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Economic Interpretations of Yield Data from a Nitrogen Rate Experiment with Irrigated Grain Sorghum¹

ABSTRACT

Yield data from a nitrogen rate experiment with grain sorghum on newly developed irrigated land at Tucumcari, N. Mex., were analyzed to ascertain the most profitable rate of nitrogen application for each of four treatment combinations of moisture and plant spacing. The principle of diminishing yield increments is used in calculating the most profitable rate.

As the response of crops to nitrogen is known to vary with soil, season, and other environmental factors, the economic interpretations developed herein are intended to apply only to the conditions of this experiment. With the price of sorghum at $1.12 a bushel and the price of nitrogen at 15 cents a pound, the most profitable rate of nitrogen application ranges from 75 to 152 pounds per acre. The most profitable rate is highest with high moisture (8 irrigations) and thick spacing (43,560 plants per acre) and lowest with low moisture (5 irrigations) and thin spacing (20,028 plants per acre). Moisture level influences the most profitable rate of nitrogen application more than does plant population. When nitrogen is applied at its most profitable rate, the return to nitrogen above its cost with high moisture is $33 for thick and $11 per acre for thin spacing. With low moisture, the return is $15 and $19 per acre for thick and thin spacing, respectively.

The most profitable rate of nitrogen application and necessarily the return to nitrogen above its cost at this rate depend also on the price of sorghum a bushel and the price of nitrogen a pound. Under conditions of constant price and application rate of nitrogen, returns are directly proportional to the price of sorghum. As the price of sorghum rises, the most profitable rate of nitrogen application rises at a decreasing rate. Unless the rate is adjusted with changes in the price of sorghum, loss in return to nitrogen above its cost will result. In most instances, variations of 28 cents a bushel in the price of sorghum above 84 cents affect the most profitable rate of nitrogen application by 25 pounds or less per acre. Exclusive of the direct effect of a change in the price of sorghum on return, failure to apply the most profitable rate when the price changes by $0.28 a bushel results in a loss in returns of $1.00 or less per acre for each moisture-plant spacing treatment.

With the price of sorghum constant at $1.12 a bushel, moderate changes in the price of nitrogen do not greatly affect either the most profitable rate of application or the return to nitrogen. The rate changes 21 pounds or less with a change of 3 cents a pound in the price of nitrogen for 3 of 4 moisture-plant spacing treatments. With a change of a cent a pound, return to nitrogen above its cost varies about $1 an acre or less for low-moisture treatments and less than $2 an acre for high-moisture treatments.

¹ Presented before Div. IV, Soil Science Society of America, Dallas, Tex., Nov. 20, 1953.

² Agricultural Economist, Production Economics Research Branch; and Soil Scientist, Soil and Water Conservation Research Branch, respectively; Agricultural Research Service, U. S. Department of Agriculture.

Received for publication February 15, 1954.