Generalizing the General: generalizing the CES production function to allow for the viability of input thresholds

The original specification of the Constant-Elasticity-of-Substitution (CES) production function introduced by Arrow, Chenery, Minhas, and Solow is considered to be a general production specification that nests multiple types of production functions, i.e. Leontief, Cobb-Douglas, and linear. However, even this general specification of production functions is restrictive in several ways. This paper proposes a generalized variant of the CES production function that allows for the inclusion of the minimum required levels of inputs. Not allowing for this potential attribute is, in fact, one shortcoming of the original CES production-function specification, which in turn could result in misleading conclusions about essential levels of inputs. Accordingly, a solution is proposed to overcome the mentioned shortcoming. Input thresholds are incorporated in the CES production specification, and empirical applications are provided for irrigation and nitrogen. To illustrate the proposed approach in this paper, two empirical applications in irrigation and fertilizer response using the famous Hexem-Heady experimental dataset as well as several datasets produced using Monte-Carlo experiments with different data-generating processes are provided. Finally, implications for modelling input thresholds are considered and discussed.