of banking intermediaries, and secondly, isolating the whole economy from
the real impact of systemic instability and failures. Hence, a systemic super-
visor assigns negative value to bank failure as bankruptcy triggers costs for
the banking system and the whole economy. These costs are supposed to be
proportional to the depositors’ loss.
The negative value which the prudential and systemic supervisor assigns
to bankruptcy is, thus, given by
S(q0)=(1+b)
rb
Гт
(rL - γ(L) - (1 - k(q0))L)dG(r|q(q0))
(6)
with b> 0 reflecting the triggered costs above the actual loss to depositors.
Icallb the excess cost factor. The dependence of k and q on the level of
innate quality follows from the fact that the bank abides by the regulation.
Apart from the negative value of possible financial distress, the supervisor
assigns positive value to the bank’s rents π:
rr
(q0) =
rb
[rL - γ(L) - (1 - k(q0))L]
(7)
dG(r|q(q0)) - rek(q0)L - C(q(q0) - q0).
This expression follows directly from (5) using the fact that the bank’s
operations must be consistent with the regulatory terms. Recall that these
rents reflect the bank’s efficiency plus the surplus of the companies’ invest-
ment projects.
The regulator’s problem [RP] can, thus, be written as:
(8)
max S(q0) + π(q0).
q,k
4 Optimal Regulation
The regulator‘s problem [RP]can be rewritten as:
max S(q0)+π
q,k
rτ
(qoy) = к
δ(rL - γ(L) - (1 - k(q0))L)dG(r|q(q0)) (9)
-rek(q0)L - C(q(q0) - q0)
where
δ(x) = [1 +xb]x
for x ≤ 0
for x> 0.
10