Econ 138
Problem Set 4
Professor Ulrike Malmendier
March 20, 2008
1
More on Asymmetric Information
We consider a variation of our standard asymmetricinformation model. As before we have two
types of
f
rms, a fraction
μ
of ‘Htypes’ and a fraction 1
−
μ
of ‘Ltypes.’ We now assume that
f
rms have illiquid assets that are worth either
A
H
(for the Htypes) or
A
L
(for the Ltypes).
In addition to having di
f
erent assets, the two types also have di
f
erent investment projects.
The Htypes have a project that returns
R
H
with probability
p
(and returns 0 otherwise). The
Ltypes have a project that returns
R
L
with probability
p
(and 0 otherwise). Both projects
cost
I
.
1.1
Part 1 (3 points)
Suppose the
f
rms would like to
f
nance investment by issuing equity. We now model issuing
equity more realistically, namely as pledging a percentage
θ
of the company to investors. (In
class, we typically assumed a
f
xed contingent payment
R
−
R
m
in case of success and 0 in case
of failure. As we discussed, this can be interpreted as an equity issuance. In this exercise, we
model the equity issuance more directly to illustrate the equivalence.)
Let’s
f
rstassumethat
,forag
iven
f
nancing contract that pledges a fraction
θ
of the
f
rm
to investors, both types of
f
rms would seek
f
nancing. How large does
θ
need to be to convince
investors to
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 Spring '08
 Malmendier
 Professor Ulrike Malmendier

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