Two Countries, Albania and Bolivia A and B
Identical Cobb-Douglas Technologies to Produce X and Y
X= KαL(1-α) And Y = KβL(1-β)
This gives us constant returns to scale with α and β < 1 . if α<>β we will have the standard Concave PPF.
World Labor Is 300 as is World Capital
Ka = 100 La = 200
Kb =200 Lb= 100
Albanian is Labor Rich relative to Bolivia. Hence, Bolivia is, definition relatively capital rich We will let α=.25 and β=.75 which means x is a labor intensive technology relative to y.
The two PPF’s
Are given Look Like This.
If Capital and Labor could migrate Labor would emigrate from labor rich country to labor poor country. Capital would Flow in the opposite direction. If capital in labor were equal in both country. then they would each have a scaled down endowment of the world. The world PPF would look like this:
Given The Current factor endowments we Can see the maximum production levels of each good in each country and we can see how a lack of factor mobility affects the PPF.
The lack of factor mobility prevents factors from migrating to where they are most need, Hence, We can not be on the Worlds PPF with complete specialization in either good even if all resources are being fully employed.
However, The will be a region of specialization where we can be on the world PPF. This requires production bundles to have the same MRT (marginal rate of transformation) or opportunity costs. If the are not it would be possible for both countries to alter production and lead to an increase in the production of both goods. (a Pareto improvement).
The Range of the MRT’s for Albanian are .41 to 1.18 for B the range is .82 and 2.35. The overlap is .82 to 1.17. So It is possible for joint production to lie on the World PPF. When MRT in both countries are the same between .82 and 1.18. If one country chooses an output mix and the MRT lies on this interval hen the other country can choose any output mix it wants. However, only one output mix, when combined with the other country’s production will lie on the World possibilities frontier.
In Summary. For a single country it is necessary that all inputs be employed to be on their PPF. IF all inputs are Efficiently employed then the MRTS in both industries will equal the common w/r ratio. This is necessary and sufficient. It is called Technical efficiency
For world resources to be used efficiently (on the world PPF) it is necessary for both (all) counties to be on their respective frontiers. If all countries are producing at the same MRT on the frontiers is both necessary and sufficient for world resources to be employed efficiently. If global markets are competitive then all countries will be facing the same product prices which is where Profit maximization drives the MRT