A normalized quadratic input distance system is applied to estimate inverse demand relationships for wheat by class. Semi-nonparametric and Bayesian estimators are used to impose curvature on inputs and outputs. Price flexibilities are estimated for hard red winter, hard red spring, soft red wheat, soft white winter, and durum wheat. Durum wheat is found to be the most price flexible. Economically and statistically important differences in price formation across classes of wheat are found and are supportive of government programs differentiating wheat by class.