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1
Exercise 10, page 107
Initially, there are 2000 workers, of which 1900 are employed. Each works 40 hours per week.
The production function is
Y
= 10
L;
where
L
is measured in hours of labor.
(a) Total hours worked per week =1900 workers
40 hours per worker =76,000 hours per
week. Total output per week =76,000 total hours per week
10 units of output per hour
=760,000 units of output. The unemployment rate is 100 unemployed/2000 labor supply
=0.05, or 5%.
1900 =1824. The labor force falls
2000 = 1996. With a labor force of 1996 and employment
40 =39.
Total hours per week = 39 hours per worker
1824 workers =71,136. So total hours per
every 1% drop in hours, so output falls by 6.4%
1.4 =8.96%. Since output was 760,000, it
now falls to 760,000
2
Exercise 6, page 107
Let
E
denotes total employment,
U
total unemployment,
E
+
U
the labor force,
O
the people
out of the labor force, and
E
+
U
+
O
the working age population.
(a) The unemployment rate is:
u
=
U
E
+
U
and the employment ratio
er
=
E
E
+
U
+
O
:
The answer is yes. We can have
u
and
er
go up at the same time. For example, initially,
E
+
U
= 100
; U
= 10
;
and
O
= 50
. Thus:
u
= 0
:
10
;
er
= 0
:
60
:
Now, reduce
O
to
40
and
E
to 89, while
U
becomes
11
. You get:
u
= 0
:
11
;
er
= 0
:
64
:
(b) The participation rate is
pr
=
E
+
U
E
+
U
+
O
:
It can fall when
er
rises. Suppose that in the example above
O
remains at 50, while
E
+
U
falls to 95,
U
falls to 4 and
E
goes to 91. Then,
pr
goes from
100
=
150 = 0
:
67
to
pr
= 95
=
145 = 0
:
65
:
The employment rate
er
goes from 0.60 to
91
=
145 = 0
:
63
:
1
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Exercise 7, page 107
Let
W
denote the hourly wage (in $) and
l
the number of hours worked by an individual in
a year, so that
Wl
is his/her annual income. The social security tax
T
for a selfemployed
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 Spring '08
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