A generalization of a class of production functions

In this article we shall give a generalization of Cobb--Douglas, Constant Elasticity of Substitution (CES), Lu--Fletcher, Liu--Hildebrand, Variable Elasticity of Substitution (VES) and Kadiyala production functions. We compute the principal indicators such as the marginal products, the marginal rate of substitution, the elasticities of factors and the elasticity of substitution. Finally, we formulate three theorems of characterization for the functions with a proportional marginal rate of substitution, with constant elasticity of labour and for those with constant elasticity of substitution (for <italic>n</italic> = 1).