divide both sides by L
^L = λ_{L1} ^y_{1} + λ_{L2}
^y_{2}.
where λL1 = a_{L1} y_{1}/L =
L_{1}/L = the percentage of labor forced employed in industry
1.
This shows that the percentage change in labor is a
weighted average of the growth rates of the two outputs. That is, labor
growth lies somewhere between the two output growth rates, ^y_{1}
and ^y_{2}.
If both outputs grew at the same rate, say 10%, then
labor demand would also grow by the same rate. However, by the Rybczynski
Theorem, the output of one industry actually declines. This implies
that the other industry must grow more than proportionately. That is,
if labor grows by 10%, one industry declines but the other industry
must grow more than 10%. This is the intuition behind the Magnification
Effect.
For example, assume that labor shares of two industries
are equal (50%) and that labor supply rises by 10% and the capital-intensive
industry contracts by 5%. the above equation reduces to:
10% = (1/2)^y_{1} + (1/2)(-5%).
Even when industry 2 does not contract, output of the
labor intensive industry must expand 20% ( which is more than 10%).
Since the capital-intensive sector declines, industry 1 has to grow
even faster to offset this negative effect. |