<p>It is, as you say, a mathematical device to define the production set in a way that is analytically tractable</p>

<p>I have seen <a href="https://web.stanford.edu/~jdlevin/Econ%20202/Producer%20Theory.pdf" rel="nofollow noreferrer">one description</a> as thinking of it as a measure of <em>the amount of technical progress now required to make the combination $y$ a feasible one</em>, so </p>

<ul>
<li>if $F(y)=0$ then that combination is just feasible with current technology, </li>
<li>if $F(y)\lt 0$ that combination is feasible with less than current technology, </li>
<li>if $F(y)\gt 0$ that combination requires more than current technology enables and so is currently not feasible</li>
</ul>

<p>though this looks more like handwaving and rationalisation rather than something actually meaningful  </p>

CC BY-SA 4.0
2018-05-26T17:18:02.647Z
2018-05-26T17:18:02.647Z
Henry
<p>One reason a direct interpretation may be difficult is that the function is seemingly without unit. That is if for a function $F()$ the inequality $F(y) \leq 0$ yields the set of feasible productions then the function $G() = 2F()$ works as well. The same is true for any other scalar multiplication or any monotonic transformation of $F$ that leaves the $F(y) = 0$ level curve in place.  </p>

CC BY-SA 4.0
2018-05-26T17:43:07.530Z
2018-05-26T17:43:07.530Z
Giskard
<p>The production set has a simple meaning: It is the set of all production vectors that are feasible to a firm. </p>

<p>The production function also has a simple meaning: It gives the output quantity for a given vector of input quantities (for a firm that produces only one output. )</p>

<p>But what is the production transformation function? It is defined as the function $F(y)$ such that the production set is $\{y: F(y)\leq 0 \}$. Essentially, it is a way to encode the production set. </p>

<p><strong>But is there also a meaningful interpretation of this function itself, rather than merely as a mathematical device to define the production set in a way that's analytically tractable?</strong> </p>

CC BY-SA 4.0
2019-06-14T17:41:44.943Z
See a similar question (and my response) here: https://economics.stackexchange.com/a/29786/21170
Julia B
<production-function>
Is there an economic interpretation of the production transformation function?
user56834
# Is there an economic interpretation of the production transformation function?

(Asked by: username_0 on 2018-05-26)

The production set has a simple meaning: It is the set of all production vectors that are feasible to a firm.

The production function also has a simple meaning: It gives the output quantity for a given vector of input quantities (for a firm that produces only one output. )

But what is the production transformation function? It is defined as the function $F(y)$ such that the production set is $\{y: F(y)\leq 0 \}$. Essentially, it is a way to encode the production set.

**But is there also a meaningful interpretation of this function itself, rather than merely as a mathematical device to define the production set in a way that's analytically tractable?**

**Tags:** production-function
> **Comments:**
> **username_1**: See a similar question (and my response) here: https://economics.stackexchange.com/a/29786/21170  

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## 2 answers

### Answer by username_2 on 2018-05-26. Score: 2

It is, as you say, a mathematical device to define the production set in a way that is analytically tractable

I have seen [one description](https://web.stanford.edu/~jdlevin/Econ%20202/Producer%20Theory.pdf) as thinking of it as a measure of *the amount of technical progress now required to make the combination $y$ a feasible one*, so

* if $F(y)=0$ then that combination is just feasible with current technology,
* if $F(y)\lt 0$ that combination is feasible with less than current technology,
* if $F(y)\gt 0$ that combination requires more than current technology enables and so is currently not feasible

though this looks more like handwaving and rationalisation rather than something actually meaningful


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### Answer by username_3 on 2018-05-26. Score: 2

One reason a direct interpretation may be difficult is that the function is seemingly without unit. That is if for a function $F()$ the inequality $F(y) \leq 0$ yields the set of feasible productions then the function $G() = 2F()$ works as well. The same is true for any other scalar multiplication or any monotonic transformation of $F$ that leaves the $F(y) = 0$ level curve in place.


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