7
NAME
Revealed Chapter Preference
Introduction. In the last section, you were given a consumers preferences and then you solved for his or her demand behavior. In this
chapter we turn this process around: you are given information about a
consumers demand behavior and you must deduce something about the
consumers preferences. The main tool is the weak axiom of revealed preference. This axiom says the following. If a consumer chooses commodity
bundle A when she can aord bundle B , then she will never choose bundle
B from any budget in which she can also aord A. The idea behind this
axiom is that if you choose A when you could have had B , you must like
A better than B . But if you like A better than B , then you will never
choose B when you can have A. If somebody chooses A when she can
aord B , we say that for her, A is directly revealed preferred to B . The
weak axiom says that if A is directly revealed preferred to B , then B is
not directly revealed preferred to A.
Example: Let us look at an example of how you check whether one bundle
is revealed preferred to another. Suppose that a consumer buys the bundle
(xA , xA ) = (2, 3) at prices (pA , pA ) = (1, 4). The cost of bundle (xA , xA )
1
2
1
2
1
2
at these prices is (2 1) + (3 4) = 14. Bundle (2, 3) is directly revealed
preferred to all the other bundles that she can aord at prices (1, 4), when
she has an income of 14. For example, the bundle (5, 2) costs only 13 at
prices (1, 4), so we can say that for this consumer (2, 3) is directly revealed
preferred to (1, 4).
You will also have some problems about price and quantity indexes.
A price index is a comparison of average price levels between two dierent
times or two dierent places. If there is more than one commodity, it is not
necessarily the case that all prices changed in the same proportion. Let us
suppose that we want to compare the price level in the current year with
the price level in some base year. One way to make this comparison
is to compare the costs in the two years of some reference commodity
bundle. Two reasonable choices for the reference bundle come to mind.
One possibility is to use the current years consumption bundle for the
reference bundle. The other possibility is to use the bundle consumed
in the base year. Typically these will be dierent bundles. If the baseyear bundle is the reference bundle, the resulting price index is called the
Laspeyres price index. If the current years consumption bundle is the
reference bundle, then the index is called the Paasche price index.
Example: Suppose that there are just two goods. In 1980, the prices
were (1, 3) and a consumer consumed the bundle (4, 2). In 1990, the
prices were (2, 4) and the consumer consumed the bundle (3, 3). The cost
of the 1980 bundle at 1980 prices is (1 4) + (3 2) = 10. The cost of this
same bundle at 1990 prices is (2 4) + (4 2) = 16. If 1980 is treated
as the base year and 1990 as the current year, the Laspeyres price ratio
82
REVEALED PREFERENCE
(Ch. 7)
is 16/10. To calculate the Paasche price ratio, you nd the ratio of the
cost of the 1990 bundle at 1990 prices to the cost of the same bundle at
1980 prices. The 1990 bundle costs (2 3) + (4 3) = 18 at 1990 prices.
The same bundle cost (1 3) + (3 3) = 12 at 1980 prices. Therefore
the Paasche price index is 18/12. Notice that both price indexes indicate
that prices rose, but because the price changes are weighted dierently,
the two approaches give dierent price ratios.
Making an index of the quantity of stu consumed in the two
periods presents a similar problem. How do you weight changes in the
amount of good 1 relative to changes in the amount of good 2? This time
we could compare the cost of the two periods bundles evaluated at some
reference prices. Again there are at least two reasonable possibilities, the
Laspeyres quantity index and the Paasche quantity index. The Laspeyres
quantity index uses the base-year prices as the reference prices, and the
Paasche quantity index uses current prices as reference prices.
Example: In the example above, the Laspeyres quantity index is the ratio
of the cost of the 1990 bundle at 1980 prices to the cost of the 1980 bundle
at 1980 prices. The cost of the 1990 bundle at 1980 prices is 12 and the
cost of the 1980 bundle at 1980 prices is 10, so the Laspeyres quantity
index is 12/10. The cost of the 1990 bundle at 1990 prices is 18 and
the cost of the 1980 bundle at 1990 prices is 16. Therefore the Paasche
quantity index is 18/16.
When you have completed this section, we hope that you will be able
to do the following:
Decide from given data about prices and consumption whether one
commodity bundle is preferred to another.
Given price and consumption data, calculate Paasche and Laspeyres
price and quantity indexes.
Use the weak axiom of revealed preferences to make logical deductions about behavior.
Use the idea of revealed preference to make comparisons of well-being
across time and across countries.
7.1 (0) When prices are (4, 6), Goldie chooses the bundle (6, 6), and
when prices are (6, 3), she chooses the bundle (10, 0).
(a) On the graph below, show Goldies rst budget line in red ink and
her second budget line in blue ink. Mark her choice from the rst budget
with the label A, and her choice from the second budget with the label
B.
(b) Is Goldies behavior consistent with the weak axiom of revealed preference?
No.
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83
Good 2
20
15
Blue line
10
5
a
Red line
b
0
5
10
15
20
Good 1
7.2 (0) Freddy Frolic consumes only asparagus and tomatoes, which are
highly seasonal crops in Freddys part of the world. He sells umbrellas for
a living, which provides a uctuating income depending on the weather.
But Freddy doesnt mind; he never thinks of tomorrow, so each week he
spends as much as he earns. One week, when the prices of asparagus and
tomatoes were each $1 a pound, Freddy consumed 15 pounds of each. Use
blue ink to show the budget line in the diagram below. Label Freddys
consumption bundle with the letter A.
(a) What is Freddys income?
$30.
(b) The next week the price of tomatoes rose to $2 a pound, but the price
of asparagus remained at $1 a pound. By chance, Freddys income had
changed so that his old consumption bundle of (15,15) was just aordable
at the new prices. Use red ink to draw this new budget line on the graph
below. Does your new budget line go through the point A?
What is the slope of this line?
Yes.
1/2.
(c) How much asparagus can he aord now if he spent all of his income
on asparagus?
45 pounds.
(d) What is Freddys income now?
$45.
84
REVEALED PREFERENCE
(Ch. 7)
(e) Use pencil to shade the bundles of goods on Freddys new red budget
line that he denitely will not purchase with this budget. Is it possible
that he would increase his consumption of tomatoes when his budget
changes from the blue line to the red one?
No.
Tomatoes
40
30
20
10
Blue line
Pencil
,,,,,,,,,,,,,,,,,,
,,,,,,,,,,,,,,,,,,
shading
,,,,,,,,,,,,,,,,,,
a
,,,,,,,,,,,,,,,,,,
,,,,,,,,,,,,,,,,,, line
Red
,,,,,,,,,,,,,,,,,,
,,,,,,,,,,,,,,,,,,
,,,,,,,,,,,,,,,,,,
,,,,,,,,,,,,,,,,,,
,,,,,,,,,,,,,,,,,,
,,,,,,,,,,,,,,,,,,
,,,,,,,,,,,,,,,,,,
,,,,,,,,,,,,,,,,,,
,,,,,,,,,,,,,,,,,,
0
10
20
30
40
Asparagus
7.3 (0) Pierre consumes bread and wine. For Pierre, the price of bread
is 4 francs per loaf, and the price of wine is 4 francs per glass. Pierre has
an income of 40 francs per day. Pierre consumes 6 glasses of wine and 4
loaves of bread per day.
Bob also consumes bread and wine. For Bob, the price of bread is
1/2 dollar per loaf and the price of wine is 2 dollars per glass. Bob has
an income of $15 per day.
(a) If Bob and Pierre have the same tastes, can you tell whether Bob is
better o than Pierre or vice versa? Explain.
off.
Bob is better
He can afford Pierres bundle and
still have income left.
(b) Suppose prices and incomes for Pierre and Bob are as above and that
Pierres consumption is as before. Suppose that Bob spends all of his
income. Give an example of a consumption bundle of wine and bread such
that, if Bob bought this bundle, we would know that Bobs tastes are not
the same as Pierres tastes.
7.5 wine and 0 bread, for
example. If they had the same preferences,
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85
this violates WARP, since each can afford
but rejects the others bundle.
7.4 (0) Here is a table of prices and the demands of a consumer named
Ronald whose behavior was observed in 5 dierent price-income situations.
Situation
A
B
C
D
E
p1
1
1
1
3
1
p2
1
2
1
1
2
x1
5
35
10
5
10
x2
35
10
15
15
10
(a) Sketch each of his budget lines and label the point chosen in each case
by the letters A, B, C, D, and E.
(b) Is Ronalds behavior consistent with the Weak Axiom of Revealed
Preference?
Yes.
(c) Shade lightly in red ink all of the points that you are certain are worse
for Ronald than the bundle C.
(d) Suppose that you are told that Ronald has convex and monotonic
preferences and that he obeys the strong axiom of revealed preference.
Shade lightly in blue ink all of the points that you are certain are at least
as good as the bundle C.
x2
40
30
20
10
0
yyyyyyyyyyyyyyyyyyyyy
,,,,,,,,,,,,,,,,,,,,,
yyyyyyyyyyyyyyyyyyyyy
,,,,,,,,,,,,,,,,,,,,,
a
yyyyyyyyyyyyyyyyyyyyy
,,,,,,,,,,,,,,,,,,,,,
yyyyyyyyyyyyyyyyyyyyy
,,,,,,,,,,,,,,,,,,,,,
yyyyyyyyyyyyyyyyyyyyy
,,,,,,,,,,,,,,,,,,,,,
Blue shading
yyyyyyyyyyyyyyyyyyyyy
,,,,,,,,,,,,,,,,,,,,,
yyyyyyyyyyyyyyyyyyyyy
,,,,,,,,,,,,,,,,,,,,,
,,,,,,,,,,,,,,,,,,
yyyyyyyyyyyyyyyyyyyyy
,,,,,,,,,,,,,,,,,,,,,
,,,,,,,,,,,,,,,,,,
yyyyyyyyyyyyyyyyyyyyy
,,,,,,,,,,,,,,,,,,,,,
,,,,,,,,,,,,,,,,
,,,,,,,,,,,,,,,,,,
yyyyyyyyyyyyyyyyyyyyy
,,,,,,,,,,,,,,,,,,,,,
,,,,,,,,,,,,,,,,
,,,,,,,,,,,,,,,,,,
yyyyyyyyyyyyyyyyyyyyy
,,,,,,,,,,,,,,,,,,,,,
,,,,,,,,,,,,,,,,
,,,,,,,,,,,,,,,,,,
yyyyyyyyyyyyyyyyyyyyy
,,,,,,,,,,,,,,,,,,,,,
,,,,,,,,,,,,,,,,
,,,,,,,,,,,,,,,,,,
yyyyyyyyyyyyyyyyyyyyy
,,,,,,,,,,,,,,,,,,,,,
,,,,,,,,,,,,,,,,
,,,,,,,,,,,,,,,,,,
c
yyyyyyyyyyyyyyyyyyyyy
,,,,,,,,,,,,,,,,,,,,,
,,,,,,,,,,,,,,,,
,,,,,,,,,,,,,,,,,,
d
yyyyyyyyyyyyyyyyyyyyy
,,,,,,,,,,,,,,,,,,,,,
,,,,,,,,,,,,,,,,
,,,,,,,,,,,,,,,,,,
yyyyyyyyyyyyyyyyyyyyy
,,,,,,,,,,,,,,,,,,,,,
,,,,,,,,,,,,,,,,
,,,,,,,,,,,,,,,,,, b
yyyyyyyyyyyyyyyyyyyyy
,,,,,,,,,,,,,,,,,,,,,
,,,,,,,,,,,,,,,,
,,,,,,,,,,,,,,,,,,
e
yyyyyyyyyyyyyyyyyyyyy
,,,,,,,,,,,,,,,,,,,,,
,,,,,,,,,,,,,,,,
,,,,,,,,,,,,,,,,,,
,,,,,,,,,,,,,,,,
,,,,,,,,,,,,,,,,,,
Red shading
,,,,,,,,,,,,,,,,
,,,,,,,,,,,,,,,,,,
,,,,,,,,,,,,,,,,
,,,,,,,,,,,,,,,,,,
,,,,,,,,,,,,,,,,
,,,,,,,,,,,,,,,,,,
,,
,,,,,,,,,,,,,,,,,,,,,,,,
,,,,,,,,,,,,,,,,
,,,,,,,,,,,,,,,,,,
,
,,,,,,,,,,,,,,,,,,,,,,,
,,
,,,,,,,,,,,,,,,,,,,,,,,,
,,,,,,,,,,,,,,,,
,,,,,,,,,,,,,,,,,,
,
,,,,,,,,,,,,,,,,,,,,,,,
10
20
30
40
x1
86
REVEALED PREFERENCE
(Ch. 7)
7.5 (0) Horst and Nigel live in dierent countries. Possibly they have
dierent preferences, and certainly they face dierent prices. They each
consume only two goods, x and y . Horst has to pay 14 marks per unit of
x and 5 marks per unit of y . Horst spends his entire income of 167 marks
on 8 units of x and 11 units of y . Good x costs Nigel 9 quid per unit and
good y costs him 7 quid per unit. Nigel buys 10 units of x and 9 units of
y.
(a) Which prices and income would Horst prefer, Nigels income and prices
or his own, or is there too little information to tell? Explain your answer.
Horst prefers Nigels budget to his own.
With Nigels budget, he can afford his own
bundle with money left over.
(b) Would Nigel prefer to have Horsts income and prices or his own, or
is there too little information to tell?
There is too little
information to tell.
7.6 (0) Here is a table that illustrates some observed prices and choices
for three dierent goods at three dierent prices in three dierent situations.
Situation
A
B
C
p1
1
4
3
p2
2
1
1
p3
8
8
2
x1
2
3
2
x2
1
4
6
x3
3
2
2
(a) We will ll in the table below as follows. Where i and j stand for any
of the letters A, B, and C in Row i and Column j of the matrix, write
the value of the Situation-j bundle at the Situation-i prices. For example,
in Row A and Column A, we put the value of the bundle purchased in
Situation A at Situation A prices. From the table above, we see that in
Situation A, the consumer bought bundle (2, 1, 3) at prices (1, 2, 8). The
cost of this bundle A at prices A is therefore (1 2)+(2 1)+(8 3) = 28,
so we put 28 in Row A, Column A. In Situation B the consumer bought
bundle (3, 4, 2). The value of the Situation-B bundle, evaluated at the
situation-A prices is (1 3) + (2 4) + (8 2) = 27, so put 27 in Row
A, Column B. We have lled in some of the boxes, but we leave a few for
you to do.
NAME
Prices/Quantities
87
A
B
C
A
28
27
30
B
33
32
30
C
13
17
16
(b) Fill in the entry in Row i and Column j of the table below with a D if
the Situation-i bundle is directly revealed preferred to the Situation-j bundle. For example, in Situation A the consumers expenditure is $28. We
see that at Situation-A prices, he could also aord the Situation-B bundle, which cost 27. Therefore the Situation-A bundle is directly revealed
preferred to the Situation-B bundle, so we put a D in Row A, Column
B. Now let us consider Row B, Column A. The cost of the Situation-B
bundle at Situation-B prices is 32. The cost of the Situation-A bundle
at Situation-B prices is 33. So, in Situation B, the consumer could not
aord the Situation-A bundle. Therefore Situation B is not directly revealed preferred to Situation A. So we leave the entry in Row B, Column
A blank. Generally, there is a D in Row i Column j if the number in the
ij entry of the table in part (a) is less than or equal to the entry in Row
i, Column i. There will be a violation of WARP if for some i and j , there
is a D in Row i Column j and also a D in Row j , Column i. Do these
observations violate WARP?
No.
Situation
A
B
C
A
D
I
B
I
D
C
D
I
(c) Now ll in Row i, Column j with an I if observation i is indirectly
revealed preferred to j . Do these observations violate the Strong Axiom
of Revealed Preference?
Yes.
7.7 (0) It is January, and Joe Grad, whom we met in Chapter 5, is
shivering in his apartment when the phone rings. It is Mandy Manana,
one of the students whose price theory problems he graded last term.
Mandy asks if Joe would be interested in spending the month of February
in her apartment. Mandy, who has switched majors from economics to
political science, plans to go to Aspen for the month and so her apartment
will be empty All (alas). Mandy asks is that Joe pay the monthly service
charge of $40 charged by her landlord and the heating bill for the month
of February. Since her apartment is much better insulated than Joes,
it only costs $1 per month to raise the temperature by 1 degree. Joe
88
REVEALED PREFERENCE
(Ch. 7)
thanks her and says he will let her know tomorrow. Joe puts his earmus
back on and muses. If he accepts Mandys oer, he will still have to pay
rent on his current apartment but he wont have to heat it. If he moved,
heating would be cheaper, but he would have the $40 service charge. The
outdoor temperature averages 20 degrees Fahrenheit in February, and it
costs him $2 per month to raise his apartment temperature by 1 degree.
Joe is still grading homework and has $100 a month left to spend on food
and utilities after he has paid the rent on his apartment. The price of
food is still $1 per unit.
(a) Draw Joes budget line for February if he moves to Mandys apartment
and on the same graph, draw his budget line if he doesnt move.
(b) After drawing these lines himself, Joe decides that he would be better
o not moving. From this, we can tell, using the principle of revealed
preference that Joe must plan to keep his apartment at a temperature of
60 degrees.
less than
(c) Joe calls Mandy and tells her his decision. Mandy oers to pay half
the service charge. Draw Joes budget line if he accepts Mandys new
oer. Joe now accepts Mandys oer. From the fact that Joe accepted
this oer we can tell that he plans to keep the temperature in Mandys
apartment above
40 degrees.
Food
120
100
Don't move budget line
80
60
Move budget line
40
'New offer'
budget line
20
0
10
20
30
40
50
60
70
80
Temperature
7.8 (0) Lord Peter Pommy is a distinguished criminologist, schooled
in the latest techniques of forensic revealed preference. Lord Peter is investigating the disappearance of Sir Cedric Pinchbottom who abandoned
his aging mother on a street corner in Liverpool and has not been seen
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89
since. Lord Peter has learned that Sir Cedric left England and is living
under an assumed name somewhere in the Empire. There are three suspects, R. Preston McAfee of Brass Monkey, Ontario, Canada, Richard
Manning of North Shag, New Zealand, and Richard Stevenson of Gooey
Shoes, Falkland Islands. Lord Peter has obtained Sir Cedrics diary, which
recorded his consumption habits in minute detail. By careful observation,
he has also discovered the consumption behavior of McAfee, Manning, and
Stevenson. All three of these gentlemen, like Sir Cedric, spend their entire
incomes on beer and sausage. Their dossiers reveal the following:
Sir Cedric Pinchbottom In the year before his departure, Sir
Cedric consumed 10 kilograms of sausage and 20 liters of beer per
week. At that time, beer cost 1 English pound per liter and sausage
cost 1 English pound per kilogram.
R. Preston McAfee McAfee is known to consume 5 liters of beer
and 20 kilograms of sausage. In Brass Monkey, Ontario beer costs 1
Canadian dollar per liter and sausage costs 2 Canadian dollars per
kilogram.
Richard Manning Manning consumes 5 kilograms of sausage
and 10 liters of beer per week. In North Shag, a liter of beer costs
2 New Zealand dollars and sausage costs 2 New Zealand dollars per
kilogram.
Richard Stevenson Stevenson consumes 5 kilograms of sausage
and 30 liters of beer per week. In Gooey Shoes, a liter of beer costs 10
Falkland Island pounds and sausage costs 20 Falkland Island pounds
per kilogram.
(a) Draw the budget line for each of the three fugitives, using a dierent
color of ink for each one. Label the consumption bundle that each chooses.
On this graph, superimpose Sir Cedrics budget line and the bundle he
chose.
90
REVEALED PREFERENCE
(Ch. 7)
Sausage
40
30
McAfee
20
10
Pinchbottom
Stevenson
Manning
0
10
20
30
40
Beer
(b) After pondering the dossiers for a few moments, Lord Peter announced. Unless Sir Cedric has changed his tastes, I can eliminate one
of the suspects. Revealed preference tells me that one of the suspects is
innocent. Which one?
McAfee.
(c) After thinking a bit longer, Lord Peter announced. If Sir Cedric
left voluntarily, then he would have to be better o than he was before.
Therefore if Sir Cedric left voluntarily and if he has not changed his tastes,
he must be living in
Falklands.
7.9 (1) The McCawber family is having a tough time making ends meet.
They spend $100 a week on food and $50 on other things. A new welfare
program has been introduced that gives them a choice between receiving
a grant of $50 per week that they can spend any way they want, and
buying any number of $2 food coupons for $1 apiece. (They naturally
are not allowed to resell these coupons.) Food is a normal good for the
McCawbers. As a family friend, you have been asked to help them decide
on which option to choose. Drawing on your growing fund of economic
knowledge, you proceed as follows.
(a) On the graph below, draw their old budget line in red ink and label
their current choice C. Now use black ink to draw the budget line that
they would have with the grant. If they chose the coupon option, how
much food could they buy if they spent all their money on food coupons?
$300.
How much could they spend on other things if they bought
NAME
91
no food? $150. Use blue ink to draw their budget line if they choose
the coupon option.
Other things
180
Black budget line
150
120
a
90
Blue budget line
Red budget line
60
c
30
b
0
30
60
90
120
150
180
210
240
Food
(b) Using the fact that food is a normal good for the McCawbers, and
knowing what they purchased before, darken the portion of the black
budget line where their consumption bundle could possibly be if they
chose the lump-sum grant option. Label the ends of this line segment A
and B.
(c) After studying the graph you have drawn, you report to the McCawbers. I have enough information to be able to tell you which choice to
make. You should choose the
coupon
because
you can
get more food even when other expenditure
is constant.
(d) Mr. McCawber thanks you for your help and then asks, Would you
have been able to tell me what to do if you hadnt known whether food
was a normal good for us? On the axes below, draw the same budget
lines you drew on the diagram above, but draw indierence curves for
which food is not a normal good and for which the McCawbers would be
better o with the program you advised them not to take.
92
REVEALED PREFERENCE
(Ch. 7)
Other things
180
150
Black budget
line
120
a
90
Blue budget line
Red budget line
60
c
30
b
0
30
60
90
120
150
180
210
240
Food
7.10 (0) In 1933, the Swedish economist Gunnar Myrdal (who later won
a Nobel prize in economics) and a group of his associates at Stockholm
University collected a fantastically detailed historical series of prices and
price indexes in Sweden from 1830 until 1930. This was published in a
book called The Cost of Living in Sweden. In this book you can nd
100 years of prices for goods such as oat groats, hard rye bread, salted
codsh, beef, reindeer meat, birchwood, tallow candles, eggs, sugar, and
coee. There are also estimates of the quantities of each good consumed
by an average working-class family in 1850 and again in 1890.
The table below gives prices in 1830, 1850, 1890, and 1913, for our,
meat, milk, and potatoes. In this time period, these four staple foods
accounted for about 2/3 of the Swedish food budget.
Prices of Staple Foods in Sweden
Prices are in Swedish kronor per kilogram, except for milk, which is in
Swedish kronor per liter.
Grain Flour
Meat
Milk
Potatoes
1830
.14
.28
.07
.032
1850
.14
.34
.08
.044
1890
.16
.66
.10
.051
1913
.19
.85
.13
.064
Based on the tables published in Myrdals book, typical consumption bundles for a working-class Swedish family in 1850 and 1890 are
listed below. (The reader should be warned that we have made some
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93
approximations and simplications to draw these simple tables from the
much more detailed information in the original study.)
Quantities Consumed by a Typical Swedish Family
Quantities are measured in kilograms per year, except for milk, which is
measured in liters per year.
Grain Flour
Meat
Milk
Potatoes
1850
165
22
120
200
1890
220
42
180
200
(a) Complete the table below, which reports the annual cost of the 1850
and 1890 bundles of staple foods at various years prices.
Cost of 1850 and 1890 Bundles at Various Years Prices
Cost
1850 bundle
1890 bundle
Cost at 1830 Prices
44.1
61.6
Cost at 1850 Prices
49.0
68.3
Cost at 1890 Prices
63.1
91.1
Cost at 1913 Prices
78.5
113.7
(b) Is the 1890 bundle revealed preferred to the 1850 bundle?
Yes.
(c) The Laspeyres quantity index for 1890 with base year 1850 is the ratio
of the value of the 1890 bundle at 1850 prices to the value of the 1850
bundle at 1850 prices. Calculate the Laspeyres quantity index of staple
food consumption for 1890 with base year 1850.
1.39.
(d) The Paasche quantity index for 1890 with base year 1850 is the ratio
of the value of the 1890 bundle at 1890 prices to the value of the 1850
bundle at 1890 prices. Calculate the Paasche quantity index for 1890 with
base year 1850.
1.44.
(e) The Laspeyres price index for 1890 with base year 1850 is calculated
using 1850 quantities for weights. Calculate the Laspeyres price index for
1890 with base year 1850 for this group of four staple foods.
1.29.
94
REVEALED PREFERENCE
(Ch. 7)
(f ) If a Swede were rich enough in 1850 to aord the 1890 bundle of staple
foods in 1850, he would have to spend 1.39 times as much on these
foods as does the typical Swedish worker of 1850.
(g) If a Swede in 1890 decided to purchase the same bundle of food staples
that was consumed by typical 1850 workers, he would spend the fraction
.69 of the amount that the typical Swedish worker of 1890 spends on
these goods.
7.11 (0) This question draws from the tables in the previous question.
Let us try to get an idea of what it would cost an American family at
todays prices to purchase the bundle consumed by an average Swedish
family in 1850. In the United States today, the price of our is about $.40
per kilogram, the price of meat is about $3.75 per kilogram, the price of
milk is about $.50 per liter, and the price of potatoes is about $1 per
kilogram. We can also compute a Laspeyres price index across time and
across countries and use it to estimate the value of a current US dollar
relative to the value of an 1850 Swedish kronor.
(a) How much would it cost an American at todays prices to buy the bundle of staple food commodities purchased by an average Swedish workingclass family in 1850?
$408.
(b) Myrdal estimates that in 1850, about 2/3 of the average familys
budget was spent on food. In turn, the four staples discussed in the last
question constitute about 2/3 of the average familys food budget. If the
prices of other goods relative to the price of the food staples are similar
in the United States today to what they were in Sweden in 1850, about
how much would it cost an American at current prices to consume the
same overall consumption bundle consumed by a Swedish working-class
family in 1850?
$919.
(c) Using the Swedish consumption bundle of staple foods in 1850 as
weights, calculate a Laspeyres price index to compare prices in current
American dollars relative to prices in 1850 Swedish kronor. 8.35. If
we use this to estimate the value of current dollars relative to 1850 Swedish
kronor, we would say that a U.S. dollar today is worth about
Swedish kronor.
.12
1850
7.12 (0) Suppose that between 1960 and 1985, the price of all goods
exactly doubled while every consumers income tripled.
NAME
95
(a) Would the Laspeyres price index for 1985, with base year 1960 be less
Exactly 2.
than 2, greater than 2, or exactly equal to 2?
about the Paasche price index?
What
Exactly 2.
(b) If bananas are a normal good, will total banana consumption increase? Yes. If everybody has homothetic preferences, can you determine by what percentage total banana consumption must have increased? Explain.
Yes, by 50%. Everybodys budget
line shifted out by 50%. With homothetic
preferences, the consumption of each good
increases in the same proportion.
7.13 (1) Norm and Sheila consume only meat pies and beer. Meat pies
used to cost $2 each and beer was $1 per can. Their gross income used
to be $60 per week, but they had to pay an income tax of $10. Use red
ink to sketch their old budget line for meat pies and beer.
Beer
60
50
Red budget line
40
30
20
10
0
Blue budget line
Black
budget
line
10
20
30
40
50
60
Pies
96
REVEALED PREFERENCE
(Ch. 7)
(a) They used to buy 30 cans of beer per week and spent the rest of their
income on meat pies. How many meat pies did they buy?
10.
(b) The government decided to eliminate the income tax and to put a
sales tax of $1 per can on beer, raising its price to $2 per can. Assuming
that Norm and Sheilas pre-tax income and the price of meat pies did not
change, draw their new budget line in blue ink.
(c) The sales tax on beer induced Norm and Sheila to reduce their beer
consumption to 20 cans per week. What happened to their consumption
of meat pies?
Stayed the same--10.
did this tax raise from Norm and Sheila?
How much revenue
$20.
(d) This part of the problem will require some careful thinking. Suppose
that instead of just taxing beer, the government decided to tax both beer
and meat pies at the same percentage rate, and suppose that the price
of beer and the price of meat pies each went up by the full amount of
the tax. The new tax rate for both goods was set high enough to raise
exactly the same amount of money from Norm and Sheila as the tax on
beer used to raise. This new tax collects $
.50
for every bottle of beer
sold and $
1
for every meat pie sold. (Hint: If both goods are
taxed at the same rate, the eect is the same as an income tax.) How
large an income tax would it take to raise the same revenue as the $1 tax
on beer? $20. Now you can gure out how big a tax on each good
is equivalent to an income tax of the amount you just found.
(e) Use black ink to draw the budget line for Norm and Sheila that corresponds to the tax in the last section. Are Norm and Sheila better o
having just beer taxed or having both beer and meat pies taxed if both
sets of taxes raise the same revenue?
principle of revealed preference.)
Both.
(Hint: Try to use the