The magnification effect for quantities is a more general version of the Rybczynski theorem. It
allows for changes in both endowments simultaneously and allows a comparison of the
magnitudes of the changes in endowments and outputs.
The simplest way to derive the magnification effect is with a numerical example.
Suppose the exogenous variables of the model take the following values for one country:
With these numbers which means that steel production is capitalintensive
and clothing is laborintensive.
The labor and capital constraints are,
Labor constraint:
Capital constraint:
We graph these on the adjacent Figure. The steeper red line is the labor
constraint and the flatter blue line is the capital constraint. The output
quantities on the PPF can be found by solving
the two constraint equations simultaneously.
A simple method to solve these equations follows.
First, multiply the second equation by (2) to get,
Adding these two equations vertically yields,
which implies, . Plugging this into the first equation above (any equation
will do) yields, . Simplifying we get, .
Thus, the solution to the two equations is: Q_{C} = 24 and Q_{S} = 24
Next suppose the capital endowment, K, increases to 150. This changes the capital constraint
but leaves the labor constraint unchanged. The labor and capital constraints now are,
Labor constraint:
Capital constraint:
Follow the same procedure to solve for the outputs in the new full employment equilibrium.
First, multiply the second equation by (2) to get,
Adding these two equations vertically yields,
which implies, . Plugging this into the first equation above (any equation
will do) yields, . Simplifying we get, .
Thus the new solution is: Q_{C} = 6 and Q_{S} = 36.
The Rybczynski theorem says that if the capital endowment rises it will
cause an increase in output of the capitalintensive good (in this case
steel) and a decrease in output of the laborintensive good (clothing).
In this numerical example Q_{S} rises from 24 to
36, Q_{C} falls from 24 to 6.
The magnification effect for quantities ranks the percentage changes in endowments and the
percentage changes in outputs. We'll denote the percentage change by using a ^ above the
variable. (that is, = % change in X).
Percentage Changes in the Endowments and Outputs
The capital stock rises by 25%.
The quantity of steel rises by 50%.
The quantity of clothing falls by 75%.
The labor stock is unchanged.
The rank order of these changes is the Magnification Effect for Quantities,
The effect is initiated by changes in the endowments. If the endowments change by some
percentages, ordered as above, then the quantity of the capitalintensive good (steel) will rise by a
larger percentage than the capital stock change. The size of the effect is magnified relative to
the cause.
The quantity of cloth (Q_{C}) changes by a smaller percentage than the smaller labor endowment
change. Its effect is magnified downward.
Although this effect was derived only for the specific numerical values assumed in the example, it
is possible to show, using more advanced methods, that the effect will arise for any endowment
changes that are made. Thus if the labor endowment were to rise with no change in the capital
endowment, the magnification effect would be,
This implies that the quantity of the laborintensive good (clothing) would rise by a greater
percentage than the quantity of labor, while the quantity of steel would fall.
The magnification effect for quantities is a generalization of the Rybczynski
theorem. The effect allows for changes in both endowments simultaneously
and provides information about the magnitude of the effects. The Rybczynski
theorem is one special case of the magnification effect that assumes one
of the endowments is held fixed.
Although the magnification effect is shown here under the special assumption of fixed factor
proportions and for a particular set of parameter values, the result is much more general. It is
possible, using calculus, to show that the effect is valid under any set of parameter values and in a
more general variable proportions model.
International Trade Theory and Policy Lecture
Notes:
©19972006 Steven M. Suranovic, Last Updated on 7/31/06
