Cotton (Gossypium hirsutum L.) yield has gone up while nitrogen recommendations per bale has trended down. This study seeks to explain why nitrogen recommendations have changed by determining the changes in the production function for cotton. The gain in productivity has several likely explanations including but not limited to successful efforts in plant genetics and improved pest management. The changes in the yield function suggest the sources of increased yields and nitrogen efficiency in cotton. A linear stochastic plateau response function was fit with long-term experimental data from the Altus (Oklahoma) experimental station. The experiment was a randomized complete block design with a combination of nitrogen (N), phosphorus (P), and potassium (K). Only yields of plots where P and K are kept at a constant rate of 59 kg ha-1 and 75 kg ha-1 were used. Data were collected during the period 1972 to 2010. The maximum likelihood method was used to estimate the parameters of each response function. Because some varieties were only observed in a short period of time (less than three years of observations), the response function could not be estimated for all varieties individually. Data from the first two varieties (Stoneville 213 and Lankart LX-571) and those from the last two varieties (Paymaster 2280 BG RR and Delta Pine 0924 B2RF) were pooled together. The results indicate an increase in the slope that is synonymous with an increased efficiency in nitrogen utilization. The plateau has also shown an increase, which implies improvements in yield potential. The intercept, which represents yield with no nitrogen applied, has increased, but not as much as the slope or plateau. The economically optimal rate of nitrogen was determined for each variety group and the results indicate that optimal nitrogen level ranged between 33 kg ha-1 and 85 kg ha-1.