Factor-specific technology choice

We analyze 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. By considering the problem in its generality, we are able to reach beyond the known results for Cobb–Douglas, CES, Leontief (minimum) and maximum functions. We demonstrate 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. Invoking Bergson’s theorem, we also comment on the consequences of assuming homotheticity of the three objects, with a particular focus on technology menus constructed as level curves of idea (unit factor productivity) distributions.