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Economics 5
D. Richards
Principles of economics
Fall, 2007
Answers to Fifth Problem Set
1.
Two adolescent boys who share living quarters with my wife and I are given a weekly payment in
return for leaving us alone and not bothering us for most of each day, as well as for joining us at meal
times but keeping quiet unless asked to speak.
For lack of a better term, we will call this payment an
allowance.
As we are about to enter a new year, these two young people have been asking for an increase
in their allowance.
They claim that the cost of entertainment goods, XBox and PS3 games, CD’s,
DVD’s, sports equipment as well as the cost of necessities—transportation, lunches and so forth—have
both increased over the last year so that the allowance payment to which we all agreed earlier is no long
sufficient.
The question is, how should we measure the extent to which the “cost of adolescence” has
risen.
We are considering two basic alternatives.
The first of these is to use a means similar to that long
used in constructing the Consumer Price Index, i.e., a Laspeyres Index.
This Index measures the increase
as the rise in expenditure necessary to buy the same quantities of entertainmentrelated items and
necessities in the second year as were bought in the first.
That is:
Laspeyres Index =
S
NECESSITIE
NECESSITIE
ENT
ENTERTAINM
ENT
ENTERTAINM
S
NECESSITIE
S
NECESSITIE
ENT
ENTERTAINM
ENT
ENTERTAINM
Q
P
Q
P
Q
P
Q
P
2007
2007
2007
2007
2007
2008
2007
2008
+
+
The alternative is to use a Paasche Index.
This index is measured as what it cost to buy the combination
of video items and sports equipment actually purchased in 2007, relative to what it would have cost to
buy that same 2008 bundle if prices had remained at their 2007 level.
Hence, the Paasche Index is
calculated as:
Paasche Index =
S
NECESSITIE
S
NECESSITIE
ENT
ENTERTAINM
ENT
ENTERTAINM
SS
NECESSITIE
S
NECESSITIE
ENT
ENTERTAINM
ENT
ENTERTAINM
Q
P
Q
P
Q
P
Q
P
2008
2007
2008
2007
2008
2008
2008
2008
+
+
The boys had studied sampling theory and gone out and gathered data for the individual prices of toys
and sports equipment for 2007 and 2008, as well as the amount of each product purchased by a typical
adolescent American male.
These data are shown below.
Based on this data, which index will the boys
prefer to be used for determining the increase in their allowance?
The Laspeyres Index is:
(
29
(
29
(
29
(
29
1563
1
800
925
10
30
100
5
10
40
100
25
5
.
$
$
$
$
$
.
$
=
=
⋅
+
⋅
⋅
+
⋅
or 115.63 if multiplied by
100.
In other words, the Laspeyres Index implies a rise in the cost of adolescence of about 15.6%.
The
Paasche Index is:
(
29
(
29
(
29
(
29
131
1
1050
5
1187
10
30
150
5
10
40
150
25
5
.
$
.
$
$
$
$
.
$
=
=
⋅
+
⋅
⋅
+
⋅
or 113.1 if multiplied by 100.
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 Spring '08
 RICHARDS
 Economics

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