<p>Consider the following 2 goods (X and Y), 2 inputs model (L and K):</p>
<ul>
<li>Production functions (with IRS): <span class="math-container">$x=(l_x+k_x)^2$</span>, <span class="math-container">$y=l_y^2$</span></li>
<li>Input constraint: <span class="math-container">$l_x+l_y=1$</span>, <span class="math-container">$k_x=1$</span></li>
</ul>
<p>In this case, production possibility frontier (PPF) is <span class="math-container">$\sqrt{x}+\sqrt{y}=2$</span>, where <span class="math-container">$1\leq x\leq 4$</span>. Observe that the PPF is convex.</p>
<p>Here is the graph of the PPF:
<a href="https://i.sstatic.net/Olb6qlm1.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/Olb6qlm1.png" alt="enter image description here" /></a></p>

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2024-09-15T01:13:10.350Z
2024-09-15T04:40:44.057Z
2024-09-15T04:40:44.057Z
Amit
<p>Given a 2X2 model (2 goods, 2 inputs), if the factor intensities (capital/labour ratio) of the two goods along the Pareto set are unequal, then we get a concave PPF. Can we get a convex PPF in some cases, for example with increasing returns to scale? </p>

<production-function>
When is the PPF convex to the origin?
PGupta
# When is the PPF convex to the origin?

(Asked by: username_0 on 2019-03-08)

Given a 2X2 model (2 goods, 2 inputs), if the factor intensities (capital/labour ratio) of the two goods along the Pareto set are unequal, then we get a concave PPF. Can we get a convex PPF in some cases, for example with increasing returns to scale?

**Tags:** production-function

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## 1 answers

### Answer by username_1 on 2024-09-15. Score: 1

Consider the following 2 goods (X and Y), 2 inputs model (L and K):

* Production functions (with IRS): $x=(l\_x+k\_x)^2$, $y=l\_y^2$
* Input constraint: $l\_x+l\_y=1$, $k\_x=1$

In this case, production possibility frontier (PPF) is $\sqrt{x}+\sqrt{y}=2$, where $1\leq x\leq 4$. Observe that the PPF is convex.

Here is the graph of the PPF:
[![enter image description here](https://i.sstatic.net/Olb6qlm1.png)](https://i.sstatic.net/Olb6qlm1.png)


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