The Bayesian method is used to estimate a wheat yield response function using a stochastic plateau model. The objective is to extend the stochastic plateau functions by relaxing the normality assumption for the plateau random effect. The beta distribution was chosen so that the plateau can exhibit either right or left skewness. The economically optimal rate of nitrogen is determined using the plug-in approach, which is commonly used in the literature and the Monte Carlo optimization technique. The plug-in method ignores the parameter uncertainty, which might affect the accuracy of the nitrogen recommendation. The results indicate that the normal plateau model fits the wheat data better than the beta distribution. In addition, the plug-in method results on average in 0.6% lower nitrogen recommendation than the Monte Carlo approach.