# Do points inside the PPF curve always mean productive inefficiency?

If a firm produces combinations of goods along the PPF curve, it has achieved its productive efficiency. And when a firm reaches productive efficiency, it means that all factors of production have been fully utilized. And another way of measuring productive efficiency is to look at its average cost. If a firm has reached productive efficiency, it means that the firm is producing at the lowest average cost.

But what about the points that fall inside the PPF?

Let’s say A (15,10) is on the PPF curve, and B (15,5) lies beneath it. Assume that a firm is producing at point B, and the reason why it isn’t producing at a higher level is that there’s still some cash deposit in its business account that hasn’t been withdrawn yet.

Since cash deposit is NOT a factor of production, even the firm is producing at points beneath the PPF, it doesn’t necessarily imply that the firm has not utilized all factors of production. Where did I go run?

For example, take very simple production function $$F=L^{1/2}$$ and firm has access to 100 units of labor, with all the standard background assumptions. I used this simplistic case because here PPF is just one point instead of set of points, and in this case the PPF would just be point F=10. If firm would be using 100 units of labor it would be operating at PPF and if not it would be operating below PPF. However, you cant just arbitrary announce that this firm is producing F=8, due to not using all cash if cash does not enter as factor of production. That is simply inconsistent with having production function $$F=L^{1/2}$$
Furthermore, let us assume that firm does not just have 100 units of labor but that it has 100 dollars and has to purchase labor on labor market for 1 dollar per labor. Well in this case if firm has still some excess cash, for example if it purchased only 70 units of labor, then it still does not uses all factors of production in most efficient manner because given its 100 dollars it still has 30 units of labor avaiable for hire that it could use. Consequently, the problem in the setting above is that it just arbitrary announces that firm is utilizing all factors of production as much as possible while not being at PPF. That is like asking, from math we know that unit circle is given by all points that satisfy equation $$1=x^2+y^2$$, but I assume point (100,10) lies on unit circle and it clearly does not satisfy the equation. It is just inconsistent reasoning.