Econ 387L: Macro II
Spring 2008, University of Texas
Instructor: Dean Corbae
Problem Set #9  Due 4/10/08
Consider a version of the environment studied by Stokey (1989) that was taught in
class. Let
(
x, X, y
)
be the choice variables available to a representative agent, the market
as a whole, and a benevolent government, respectively, where
x, X
∈
X
=
{
x
L
, x
H
}
and
y
∈
Y
=
{
y
L
, y
H
}
. Let per period payoffs to the government be denoted
u
(
x
i
, X
j
, y
k
)
.
In
the case where
x
j
=
X
j
let payoffs be given as in the table
u
(
x
j
, X
j
, y
k
)
X
L
X
H
y
L
0
∗
20
y
H
1
10
∗
The values of
u
(
x
i
, X
j
, y
k
)
not reported in the table are such that the competitive
equilibria (i.e. ones where
x
=
X
=
h
(
y
))
are the outcome pairs denoted by the
asterisk.
1
For completeness assume that if an agent deviates, she gets exactly what
the average person gets in all cases except one (where
x
L
, X
H
, y
L
). In particular, we
assume
u
(
x
L
, X
H
, y
L
)
>
20
and for all other cases she gets the average payoff (i.e.
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 Spring '07
 CORBAE
 Game Theory, Subgame perfect equilibrium, Ramsey

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