Plants in agricultural marketing and processing industries, generally speaking, function in an imperfectly competitive environment and therefore do not necessarily face perfectly elastic supply functions for inputs, or perfectly elastic demand functions for outputs. Relevant coefficients in cost functions of such firms often are dependent on supply as well as production coefficients. Indeed, in contrast to farm production, here the more interesting relationships may arise from price functions rather than production functions. Determination of reliable cost-function estimates under such conditions presents a real challenge to researchers. The accompanying discussion of the estimation of empirical cost functions in such firms is published as journal paper number J-2860 of the Iowa Agricultural Experiment Station, Ames, Iowa, project number 1224.