Econ 3140
Spring 2010
Problem Set 2
Answer Key
1. De°ne the Laspeyres quantity index (using year 1 prices) for year 1 as the value of
year 1 output at year 1 prices:
L
1
= $46
;
000
; the Laspeyres quantity index of year 2
output is
L
2
= $62
;
000
.
De°ne the Paasche quantity index (using year 2 prices) for year 1 as the value of year
1 output at year 2 prices:
P
1
= $51
;
000
; the Paasche quantity index of year 2 output
is
P
2
= $66
;
000
.
(These amounts are all calculated in Table 2.4, they just are not
labeled this way.)
The chainweighted index is just the geometric mean of the Laspeyres and Paasche
indexes:
C
1
= (
L
1
°
P
1
)
1
2
= (46
;
000
°
51
;
000)
1
2
= $48
;
400
;
C
2
= (
L
2
°
P
2
)
1
2
= (62
;
000
°
66
;
000)
1
2
= $63
;
970
:
Note that the growth rate of real GDP in this case is
($63
;
970
±
$48
;
400)
=
$48
;
400 =
32
:
06%
, which is close to the average growth rate calculated by the Laspeyres (
34
:
8%
)
and Paasche (
29
:
4%
) indexes, which is
32
:
095%
:
2. Plugging the new values of capital
(
K
)
and labor
(
N
)
into the production function, we
can conclude that output increases in
20%
.
Note: Recall the concept of Constant Returns of Scale (CRS), that means that if the
exponents of
K
and
N
sum to one, that means that if factors (capital and labor)
double, output doubles.
Therefore, in this example if inputs increase in
20%
, then
output rise
20%
.
So you do not need to make calculations.
3. Social Security Taxes
(a) Since Sally earns
$150
;
000
per year, she is far above the cap, so the Social Security
tax doesn±t a/ect her aftertax wage (so there±s no substitution e/ect) the higher
tax only a/ects her income and thus has only an income e/ect.
Since both
proposals reduce Sally±s income by the same amount, she±
ll increase her labor
supply by the same amount under both proposals.
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 Spring '07
 MBIEKOP
 Macroeconomics, Unemployment, Supply And Demand, real wage, labor demand

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