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Expectations, Variances, and Sensitivity of Net Returns from Corn Fertilization Experiments¹

Many experiments designed to provide data for estimating production response surfaces have been conducted for only one year and as a result, the findings were applicable to only one set of environmental conditions. To obtain more general results a series of experiments measuring corn (Zea mays L.) yield response to applied N and plant population were conducted at three locations for several years in northern Missouri. Expected profit functions were estimated for each experiment and the input amounts that would have maximized profits for the time period of the experiments were derived. The resulting amounts (expected optima) were 197 kg of N and 45,360 plants/ha for Grundy County, 140 kg of N and 40,488 plants for Saline County, and 135 kg of N and 34,455 plants in Boone County. These amounts were lower than many of the annual optima. Furthermore, expected profits over the experimental periods were relatively insensitive to departures from the annual optima. Additional analyses determined input rates that (i) minimized the cost or (ii) minimized the variance of a fixed expected profit level for the period. Expected profits from many of the annual optima could have been produced at substantially lower cost. Compared to cost minimization, variance minimization increased N and reduced stand; although N is more expensive than plant population, it "costs less" in terms of variance. Expected profits were quite sensitive to corn price and, to a lesser degree, N price; optimal inputs were much less sensitive to these same prices.

Key Words: Zea mays L. • Nitrogen • Plant population expected profit • Economic optima

² Research Assistant, Professor of Economics, and Associate Professor of Soils, University of Missouri; and Professor of Agricultural Economics, West Virginia University, respectively.

Received for publication November 8, 1971.