Some comparative-statics results for nonlinear input-output models of a multisectored economy,and related results for nonlinear price-demand relations

For a nonlinear version of the linear input-output model of Leontief, we consider the effect, on the vector x of total gross outputs, of changes in the components of the final-demand vector c. For example, it is shown that, for a certain important class of models, the “large-change elasticity” of any component of x, with respect to any component of c, is less than or equal to unity. Some similar results are proved concerning properties of nonlinear price-demand relations for the case in which all goods are weak gross substitutes. Unlike earlier work in this general area, we do not introduce hypotheses concerning the indecomposability or homogeneity of certain mappings. For that reason, the results are valid for the price-demand relation for a single firm, or for any collection of firms.