The assumptions on production were not the same as those used in the
analysis of production itself. In the latter, a common, though not universal,
assumption was that of constant returns to scale; if any production process
can be carried out, with given inputs and outputs, then the process can be
carried out at any scale. That is, if the inputs are all multiplied by the same
positive number, then it is possible to produce the same multiple of all the
outputs. But in this case, there cannot be a unique profit-maximizing position
for any set of prices. For suppose there were a position which yielded positive
profits. Then doubling all inputs and outputs is feasible and yields twice as
great profits. Hence, there would be no profit-maximizing position, since any
one could be improved upon. On the other hand, zero profits can always be
obtained by having no inputs and no outputs. It can be concluded that, if
prices are such that there is some profit-maximizing set of inputs and outputs not all zero, the corresponding profits must be zero, and the same profits can
be achieved by multiplying all inputs and outputs by any positive number.