The specification and estimation of models of consumer and producer demand with kink points are considered. The presence of kink points divides the demand or production schedule into different regimes. Our approach utilizes the concept of virtual prices. The virtual prices transform binding quantities into nonbinding ones and provide a rigorous justification for structural change in the observed demand functions across regimes. The comparison of virtual prices with market prices determines regime occurences. An application to energy demand in Indonesian manufacturing firms based on the translog cost function is provided.