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Economics 202A Lecture Outline, December 6, 2007
(Version 1.0)
Maurice Obstfeld
Financial Instability
In this lecture I describe the DiamondDybvig model of bank runs, from
Journal of Political Economy
intermediaries promote risk sharing among individuals, but they are subject
to arbitrary panics.
The model
There are three periods,
T
= 0
;
1
;
2
:
There are two possible technologies on date 0, short and long.
Investment of 1 unit of output in the short technology at
T
= 0 yields 1
unit of output in period 1 and 0 in period 2.
Investment of 1 unit of output in the long technology at
T
= 0 yields 0
units of output in period 1 and
R >
1 units in period 2.
Individuals need not specify the technology they are choosing
ex ante
.
They opt for the short or long technology simply by \harvesting" the yield
either on date 1 or 2, respectively.
The idea is that more roundabout technologies are more productive.
At time 0, a depositor does not know his/her \type," patient or impatient.
Depositors are indexed by the unit interval, [0
;
1]. at the start of period 1,
a fraction
p
is revealed to be of type 1, or impatient. The rest (of measure
1
p
) are of type 2, patient. An agent has an endowment 1 in period 0 and
consumes in period 1 and/or 2. The utility functions of types 1 and 2 are
U
(
c
1
; c
2
; 1) =
u
(
c
1
)
;
U
(
c
1
; c
2
; 2) =
u
(
c
1
+
c
2
)
;
where lim
c
!
0
u
0
(
c
) =
1
, lim
c
!1
u
0
(
c
) = 0, and
cu
00
(
c
)
=u
0
(
c
)
>
1.
1
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View Full DocumentFirst consider an autarkic individual. That person will pick
c
1
= 1 if
he/she turns out to be impatient,
c
2
=
R
if patient. That person’s
ex ante
expected utility is an average over the utilities of the two types:
E
U
=
pu
(1) + (1
p
)
u
(
R
)
:
People can do better than this, however, if there are &nancial intermedi
aries.
Social optimum
A benevolent and omnipotent planner would withdraw an amount 1
x
from investment on
T
= 1 so as to maximize the expected utility of a
representative individual
pu
c
1
1
±
+ (1
p
)
u
(
c
2
1
+
c
2
2
)
subject to the aggregate resource constraints
pc
1
1
+ (1
p
)
c
2
1
= 1
x;
(1
p
)
c
2
2
=
Rx:
Here,
c
i
j
is the amount type
i
consumes in period
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 Fall '07
 AKERLOF
 Economics

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