# 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it isn’t producing at a higher level is that there’s still some cash deposit in its business account that hasn’t been withdrawn yet.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?

## 1 Answer

Well the problem here is in a set up. It is inconsistent to say that firm is producing below PPF not due to underutilization of factors of production but due to cash, since cash will not enter production function, or if you assume that cash is here used to buy factors of production it is inconsistent to say that firm fully utilizes all avaiable factors while having excess cash.

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.

• @ 1muflon1♦ thank you for your answer. To make no mistake about it, you are suggesting that if I don't consider cash in the production function, then I can't just announce that the firm hasn't achieved its productive efficiency because there's still excess cash. Thus, in this case, the points lying beneath the PPF simply indicates that the firm is not producing in the most efficient way, or not using the best technology. Either way, it's not due to the excess cash. Did I get you wrong? – Underwood Jan 20 at 12:59
• @Underwood yes and in addition even if you assume firm uses cash to purchase factors, it would not be appropriate to say that firm uses all factors of production that are available to it until it is not able to purchase more. – 1muflon1 Jan 20 at 13:12
• @Underwood the key to understand this is to understand the definition of productive efficiency, productive efficiency is a situation in which the economy or an economic system could not produce any more of one good without sacrificing production of another good and without improving the production technology. In a perfectly competitive market you can prove that any such allocation above will also be such where the average total cost for each good is minimized, but that result wont hold necessarily in other market structures. In addition, min. of cost does not imply firm has free cash. – 1muflon1 Jan 20 at 16:59
• in a model of perfect competition with no opportunity cost all profits (including accounting ones) are zero and firm is not left with anything extra after minimizing all cost. Efficiency, especially productive efficiency is not the same as maximizing profit. In fact in non-competitive market structures often the way how firm achieve profit is to not produce as much as possible given productive efficiency, but to lets say underproduce to increase market price, like a monopoly would (i.e. monopoly will not produce at point where MC=P, but at point where MR=P). – 1muflon1 Jan 20 at 17:02
• @Underwood you can prove it by setting up a mathematical model with perfectly competitive firms, no market imperfections and host of other standard assumptions and examining allocation of factors in equilibrium - at least that is the gist of it. That summary sounds simple but the model itself is of course more complex and requires a good command of math and definitely too long to just walk you through it in the comments, but you can see it in most graduate level micro textbooks. – 1muflon1 Jan 20 at 18:01