Mathematical-Economic Analysis to Determine Optimal Applied Water in Case of Crop Price Depends on Its Quality

Abstract

In some crops, crop price is variable and dependent on yield quality e.g., price of sugar beet root. Therefore, all parameters that increase the sugar content, increase the unit sugar beet root price e.g., irrigation water and nitrogen application rate. In this study, the required equations were derived for determining optimum applied water for sugar beet at variable crop price as a function of sum of irrigation water and seasonal rainfall under land and water limiting conditions. Results showed that the optimum applied water depth under land limited resulted in 1.2% increase in net income per unit area compared to maximum yield condition. Whereas, under water limiting condition, the net benefit per unit water is maximized and increased by 12% compared to maximum yield conditions. Increase in base crop price resulted in decrease and increase in optimum water depth under water and land limiting conditions, respectively. Under water limiting conditions, increase in seasonal rainfall from 0 to 6 and 12 cm decreased the optimum applied water from 47.4 to 54.8 and 65.3% and increased the irrigated area from 90 to 135 and 225%, respectively, compared with the full irrigation conditions.