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104 SLUTSKY EQUATION (Ch. 8)
(c) On the axes below, use blue ink to draw Douglas Cornfield’s budget
line before the price change. Locate the bundle he chooses at these prices
on your graph and label this point A. Use black ink to draw Douglas
Cornfield’s budget line after the price change. Label his consumption
bundle after the change by B.
0 40 80 120 160 200 240 280 320
20
40
60
80
y
x
a
b
c
Blue line
Black line
Black line
(d) On the graph above, use black ink to draw a budget line with the new
8.7 (1) Mr. Consumer allows himself to spend $100 per month on
(a) In January, the price of cigarettes was $1 per pack, while ice cream
cost $2 per pint. Faced with these prices, Mr. C bought 30 pints of ice
NAME 105
10 20 30 40 50 60 70 80 90 100
10
20
30
40
50
60
70
80
90
100
J
F
Blue
budget
line
Red budget line
Black budget line
A
Pencil
budget
line
Cigarettes
Ice cream
0
(b) In February, Mr. C again had $100 to spend and ice cream still cost
$2 per pint, but the price of cigarettes rose to $1.25 per pack. Mr. C
consumed 30 pints of ice cream and 32 packs of cigarettes. Draw Mr. C’s
February budget line with red ink and mark his February bundle with
the letter F. The substitution effect of this price change would make him
change in his ice cream consumption was zero, it must be that the income
effect of this price change on his consumption of ice cream makes him buy
effect of this price change is like the effect of an (increase, decrease)
106 SLUTSKY EQUATION (Ch. 8)
(c) In March, Mr. C again had $100 to spend. Ice cream was on sale for $1
per pint. Cigarette prices, meanwhile, increased to $1.50 per pack. Draw
his March budget line with black ink. Is he better off than in January,
8.8 (1) This problem continues with the adventures of Mr. Consumer
from the previous problem.
(a) In April, cigarette prices rose to $2 per pack and ice cream was still
on sale for $1 per pint. Mr. Consumer bought 34 packs of cigarettes and
32 pints of ice cream. Draw his April budget line with pencil and label
his April bundle with the letter A. Was he better off or worse off than
(b) In May, cigarettes stayed at $2 per pack and as the sale on ice cream
ended, the price returned to $2 per pint. On the way to the store, how-
ever, Mr. C found $30 lying in the street. He then had $130 to spend on
cigarettes and ice cream. Draw his May budget with a dashed line. With-
out knowing what he purchased, one can determine whether he is better
off than he was in at least one previous month. Which month or months?
(c) In fact, Mr. C buys 40 packs of cigarettes and 25 pints of ice cream
8.9 (2) In the last chapter, we studied a problem involving food prices
and consumption in Sweden in 1850 and 1890.
(a) Potato consumption was the same in both years. Real income must
have gone up between 1850 and 1890, since the amount of food staples
purchased, as measured by either the Laspeyres or the Paasche quantity
index, rose. The price of potatoes rose less rapidly than the price of either
meat or milk, and at about the same rate as the price of grain flour. So
real income went up and the price of potatoes went down relative to
other goods. From this information, determine whether potatoes were
NAME 107
most likely a normal or an inferior good. Explain your answer.
(b) Can one also tell from these data whether it is likely that pota-
toes were a Giffen good? If potatoes were a
Giffen good, then the fall in the price
8.10 (1) Agatha must travel on the Orient Express from Istanbul to
Paris. The distance is 1,500 miles. A traveler can choose to make any
fraction of the journey in a first-class carriage and travel the rest of the
way in a second-class carriage. The price is 10 cents a mile for a second-
class carriage and 20 cents a mile for a first-class carriage. Agatha much
prefers first-class to second-class travel, but because of a misadventure in
an Istanbul bazaar, she has only $200 left with which to buy her tickets.
Luckily, she still has her toothbrush and a suitcase full of cucumber sand-
wiches to eat on the way. Agatha plans to spend her entire $200 on her
tickets for her trip. She will travel first class as much as she can afford
to, but she must get all the way to Paris, and $200 is not enough money
to get her all the way to Paris in first class.
(a) On the graph below, use red ink to show the locus of combinations
of first- and second-class tickets that Agatha can just afford to purchase
with her $200. Use blue ink to show the locus of combinations of first-
and second-class tickets that are suffcient to carry her the entire distance
from Istanbul to Paris. Locate the combination of first- and second-class
miles that Agatha will choose on your graph and label it A.
108 SLUTSKY EQUATION (Ch. 8)
0 400 800 1200 1600
400
800
1200
Second-class miles
First-class miles
1600
Red
line
Blue line
Black line
a
Pencil line
b
c
(b) Let m1be the number of miles she travels by first-class coach and m2
be the number of miles she travels by second-class coach. Write down two
equations that you can solve to find the number of miles she chooses to
travel by first-class coach and the number of miles she chooses to travel
by second-class coach. .2m1+.1m2= 200,m1+m2=
1,500.
(c) The number of miles that she travels by second-class coach is
1,000.
(d) Just before she was ready to buy her tickets, the price of second-class
tickets fell to $.05 while the price of first-class tickets remained at $.20.
On the graph that you drew above, use pencil to show the combinations
of first-class and second-class tickets that she can afford with her $200
at these prices. On your graph, locate the combination of first-class and
second-class tickets that she would now choose. (Remember, she is going
to travel as much first-class as she can afford to and still make the 1,500
mile trip on $200.) Label this point B. How many miles does she travel
by second class now? 666.66. (Hint: For an exact solution you
will have to solve two linear equations in two unknowns.) Is second-class
travel a normal good for Agatha? No. Is it a Giffen good for her?
Yes.
NAME 109
8.11 (0) We continue with the adventures of Agatha, from the previous
problem. Just after the price change from $.10 per mile to $.05 per mile
for second-class travel, and just before she had bought any tickets, Agatha
misplaced her handbag. Although she kept most of her money in her sock,
the money she lost was just enough so that at the new prices, she could
exactly afford the combination of first- and second-class tickets that she
would have purchased at the old prices. How much money did she lose?
to draw the locus of combinations of first- and second-class tickets that
she can just afford after discovering her loss. Label the point that she
chooses with a C. How many miles will she travel by second class now?
(a) Finally, poor Agatha finds her handbag again. How many miles will
she travel by second class now (assuming she didn’t buy any tickets before
class tickets fell from $.10 to $.05, how much of a change in Agatha’s de-
