Now let's consider our proposition known as the Rybczynski theorem.
The Rybczynski theorem basically asks:
What happens if a factor of production increases in one country?
For instance, imagine some labor migrating into a new country.
The theorem says this:
If the supply of labor increases in an economy,
we then find that the output and exports of the labor-intensive sector go up.
Perhaps a bit more counter-intuitively,
we also find that the output and exports of the capital intensive sector will go down.
Of course, that's for an increase in labor.
If we did it for an increase in capital,
we would find the output and exports of the capital intensive sector go up
and the output and exports of labor would go down.
All of this is going to be based in Heckscher-Ohlin-like assumptions
and you can review those on our Heckscher-Ohlin videos.
But basically, we have a classic two by two by two model
with two goods, two sectors,
two factors of production and two countries.
In this context in particular, I would emphasize that
we are dealing with an economically small country
which does not influence world prices.
So that is going to mean fixed prices for goods
and also fixed prices for factors of production.
Sometimes, the theorem is presented graphically as follows:
So on the vertical axis, we have the production of computers,
which is the capital intensive good
and on the horizontal axis, we have the production of shoes,
which is the labor-intensive good.
And we have two initial lines
this is called the L1, this is called the labor constraint.
It tells you how those outputs are constrained by
the quantity of available labor.
We have another line, called the capital constraint,
that is represented by C1 here,
and if we take the labor constraint and the capital constraint,
we find the economy is at this point,
and this will imply an output of computers equal to this level
and an output of shoes given by this level here.
An exogenous increase in labor then shifts out the labor-constraint to L2,
so we then have this line here,
which is out and to the right of L1.
And if we then combine the new labor constraint
with the old capital-constraint,
we will find we are at this point of intersection.
We'll have a new quantity of shoes here
and a new quantity of computers here
and if we compare the new and the old, what we can see is that
output of shoes has gone up
and output of computers has gone down,
and that is indeed illustrating the basic theorem.
Alternatively, consider how this works in intuitive terms.
So, let's assume for instance that some new labor arrives in Guatemala.
And now let's think through the steps.
That new labor will mean a bigger boost to the production of labor-intensive goods,
which in this case is shoes.
That's because the more labor you have,
well that aids the production of things which require labor.
But now think about it,
think about the ratio of capital to labor in shoe production.
It's now the case that the marginal product of labor,
the MP of labor for shoe production;
that goes down because we now have a higher ratio of labor to capital
in shoe production
and the more labor you have relative to capital,
well, that means a lower marginal product of labor
or at least that would be the case if factor prices were allowed to change.
But now recall our assumption that
the wage is fixed and general prices are fixed.
Also, the price of shoes is fixed,
so prices cannot adjust.
So, we need in this model to be keeping the MPL,
the marginal product of labor equal to the wage.
So how is it that we can get the marginal product of labor
back up in the shoe sector?
Well, what we need is that capital flows into the shoe sector
to restore a capital to labor proportion,
which will be consistent with keeping the marginal product of labor constant
and keeping the wage constant.
And so basically, capital is flowing into shoe production in Guatemala
and capital is flowing out of computer production in Guatemala
or whatever else is the capital intensive industry
and because the capital intensive industry is losing capital,
we then conclude that output in the capital intensive industry shrinks.
And that gives our eyes to the basic results of the theorem.
So, just to review all of that,
basically you are assuming prices are fixed
because they are fixed in global markets,
and we are talking about a small country here.
There is then an exogenous shock,
consider that to be the arrival of either labor or capital.
Since prices cannot adjust,
then all of the adjust has to be in quantities,
which of course will include output.
Furthermore, through a Heckscher-Ohlin mechanism,
this will include exports too.
So now that the country is more labor-intensive,
they are more likely to be exporting labor-intensive goods.
I would stress that the Rybczynski theorem is thought of as an abstract device
or part of the economist's toolbox.
It is not necessarily intended as realistic or representative,
but it's a way of helping us think through the relationships
between different quantities in an economic model
and of understanding the point that, when economic prices cannot adjust,
that in some manner, quantities will adjust instead.
Nonetheless, we can find some attempts to apply the theory
to actual real-world phenomena,
and most typically, the theory is applied when we ask the question:
Will immigration lower wages?
And the Rybczynski theorem actually is suggesting,
at least if you buy into all of the assumptions,
that immigration into a country will not lower wages
or not lower wages very much.
The adjustment will be in terms of quantities
and this will spur their production of labor-intensive goods,
and again, through Heckscher-Ohlin mechanisms,
encourage that nation to become more of a labor-intensive exporter.
For sources on this topic,
there is of course the Feenstra and Taylor text,
check the index for the page numbers.
You can simply use Google if you wish.
And on the Empirics,
there is an interesting piece by Gordon Hanson and Matt Slaughter
listed here.
You can find this online.