An Economic Evaluation of Nitrogen Fertilization of Grasses When Carry‐over is Significant

Abstract

An economic model is developed to determine optimal nitrogen fertilization policies for seeded grasses in semiarid regions where nitrogen carry-over is significant. The problem is cast in the framework of stochastic dynamic programming and an application of the model is made at two sites in the Nothern Great Plains. A new statistical method was used to estimate carry-over nitrogen and the forage yield-response function simultaneously. Nitrogen carry-over was estimated implicitly through yield response without direct measurements of nitrogen.There is considerable evidence that grasses growing in semiarid regions generally respond to nitrogen fertilizer and that nitrogen carryover from year to year can be an important source of nitrogen in subsequent growing seasons (Black;Power 1967Power , 1968Thomas and Osenbrug). Determination of optimal fertilization policies is considerably complicated by nitrogen carry-over. The decision problem is dynamic and is further complicated if carryover is stochastic. Stochastic carry-over is quite plausible when the relationships between seasonal precipitation, forage yield, and nitrogen recovery by the grass crop are considered (Stauber and Burt). The determination of optimal fertilization policies for dryland grasses must be cast in a dynamic stochastic framework. The Decision ModelEconomic analysis of nitrogen fertilization when carry-over is significant and stochastic involves a determination of the sequence of decisions regarding the application of nitrogen fertilizer which will maximize expected present value of net returns. The basic approach M. S. Stauber is an associate professor and Oscar R. Burt is a professor of agricultural economics and economics at Montana State University. Fred Linse is an agricultural economist with the Economic Research Service, U.S. Department of Agriculture.Montana Agricultural Experiment Station Journal Series 593.is to find a decision rule which specifies the amount of nitrogen to apply in a particular year, given the amount of plant-available nitrogen carried over from previous years. Formally, the decision rule is a functional relationship between the amount of fertilizer applied and the estimated amount of plantavailable nitrogen in the soil at the appropriate time for application of fertilizer. The problem can be viewed as that of maintaining an optimal inventory of plant-available nitrogen in the soil under conditions of stochastic demand arising from random precipitation. Economic considerations must include costs other than the purchase cost of fertilizer. An important trade-off exists between interest and spreading costs; infrequent applications in large amounts save spreading costs but increase interest costs through a larger average investment. Then on the revenue side is the usual consideration of crop response to total plant-available nitrogen, the sum of carry-over nitrogen and that applied currently as fertilizer.An expected value criterion applied to discounted net returns over a long planning horizon automatically weighs all of ...

Temporal Frequency of Soil Test Information Effects on Returns to Potassium Fertilization in Cotton Production

“…Total available K was always observed to be greater than zero (Table 3); thus, a negative yield would be outside the range of the data. Similarly, Watkins, Lu, and Huang (1998) and Stauber, Burt, and Linse (1975) found insignificant negative estimated intercepts in their yield response to nitrogen when carryover was considered. The remaining parameter estimates had the expected positive signs and were significant at the 1% level.…”

A Dynamic Model for Technical and Economic Analysis of Fertilizer Recommendations1

“…The known quantities of Eq. [8] are the results of the soil tests, b•tt, and the fertilizer applications which followed, xlt, t = l, ... , T. The X coefficients, the carryover parameter e" and the autocorrelation coefficient p 1 were estimated using a nonlinear least-squares procedure.…”

“…The importance of fertility carryover was emphasized by Tisdale and Nelson (9), and it was further discussed by Doll et al (1), Kennedy et al (3), Stauber et al (8), and Helyar and Godden (2). Our fertility carryover relations are specified as the following first order difference equations: b,, := e,(btt-1 + Xu •• ), i = N, P, K [2] where bu is the level of the i-th nutrient in the soil in period t, bu.…”

Economic Optima and Price Sensitivity of N Fertilization for Six Perennial Grasses1

“…N ITROGEN fertilization of perennial grasses in• creases their yield (1, 2, 4, 5,10,12,13,15) and also has been shown to be profitable (7,11,14,17). However, large increases in prices raised questions about appropriate levels of N fertilization for forage grasses.…”