Some notes on the optimization of the gross national product of economies with nonlinear input-output technology

We consider multisectored economies characterized by a not necessarily linear input-output operator
A (\cdot)
which transforms each
n
-vector of total gross outputs into some
n
-vector of final demands. Attention is focused on cases in which some prime resource must be allocated throughout an economy which does not possess decreasing returns to scale. Some general results are proved concerning the nature of the solution of the problem of globally optimizing the Gross National Product. It is proved, for example, that under certain assumptions the absolute maximum value of the Gross National Product can be determined by solving
n
nonlinear equations, each in only one unknown, in which
n
is the number of sectors into which the economy is divided.