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Implicit Estimate of Residual Nitrogen Under Fertilized Range Conditions in the Northern Great Plains¹

Information concerning carryover of fertilizer nitrogen in the plant-soil system is necessary to determine optimum fertilizer policies for dryland grasses in semiarid regions. A primary contribution of this paper is the presentation and illustration of a dynamic model for estimation of carryover nitrogen. The carryover relationship is estimated implicitly through yield response as opposed to direct measurements on nitrogen. Data from an experiment designed to evaluate the effects of nitrogen and phosphorus fertilizers and seasonal precipitation on the yield and composition of bromegrass (Bromus inermis)-crested wheatgrass (Agropyron cristatum) hay were analyzed with the model. A polynomial yield response equation in the two variables, plant-available nitrogen and seasonal precipitation, was estimated simultaneously with a first order difference equation assumed to describe the residual nitrogen relationship.

Statistical estimation was by nonlinear regression techniques. The proportion of nitrogen available in year t which was carried over to year t+1 was estimated at approximately 54%, taking precipitation at the mean of a 32-year series, and the standard error associated with percent carryover was 3.4. A maximum yield of 2072 kg/ha (1849 lb/acre) resulting from 268.99 kg/ha (240 lb/acre) of available nitrogen is predicted under average precipitation conditions. The fact that an economic determination of the optimal level of nitrogen to maintain in the soil must include a consideration of carryover and the relevant interest rate is demonstrated. In equilibrium the optimal level of nitrogen is 89 kg/ha (79 lb/ acre), assuming an interest rate of 10%, a forage value of $.0165/kg ($15/ton), and a nitrogen fertilizer cost of $.22/kg ($.10/lb) with the costs of spreading fertilizer ignored. The maintenance of this level of nitrogen in the soil would increase average net returns over unfertilized grass by $2.27/ha or by about 20%.

Key Words: Range fertilization • Residual nitrogen • Fertilizer economics

² Associate Professor of Agricultural Economics and Economics, and Professor of Agricultural Economics and Economics, Montana State University.

Received for publication January 12, 1973.