The linearization of structural models of random price production may be carried out by exploiting the mean-standard deviation approach under a location and scale parameter condition. As shown here, the linearization problem may be solved under widely employed assumptions on production technology (i.e., a homogeneous production function) and on the type of risk aversion (i.e., constant absolute risk aversion or constant relative risk aversion). The linear structural models proposed in this study are more practical than those developed using the expected utility approach, for several reasons. First, they remarkably reduce the cost of estimating agent risk parameters. Second, they facilitate the calculation of various analytic measures that are useful for understanding production behavior, such as the risk premium and the elasticity of supply. Third, they allow for geometric explanations of agent attitudes toward price uncertainty. These practical attributes would facilitate a structural examination of farmer production behavior in the face of price risk. Furthermore, since the location and scale parameter condition under which all the arguments in this study are made is satisfied in a large number of economic models, the structural model simplification procedure considered here would be effective for developing tractable structural models involving alternative types of randomness, such as yield and financial uncertainties.