100 000 m 3 of water each.Maximal total financial result may be achieved at a greater degree of irrigation capacity use, i.e. maximal water availability in July and August, e.g.110 000 m 3 of water each month.Thus, the optimal degree of irrigation system use may be found between these two points (5), i.e. system use output.

C o n c l u s i o n
The lower limit of economic justification (usefulness threshold) may be determined by comparing income with costs , i.e. it may be detected at the point of capacity use at which incomes equal costs.When determining the limit for irrigation capacity use maximal amounts of economic production results should be considered under irrigated and non-irrigated conditions.The amount may be obtained by optimizing production using well known methodological procedures.
Our research has shown that the limit may also be determined by comparing the processing price with the cost price of irrigation water.The point at which these two prices equalize represents the lower limit of economic justification of the degree of irrigation capacity use, because the change of the financial result equals zero.The possibility of ensuring greater amounts of irrigation water, namely above the lower limit would contribute to financial result increase.
4.T a b .4. -Processing price and cost price of water for different degres of irrigation use Degree of irrigation system capacity use (

Fig. 1 .
Fig. 1. -Determination of the lower limit of the degree of irrigation capacity use

Fig. 2 .
Fig. 2. -Dynamics of the average and total amount of the financial result
1.-Production structure and net income prior to the installation of the irrigation system .