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?
$\begingroup$
$\endgroup$
Add a comment
|
1 Answer
$\begingroup$
$\endgroup$
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:
