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NAME 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 sus-
pects, 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 Cedric’s 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
•R. Preston McAfee — McAfee is known to consume 5 liters of beer
•Richard Manning — Manning consumes 5 kilograms of sausage
•Richard Stevenson — Stevenson consumes 5 kilograms of sausage
(a) Draw the budget line for each of the three fugitives, using a different
color of ink for each one. Label the consumption bundle that each chooses.
On this graph, superimpose Sir Cedric’s budget line and the bundle he
chose.
90 REVEALED PREFERENCE (Ch. 7)
0102030
40
10
20
30
Beer
Sausage
40
McAfee
Manning
Pinchbottom Stevenson
(b) After pondering the dossiers for a few moments, Lord Peter an-
nounced. “Unless Sir Cedric has changed his tastes, I can eliminate one
of the suspects. Revealed preference tells me that one of the suspects is
(c) After thinking a bit longer, Lord Peter announced. “If Sir Cedric
left voluntarily, then he would have to be better off than he was before.
Therefore if Sir Cedric left voluntarily and if he has not changed his tastes,
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?
NAME 91
the coupon option.
0 30 60 90 120 150 180 210 240
30
60
90
120
150
180
Other things
Food
c
a
b
Black budget line
Blue budget line
Red budget line
(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 McCaw-
bers. “I have enough information to be able to tell you which choice to
make. You should choose the coupon because you can
(d) Mr. McCawber thanks you for your help and then asks, “Would you
have been able to tell me what to do if you hadn’t 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 indifference curves for
which food is not a normal good and for which the McCawbers would be
better off with the program you advised them not to take.
92 REVEALED PREFERENCE (Ch. 7)
0 30 60 90 120 150 180 210 240
30
60
90
120
150
180
Other things
Food
c
a
b
Black budget
line
Blue budget line
Red budget line
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 find
The table below gives prices in 1830, 1850, 1890, and 1913, for flour,
Prices are in Swedish kronor per kilogram, except for milk, which is in
Swedish kronor per liter.
1830 1850 1890 1913
Based on the tables published in Myrdal’s book, typical consump-
tion bundles for a working-class Swedish family in 1850 and 1890 are
listed below. (The reader should be warned that we have made some
NAME 93
approximations and simplifications to draw these simple tables from the
much more detailed information in the original study.)
Quantities are measured in kilograms per year, except for milk, which is
measured in liters per year.
1850 1890
(a) Complete the table below, which reports the annual cost of the 1850
Cost 1850 bundle 1890 bundle
(c) The Laspeyres quantity index for 1890 with base year 1850 is the ratio
(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
(e) The Laspeyres price index for 1890 with base year 1850 is calculated
using 1850 quantities for weights. Calculate the Laspeyres price index for
94 REVEALED PREFERENCE (Ch. 7)
(f) If a Swede were rich enough in 1850 to afford the 1890 bundle of staple
(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
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
today’s prices to purchase the bundle consumed by an average Swedish
family in 1850. In the United States today, the price of flour 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 today’s prices to buy the bun-
dle of staple food commodities purchased by an average Swedish working-
(b) Myrdal estimates that in 1850, about 2/3 of the average family’s
budget was spent on food. In turn, the four staples discussed in the last
question constitute about 2/3 of the average family’s 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
(c) Using the Swedish consumption bundle of staple foods in 1850 as
weights, calculate a Laspeyres price index to compare prices in current
we use this to estimate the value of current dollars relative to 1850 Swedish
Swedish kronor.
7.12 (0) Suppose that between 1960 and 1985, the price of all goods
exactly doubled while every consumer’s income tripled.
NAME 95
(a) Would the Laspeyres price index for 1985, with base year 1960 be less
(b) If bananas are a normal good, will total banana consumption in-
crease? Yes. If everybody has homothetic preferences, can you de-
termine by what percentage total banana consumption must have in-
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.
02030405060
10
20
30
40
50
60
10
Pies
Beer
Black
budget
line
Red budget line
Blue budget line
96 REVEALED PREFERENCE (Ch. 7)
(a) They used to buy 30 cans of beer per week and spent the rest of their
(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
(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
(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
andmeatpiesatthesame 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
taxed at the same rate, the effect is the same as an income tax.) How
large an income tax would it take to raise the same revenue as the $1 tax
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 cor-
responds to the tax in the last section. Are Norm and Sheila better off
having just beer taxed or having both beer and meat pies taxed if both
principle of revealed preference.)
