cases, the CA selects a low fee to enhance the agents’s profit and in turn
his up-front payments. In other words, the CA selects a system of private
contracting. When the default risk and the monitoring cost are low the
ex-post incomes are large. To exploit this fact, the CA uses a high fee,
i.e., it selects a system of direct collection within the government.
We next consider the distributional aspects of the model. The CA’s
net present value is given by
= n. = ___________(1 - t,________∏T.
NPV (1 + δ)(2(1 - c) - n-1 (1 + δ)) ,
and the agent’s profit is equal to
ɪ (1 - c ?
π*
πNPV=
_______n+1 ∖ tJ_________
n-1 (1 + δ) - 2(1 - c))2
(19)
The expected price level is equal to
E(p*) = ca + (1 - c ) a+£.
t 12 v t, 2
The debt, finally, is given by
Debt = 2
(1 - c )2 ( ⅛δ - n+1 )
(n+1 (1+ δ) - 2(1 - c))2
(20)
(21)
We can now study how the default risk and the monitoring cost affect
these variables.
Proposition 2 The higher the default risk, δ, and the larger the moni-
toring cost, c, the higher is the agent’s profit and the lower is the value
of the central authority’s incomes, the debt issued and the price level.
Proof. See Appendix. ■
When the default risk and the monitoring costs are high the CA re-
duces the fee, θ, to increase the agent’s profit and consequently up-front
20
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