Econometrica: Nov, 1973, Volume 41, Issue 6

A Nonlinear Input-Output Model of a Multisectored Economy

https://doi.org/0012-9682(197311)41:6<1167:ANIMOA>2.0.CO;2-3
p. 1167-1182

I. W. Sandberg

This paper reports on some mathematical and analytical properties of a static nonlinear model of a national economy or, more generally, of a multisectored economy. The model is a nonlinear version of the well-known linear input-output model of Leontief. Conditions are given for the nonlinear model to be workable in the sense that (i) there is a unique nonnegative vector of output production levels for each nonnegative final-demand vector, and (ii) the vector of output levels depends in a certain reasonable manner on the final-demand vector. Attention is also focused on several other properties of the model of economic interest. For example, it is shown that propositions completely analogous to the LeChatelier-Samuelson principle in both the weak and strong forms for workable Leontief systems are valid within the context of the nonlinear model.