Factor-specific technology choice

This paper analyzes the properties of a two-dimensional problem of factor-specific technology choice subject to a technology menu - understood as the choice of the degree of factor augmentation by a producing firm or the choice of quality of goods demanded by a consumer. The considered general setup encompasses the benchmark cases of Cobb-Douglas, CES and Leontief (minimum) functions. It is shown that the technology menu and the global function (envelope of local functions) are dual objects, in a well-defined generalized sense of duality. In the optimum, partial elasticities of (i) the local function, (ii) the technology menu and (iii) the global function are all equal and there exists a clear-cut, economically interpretable relationship between their curvatures. In particular, the elasticity of substitution of the global function is always above that of the local function. The paper also invokes Bergson's theorem to comment on the consequences of assuming homogeneity or homotheticity, with a particular focus on technology menus constructed as level curves of idea (unit factor productivity) distributions.