The relationship among cost functions, distance functions, and technical inefficiency are utilized to show how technical inefficiency scores can be incorporated into the specification of a profit function and a related system of output supply and input demands. A method also is introduced for incorporating allocative efficiency scores into the same system. The theoretical and empirical approach requires fewer assumptions than those made in many studies. An illustrative example is provided for Russian agriculture for 1194-95, a period when significant technical and allocative inefficiency was known to exist. The results demonstrate inefficiency limits the supply response to prices, thus leading to lower estimates of output response compare to a traditional supply model in which efficiency is assumed.