Page 16 - Azerbaijan State University of Economics

XiaolinQu, M.S., Lal K. Almas: The water requirement and profitability analysis of corn using irrigation
management approaches including evapotranspiration and weather data

PPET=18.734+2.216*TW (13)

Based on the production function, MPP PPET(Equation 14) and MVP PPET

(Equation 15) could be determined. Here MPP PPET requires two steps to calculate

according to the chain rule. Frist taking the first derivative of Y corn with respect to

PPET and the first derivative of PPET with respect to TW, and then multiply them

together. Next, the profit maximizing levels of PPET for corn could be determined

by equating MFC to MVP PPET. Thus, applying assumed prices of corn (P corn) and

natural gas (P NG), the optimal levels of PPET could be calculated (Equation 16).

Table 7 illustrates the optimum levels of PPET by applying the assumed corn and

natural gas price ranges to Equation 16.

d Y d PPET
MPP PPET= corn * = (-0.028*PPET+3.475)*2.216= -0.062*PPET+7.701 (14)
d PPET d TW

MVP PPET= (-0.062*PPET+7.701) *P corn (15)

. 1 08 * P  6 . 4  . 7 701 * P
PPET = NG corn (16)
 . 0 062 * P corn

It needs to remind that the variable cost regarding the level of irrigation is

obtained by subtracting the amount of average rainfall and soil water from the

optimum level of TW which meets PPET in order to determine the amount of

water required from applying irrigation. The sum of the amount of rainfall and soil

water is estimated to be 10 inches as under total available water approach of corn.

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