debtequity

that the Central Bank makes a loss for sure which has to be paid by taxpayers: we eliminate this
case. In case (ii) where R D = R B the Flex equilibrium (defined below) reduces to the banking
equilibrium studied in Section 3 with π = 0. Since we are interested in high-safe-asset demand
(HS) economies in which the standard banking equilibria are inefficient, we also eliminate this case.
We thus focus on case (iii) where R D > R B . When the realized outcome a of the bank’s payoff ã
is favorable i.e. when Ka ≥ R D D (where K denotes the capital invested by the banks), then the
Central Bank makes a profit (R D − R B )D. This profit is transferred to the Treasury which uses it
to reduce taxes. However when the realized outcome a is low i.e. when Ka < R D D, banks default
and the Central Bank recovers the value (1 − γ f )Ka of the bank’s assets and the Treasury raises
taxes to reimburse depositors and cash funds. Thus the taxes paid by investors at date 1 are given
by
t(a) =
{
R B B − (R D − R B )D, if Ka ≥ R D D
R B B − ((1 − γ f )Ka − R D D),
if Ka < R D D
The first term is the cost of reimbursing the Treasury’s debt B, and the second is the profit or loss
made by the Central Bank acting as the banks’ banker.
Agents Depositors behave as in Section 3 facing the "discounted" interest rate R d = RB
1+µ
i.e. the
riskless rate R B discounted by the cost µ of managing their funds at date 1. Cash funds behave
as in Section 3 facing the interest rate R c = R B . Investors behave as in Section 3 anticipating the
expected return on equity R E = Φ(α; R D ).
Equations of Flex equilibrium
(19)
An equilibrium of the Flexible (100%) Reserve System consists
of interest rates (R B , R D ), equity requirements α, rate on return on equity R E , and actions
(d, c, e, K, D, E) such that
(i) u ′ d (w d 0 − d) = 1 + ρ
1 + µ RB ⇔ d = d(R B )
(ii) u ′ c(w c 0 − c) = R B ⇔ c = c(R B )
(iii) D = d + c − B
(iv) E =
α
1 − α D, 1
α
∫ ∞
(1−α)R D (a − (1 − α)R D )f(a)da = R E , R E ≥ E(ã), K = D + E
(v) e = E, u ′ i (w i 0 − e) = R E ⇔ e = e(R E )
(vi) x i1 (a) = w i1 − t(a) + V (a)e with V (a) given by (6) and t(a) by (19).
As we have seen in Section 3, there are two sources of inefficiency in a standard banking
equilibrium of a high-debt economy. The first is that the interest rate and the return on equity
35