An increase in the rate of return on the invested resources reduces the amount of
stealing because it raises the marginal opportunity cost of the stolen resources.
A larger a means LSH/LR is more negative. If the manager owns more of the
"rm, then a given increase in the return on investment convinces him to put more
resources into the investment project and, therefore, to steal less. Conversely, if the
manager owns more but the return on investment declines, then he steals more.
A larger value of k means that LSH/LR is more negative. A lower cost of
stealing (higher k) both raises the equilibrium value of stealing and makes
stealing more responsive to changes in the rate of return on investment. This is
because higher k both shifts up the stealing function and makes it less concave
(i.e., the returns to stealing do not decrease so strongly.)
The outside investor receives share (1!a) of the returns from the funds that
are actually invested in the "rm. The expected value of the equity in the "rm is
therefore
P"R(I!k(1!aR)),