<p><span class="math-container">$ \textbf{Answer:}  $</span>
Simply put, it does not matter which good goes on which axis as long as the relationship between the two goods is adjusted for correctly.</p>

<p><span class="math-container">$\textbf{Explanation:}$</span> </p>

<p>This can be done as long as the relationship (i.e. the PPC curve) is correctly maintained, that is the function is inverted when you change between the x and y axis.</p>

<p><span class="math-container">$\textbf{For Example:} $</span> </p>

<p>Suppose you were given the ppf which was linearly defined <span class="math-container">$good_1$</span> as a function of <span class="math-container">$good_2$</span>  by: </p>

<p><span class="math-container">$$good_1(good_2)= -a\times good_2 +b$$</span>
<span class="math-container">$$\implies good_1= -a\times good_2 +b$$</span></p>

<p>graphically this can be seen as; </p>

<p><a href="https://i.sstatic.net/1bC5v.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/1bC5v.png" alt="enter image description here"></a></p>

<p>By inverting the function, we now make <span class="math-container">$good_2$</span> a function of <span class="math-container">$good_1$</span> (i.e. <span class="math-container">$good_2(good_1)$</span>), which simplistically means solving <span class="math-container">$good_1= -a\times good_2 +b$</span> for <span class="math-container">$good_2 $</span>; </p>

<p><span class="math-container">$$ good_2(good_1)=-\frac{1}{a}\times good_1 +\frac{b}{a}$$</span></p>

<p>i.e. From this
<span class="math-container">$$good_1= -a\times good_2 +b$$</span>
to this
<span class="math-container">$$\implies good_2=-\frac{1}{a}\times good_1 +\frac{b}{a}$$</span></p>

<p>and graphically: </p>

<p><a href="https://i.sstatic.net/yzABA.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/yzABA.png" alt="enter image description here"></a></p>

<p>We can see that everything is the same, except that our axes are different but the relationship between the two good is exactly the same. The relationship is now inverted to accommodate the change of "perspective" between having <span class="math-container">$good_1$</span> or <span class="math-container">$ good_2$</span> in the axis, which is graphically seen by the change in the intercepts. </p>

<p><span class="math-container">$*$</span> I apologise if this is not mathematically rigours, and would appreciate any feedback! </p>

CC BY-SA 4.0
2019-02-23T01:24:06.687Z
Very well explained. Thanks for your response!
Steven
CC BY-SA 4.0
2019-02-22T11:31:03.563Z
2019-02-23T07:45:42.607Z
2019-02-23T07:45:42.607Z
J.N
<p>I am trying to create a PPC, in which there are two goods (e.g. apples and oranges).</p>

<blockquote>
  <p>My question is, does it matter which goods are plotted on the x or y-axes? The opportunity cost per good remains the same, but I was wondering what the convention is.</p>
</blockquote>

<microeconomics>
Constructing a Production Possibility Curve (PPC)
Steven
# Constructing a Production Possibility Curve (PPC)

(Asked by: username_0 on 2019-02-22)

I am trying to create a PPC, in which there are two goods (e.g. apples and oranges).

> My question is, does it matter which goods are plotted on the x or y-axes? The opportunity cost per good remains the same, but I was wondering what the convention is.

**Tags:** microeconomics


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## 1 answers

### Answer by username_1 on 2019-02-22. Score: 2 | Accepted answer

$ \textbf{Answer:} $
Simply put, it does not matter which good goes on which axis as long as the relationship between the two goods is adjusted for correctly.

$\textbf{Explanation:}$

This can be done as long as the relationship (i.e. the PPC curve) is correctly maintained, that is the function is inverted when you change between the x and y axis.

$\textbf{For Example:} $

Suppose you were given the ppf which was linearly defined $good\_1$ as a function of $good\_2$ by:

$$good\_1(good\_2)= -a\times good\_2 +b$$
$$\implies good\_1= -a\times good\_2 +b$$

graphically this can be seen as;

[![enter image description here](https://i.sstatic.net/1bC5v.png)](https://i.sstatic.net/1bC5v.png)

By inverting the function, we now make $good\_2$ a function of $good\_1$ (i.e. $good\_2(good\_1)$), which simplistically means solving $good\_1= -a\times good\_2 +b$ for $good\_2 $;

$$ good\_2(good\_1)=-\frac{1}{a}\times good\_1 +\frac{b}{a}$$

i.e. From this
$$good\_1= -a\times good\_2 +b$$
to this
$$\implies good\_2=-\frac{1}{a}\times good\_1 +\frac{b}{a}$$

and graphically:

[![enter image description here](https://i.sstatic.net/yzABA.png)](https://i.sstatic.net/yzABA.png)

We can see that everything is the same, except that our axes are different but the relationship between the two good is exactly the same. The relationship is now inverted to accommodate the change of "perspective" between having $good\_1$ or $ good\_2$ in the axis, which is graphically seen by the change in the intercepts.

$\*$ I apologise if this is not mathematically rigours, and would appreciate any feedback!

> **Comments:**
> **username_0**: Very well explained. Thanks for your response!  

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