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Economics 202A Lecture Outline, November 1520, 2007
(version 1.1)
Maurice Obstfeld
The main point of the model we’ll study today is to show how agency costs
of investment can be mitigated by a larger decisionmaker stake in projects.
Thus, more plentiful internal funds can spur investment and, conversely,
sharp reductions in decisionmaker wealth can cause investment to collapse.
Idea of the BernankeGertler (
QJE;
February 1990
)
model
To set the stage, start with a setting much more simple than that of
BernankeGertler (BG). A riskneutral investor or entrepreneur with total
real wealth
w
(observable by outsiders) faces a world capital market in which
the
gross
interest rate on loans is (the given constant)
r
. There are two time
A project requires the input of 1 unit of output on date 1 and has a date
2 payo± of
R
with probability
p
and of 0 with probability 1
p
. Importantly,
p
is the entrepreneur’s private knowledge. An entrepreneur can undertake at
most one project, and has the option of instead investing his or her wealth
at the gross riskfree rate
r < R
. The cumulative distribution function for
p
within the population of entrepreneurs is
H
(
p
).
Assume tentatively that an entrepreneur with wealth
w
can borrow 1
w
at the world interest rate
r:
Lenders can observe the investment outcome
and compel repayment up to the limit of the borrower’s resources. For which
values of
p
will entrepreneurs choose to invest in their risky projects?
If
there
were no nonnegativity constraint on consumption, the cuto± value of
p
would
be where the expected returns to risky and riskless investment coincide:
p
[
R
r
(1
w
)]
(1
p
)
r
(1
w
) =
rw:
The solution is
p
fb
=
r=R;
1
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View Full Document which, you can con&rm, gives an e±cient amount of investment. But con
sumption
cannot
be negative. An entrepreneur whose investment goes sour
can only repay 0 in period 2, so that the problem he or she solves in period
1 has a cuto² probability given by
p
[
R
r
(1
w
)] =
rw;
with solution
p
=
rw
R
r
(1
w
)
±
r
R
:
(The last inequality is strict if
w <
1.) Notice that unless
w
= 1 (so the en
trepreneur bears the entire risk of the project),
p
< p
fb
. Too many projects
will be undertaken relative to the e±cient benchmark. There is a classic
problem of adverse selection, because \bad" borrowers who know they have
low
p
will borrow and invest. They have a small chance of a big win, but
default at the lender’s expense if the investment fails. Notice that the lower
is
w
, the investor stake, the greater is the incentive to gamble on highrisk
projects (d
p
=
d
w >
0).
Furthermore, rational lenders, anticipating the behavior above, would
never lend at the interest rate
r:
Instead, they o²er a loan contract designed
in the expectation that the borrower will default if the project fails. The equi
librium loan contract is simple (and is equivalent to an equity contract in this
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This note was uploaded on 08/01/2008 for the course ECON 202A taught by Professor Akerlof during the Fall '07 term at University of California, Berkeley.
 Fall '07
 AKERLOF
 Economics

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