Comparative Statics

How do wages and profits change with the $v_{lf}$? Who gains and who loses? We use the framework of monotone comparative statics to answer this question.

Suppose $v_{lf}$ increases to $v'_{lf}$ holding all else fixed. There are three cases:

• $lf$ is an in-the-money match; $x_{lf}=1$.
• $lf$ is not in the money, and remains so; $x_{lf}=x'_{lf}=0$.
• $lf$ is not in the money, but becomes so; $x_{lf}=0$ and $ x'_{lf}=1$.

But there are really only two cases. Case iii) can be decomposed into a change in $lf$ over the range where there is an optimal matching in which $l$ is not matched with $f$, and a change over the range where $lf$ is part of an optimal matching. The two ranges intersect at a point where there are (at least) two optimal matches, and all such matches have the same value.