which is the sensitivity of "rm value to changes in R. This is always positive
because we have assumed that the optimal level of stealing is less than I. The
maximum value of stealing, given by the "rst-order condition when aR is zero, is
k. We have already assumed that there cannot be `negativea stealing, so k)I,
and thus is su$cient to ensure that o!'0.
There are two e!ects of a higher R. The "rst, direct e!ect is to raise the
expected payo! and thus increase the amount that the investor is willing to put
into the "rm. Holding the level of stealing constant, the direct e!ect shows that
the value of the "rm rises. The second, indirect e!ect works because higher
returns from investment reduce the optimal level of stealing, so LS*/LR(0.
Lower stealing also raises the expected payo! for outside investors and increases
the value of the "rm.2
What is the e!ect on LP/LR of changing the penalty for managerial theft, k?
The e!ect on the absolute responsiveness is
Lo!/Lk"2Ra!1.