What is a statutory constraint?

Microeconomics: Can increasing return to scale be a great economics intuition explaining the violation of production feasibility constraint?

• Let's consider the assumption of an homothetic and homogeneous production function [q<f(Zi) or q=f(Zi) with i=1,2] (maybe a standard Cobb-Douglas could fit well in this case), let's also define the existence of a feasibility production constraint. Under these assumptions, can the ideas of Increasing Return to Scale (IRTS) and/or the price of a generic input "i" equal to zero (Pi=0) imply a violation of the feasibility production constraint? I've thought that having IRTS implies that a firm can proportionally increase its production more than the increase of the inputs, and in this way it can "double" (for example) the production infinite times; and obviously it seems that it violates the feasibility production constraint. Moreover if we consider that the price of one input is Pi=0 then the firm could use an infinite quantity of this input keeping the others fixed. I thought that it makes impossible to violate the budget constraint so from this assumption follows that cost minimization becomes impossible as well as the existence of a solution to the profit maximization problem. It implies that a firm can violate the production feasibility constraint because it can increase infinitely its output only increasing the input which has a price equal to zero (supposing the existence of an input in infinite quantity). I'm not yet an economist and i'm far from becoming, so obviously there's an high probability that my intuitions are completely wrong.

• Answer:

  Not really. In order to be useful the production feasibility constraint should be defined in such a way that it takes into account things like the increasing returns to scale or the existence of an input that was in infinite supply at a price of 0 for that matter. Although the latter is a somewhat non-standard situation.