debtequity

to have exogenously given expenditure (G) that the fiscal authority finances by issuing bonds B at
date 0 for the value B = G, imposing taxes on investors at date 1 to pay for the government debt.
It also insures banks’ deposits, imposing an insurance premium π per dollar of debt due due at
date 1, and reimburses depositors when banks go bankrupt. The insurance premium decreases the
taxes that taxpayers have to pay when banks are not bankrupt, while reimbursing the depositors
in low realizations of ã requires additional taxes. The Central Bank fixes the interest rate R B
on government bonds and the minimum equity requirement α for banks. If the cash funds are
reimbursed at date 1 when banks are bankrupt, taxes are increased to cover the cost. The taxes
imposed at date 1 in outcome a are thus given by
⎧
⎨R B B − π(R d d + R c c b ), if a ≥ â,
t(a) =
(7)
⎩
R B B + (1 + µ)R d d + R c c b − (1 − γ)Ka, if a ≤ â.
where 1−γ is the recovery rate on output when there is bankruptcy. We could introduce a separate
group of agents who pay taxes (when t(a) > 0) or receive payments (when t(a) < 0). However it is
simpler to assume directly that these taxes are paid by the investors who have sufficient resources
w i1 > 0 to pay for them at date 1.
Assumptions We introduce assumptions on agents’ endowments which ensure that there exist
equilibria with positive debt and equity for banks. In this model with constant returns in technology
and linear date 1 preferences, there is a natural rate of interest R ∗ = E(ã) determined by the
technology which is the expected return at date 1 from a one unit investment of the good at date
0. This is the benchmark interest rate that we use to express the willingness of agents to supply
debt and equity in the economy.
Assumption 1. (a) u ′ i (w i 0) < E(ã);
(b) w i1 > (w d 0 (1 + µ) + w c 0 )E(ã)
Assumption (1)(a) guarantees that investors want to invest in the technology even if the profit
of banks is not increased by leverage, while (b) guarantees that investors have sufficient resources
at date 1 to reimburse the maximum that can be due to depositors and cash funds.
In keeping with the recent literature on shadow banking which emphasizes the magnitude of the
funds on the wholesale money market seeking a safe haven, we assume that (short-term) government
bonds do not absorb all funds that cash funds are willing to lend.
Assumption 2. u ′ c(w c 0 − B) < E(ã)
Under this assumption, for all interest rates R B such that u ′ c(w c 0 − B) < R B ≤ E(ã), the cash
funds want to lend an amount which exceeds the supply of (short-term) government bonds B.
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