D . de Meza, D. Webb Journal of Public Economics 78 2000 215 –234
227
to R so p B , R
and p G . R and this equilibrium certainly has more
B G
investment than the rationing equilibrium. In considering the policy implications, note that a random sample of en-
trepreneurs are excluded from the market, but as lp G 1 1 2 lp B . R the
G B
expected surplus on a loan is positive. Hence, regardless of whether there is too much or too little lending relative to the equilibrium with full information, a
subsidy to lending, by drawing in more entrepreneurs without changing the mix of types, must once again enhance welfare.
Turning to policies which affect the return to non-participation, as the marginal entrepreneurs are type Gs, a tax on inactivity will raise the D at which they drop
out of the loan market. The associated bank return rises, increasing the volume of lending and decreasing the proportion of projects credit rationed. The policy is
therefore beneficial, but as Bs remain active, there remains an inefficient composition of projects financed, so in this model the subsidy policy fails to
achieve the first best. However, it is interesting to note that a sufficient bankruptcy penalty will achieve full efficiency, since it hits the high default Bs the hardest.
This model clearly illustrates how policy conclusions do not follow straight- forwardly from a comparison of the volume of lending under credit rationing with
the full-information equilibrium. If only second-best instruments are available, such as interest-rate subsidies, it may be best to increase the volume of lending
even further in excess of the first-best level.
6. Generalisation
We now generalise the model of Section 2 in which heterogeneous en- trepreneurial ability is combined with moral hazard. Projects are described as
follows: an investment by an entrepreneur of ability a in a project with risk characteristics
u, yields a return stream of aX u with probability p u and zero s d
s d with probability 1 2 p
u , where X u . 0. The project’s expected return varies with s d
s d the chosen risk-return characteristics. As
u increases, the return in the event of success is higher X9
u . 0, but the probability of success decreases p9 u , 0, s d
s d eventually by so much that the expected return decreases. In other words, for high
u, the risk of the project increases at the expense of a lower expected return.
10
The entrepreneur’s optimal choice of project solves p D,a
;max p u aX 2 D 2 F 12
s d
s ds d
u
and is thus characterized by p9
u aX u 2 D 1 p u aX9 u 5 0 13
s ds s d d
s d s d
10
Here we assume that S 5 0.
228 D
. de Meza, D. Webb Journal of Public Economics 78 2000 215 –234
we denote the optimal choice of u by u D,a , so that ≠p ≠a 5 p9 u ≠u ≠a .
s d
s d 0, ≠p ≠D 5 p9
u ≠u ≠D , 0. s d
ˆ For a given fixed payment D, the marginal entrepreneur has an ability a D such
s d that
ˆ p D, a D 5 0
s d
s d ˆ
and since ≠ p ≠a D,a . 0, only entrepreneurs with a . a D apply for finance.
s d
s d Moreover,
≠ p
] D,a 5 2 p D,a , 0, 14
s d
s d
≠D ˆ
so we have da dD 5 2 ≠ p ≠D ≠p ≠a . 0.
In a pooling equilibrium, the average probability of success is dG a
s d ]
]]]] p D 5
E
p D,a ,
15 s d
s d
ˆ 1 2 G a D
s d
s d
ˆ a D
s d
and satisfies ]
ˆ p D . p D,a D .
16 s
d s d
s d The expected return to the bank on this portfolio is given by
] r
;p D D 17
s d and the expected profit, obtained by deducting the return to depositors, is given by
P ; r 2 R.
Assuming that competition drives banks’ expected profits to zero, the marginal entrepreneur has a negative value project since the social surplus on the marginal
entrepreneur ]
ˆ ˆ
ˆ p D,a D 1 p D,a D D 2 R 5 0 1 p D,a D 2p D D , 0.
18 s
d s
d f s
d g
s d s d
s d s d
The effect of D on the default rate is ˆ
d r
dG a ≠pD,a
dG a s d
s d ]
] ˆ
]]] ]]]
]]] 5 p D 2 p D,a D
1
E
D 19
s d
s d s d
dD ˆ
≠D ˆ
1 2 G a 1 2 G a
s d s d
ˆ a
where the first term the advantageous-selection effect is positive by 16 and the second term the incentive effect is negative. It follows that
r may be increasing or decreasing in D. We assume that at high D moral hazard dominates and
r has a
D . de Meza, D. Webb Journal of Public Economics 78 2000 215 –234
229
11
unique turning point. If at the D for which d
r dD 5 0, P . 0 then the equilibrium is market clearing but if
P , 0 there is no interest rate at which lending is profitable.
7. Redlining
