topic 4.3
The theorem is:
If a country experiences an increase in its endowment of any one factor holding all other things constant (including prices of products and factors) then the output of the good that uses the factor intensively will rise and the output of the other good will fall.
Consider figure 4.3 (p. 115).
To orient ourselves consider two isoquants: S output valued at $1 and T output valued at $1. (This is an arbitrary starting point -the theorem does not depend on it.)
The relative goods price is Ps/Pt = 1.
Ps/Pt = 1 implies that both S and T isoquants 'use' the same isocost line. So in the figure the isocost line is really two overlapping isocost lines.
Cost equals price of production so the isocost line represents an expenditure on hiring factors of production of $1 total.
For the isocost line the intercepts are 1/R (all the value of output goes to capital) or 1/W (all the value of output goes to labor).
The Rybczynski theorem keeps Ps/Pt constant by definition so wherever production occurs the isocost slope is the same which means that:
- S production will occur along the Ks/Ls ray.
- T production will occur along the Kt/Lt ray.
All the labor and capital has to be absorbed into production. That can only occur at E if GE is the ray for T production and EH is the ray for S production.
Now suppose we increase the labor endowment so E' is the new combination of L and K that must be absorbed.
Then (keeping Ps/Pt and K constant) we can only move from E to E' if the new rays are G'E' and H'E'.
So production of T increases and S decreases.
This proves the theorem.
The intuition is: to absorb all the factors (no unemployment), if we increase the total labor available we have to increase production of the labor intensive good relative to the other good.
We get this strong result because we are not allowing 'prices' (W/R) to change. All the adjustment to the 'shock' (endogenous increase in L) has to occur on the quantity side.
