where L is the lower bound on earnings (Et), U' is the limit on the excess of
earnings over the lower bound (E 1 -L), and p is the payout percentage
defined in the bonus contract. The manager receives p(E t -L) in bonus if
earnings exceed the lower bound and are less than the bonus plan limit (the
upper bound) on earnings, U, given by the sum (U' + L). The bonus is fixed at
p U' when earnings exceed this upper bound.