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Economics for Mathsperts VI
The following describes the shirking model of unemployment. Suppose each
month an unemployed worker gets a job with probability
p
while an employed
worker loses his/her job with probability
s:
Suppose unemployed workers receive
b
wage
w:
In a baby model we assume steady state so that nothing changes over
time at the aggregate level.
1. Let
V
u
describe expected discounted earnings while unemployed,
V
E
de
scribe expected discounted earnings while employed and so are given by:
V
u
=
b
+
1
1 +
r
[
pV
E
+ (1
p
)
V
U
]
V
E
=
w
+
1
1 +
r
[
sV
U
+ (1
s
)
V
E
]
:
Solve for V
U
;
V
E
:
2. People are lazy and will only work hard if the value of being employed is
su¢ ciently high; i.e.
V
E
V
U
±
k
where
k
describes the disutility of having to
w
to the point where
V
E
V
U
=
k:
Solve
for this wage
w
and show:
w
=
b
+
r
+
s
+
p
1 +
r
k:
Explain why this wage markup increases with
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 Winter '11
 HuyDuong

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