CHAPTER 7: Revealed Preference
MULTIPLE CHOICE
1. In Problem 1, if the only information we had about Goldie were that she chooses the bundle (6, 6)
when prices are (6, 7) and she chooses the bundle (10, 0) when prices are (2, 5), then we could
conclude that
a.
the bundle (6, 6) is revealed preferred to (10, 0) but there is no evidence that she violates
WARP.
b.
neither bundle is revealed preferred to the other.
c.
Goldie violates WARP.
d.
the bundle (10, 0) is revealed preferred to (6, 6) and she violates WARP.
e.
the bundle (10, 0) is revealed preferred to (6, 6) but there is no evidence that she violates
WARP.
2. In Problem 1, if the only information we had about Goldie were that she chooses the bundle (6, 6)
when prices are (6, 7) and she chooses the bundle (10, 0) when prices are (1, 5), then we could
conclude that
a.
Goldie violates WARP.
b.
neither bundle is revealed preferred to the other.
c.
the bundle (6, 6) is revealed preferred to (10, 0) but there is no evidence that she violates
WARP.
d.
the bundle (10, 0) is revealed preferred to (6, 6) and she violates WARP.
e.
the bundle (10, 0) is revealed preferred to (6, 6) but there is no evidence that she violates
WARP.
3. In Problem 1, if the only information we had about Goldie were that she chooses the bundle (6, 6)
when prices are (6, 2) and she chooses the bundle (10, 0) when prices are (3, 5), then we could
conclude that
a.
neither bundle is revealed preferred to the other.
b.
Goldie violates WARP.
c.
the bundle (6, 6) is revealed preferred to (10, 0) but there is no evidence that she violates
WARP.
d.
the bundle (10, 0) is revealed preferred to (6, 6) and she violates WARP.
e.
the bundle (10, 0) is revealed preferred to (6, 6) but there is no evidence that she violates
WARP.
4. In Problem 1, if the only information we had about Goldie were that she chooses the bundle (6, 6)
when prices are (6, 7) and she chooses the bundle (10, 0) when prices are (2, 5), then we could
conclude that
a.
Goldie violates WARP.
b.
the bundle (6, 6) is revealed preferred to (10, 0) but there is no evidence that she violates
WARP.
c.
neither bundle is revealed preferred to the other.
d.
the bundle (10, 0) is revealed preferred to (6, 6) and she violates WARP.
e.
the bundle (10, 0) is revealed preferred to (6, 6) but there is no evidence that she violates
WARP.
5. In Problem 1, if the only information we had about Goldie were that she chooses the bundle (6, 6)
when prices are (6, 7) and she chooses the bundle (10, 0) when prices are (5, 5), then we could
conclude that
a.
the bundle (6, 6) is revealed preferred to (10, 0) but there is no evidence that she violates
WARP.
b.
Goldie violates WARP.
c.
the bundle (10, 0) is revealed preferred to (6, 6) and she violates WARP.
d.
neither bundle is revealed preferred to the other.
e.
the bundle (10, 0) is revealed preferred to (6, 6) but there is no evidence that she violates
WARP.
6. In Problem 3, Pierre’s friend Jean lives in a town where he has to pay 3 francs per glass of wine and 2
francs per loaf of bread. Jean consumes 7 glasses of wine and 4 loaves of bread per day. Recall that
Bob has an income of $15 per day and pays $.50 per loaf of bread and $2 per glass of wine. If Bob has
the same tastes as Jean and if the only thing that either of them cares about is the consumption of bread
and wine,
a.
there is not enough information to determine whether one is better off than the other.
b.
Jean is better off than Bob.
c.
Bob is better off than Jean.
d.
both of them violate the weak axiom of revealed preferences.
e.
Bob and Jean are equally well off.
7. In Problem 3, Pierre’s friend Marcel lives in a town where he has to pay 3 francs per glass of wine and
5 francs per loaf of bread. Marcel consumes 9 glasses of wine and 4 loaves of bread per day. Recall
that Bob has an income of $15 per day and pays $.50 per loaf of bread and $2 per glass of wine. If Bob
has the same tastes as Marcel and if the only thing that either of them cares about is the consumption
of bread and wine,
a.
both of them violate the weak axiom of revealed preferences.
b.
there is not enough information to determine whether one is better off than the other.
c.
Bob is better off than Marcel.
d.
Marcel is better off than Bob.
e.
Bob and Marcel are equally well off.
8. In Problem 3, Pierre’s friend Henri lives in a town where he has to pay 3 francs per glass of wine and 2
francs per loaf of bread. Henri consumes 10 glasses of wine and 4 loaves of bread per day. Recall that
Bob has an income of $15 per day and pays $.50 per loaf of bread and $2 per glass of wine. If Bob has
the same tastes as Henri and if the only thing that either of them cares about is the consumption of
bread and wine,
a.
Henri is better off than Bob.
b.
both of them violate the weak axiom of revealed preferences.
c.
there is not enough information to determine whether one is better off than the other.
d.
Bob is better off than Henri.
e.
Bob and Henri are equally well off.
9. In Problem 3, Pierre’s friend Henri lives in a town where he has to pay 3 francs per glass of wine and 7
francs per loaf of bread. Henri consumes 10 glasses of wine and 4 loaves of bread per day. Recall that
Bob has an income of $15 per day and pays $.50 per loaf of bread and $2 per glass of wine. If Bob has
the same tastes as Henri and if the only thing that either of them cares about is the consumption of
bread and wine,
a.
both of them violate the weak axiom of revealed preferences.
b.
Bob is better off than Henri.
c.
Henri is better off than Bob.
d.
there is not enough information to determine whether one is better off than the other.
e.
Bob and Henri are equally well off.
10. In Problem 3, Pierre’s friend Jacques lives in a town where he has to pay 3 francs per glass of wine
and 3 francs per loaf of bread. Jacques consumes 8 glasses of wine and 4 loaves of bread per day.
Recall that Bob has an income of $15 per day and pays $.50 per loaf of bread and $2 per glass of wine.
If Bob has the same tastes as Jacques and if the only thing that either of them cares about is the
consumption of bread and wine,
a.
there is not enough information to determine whether one is better off than the other.
b.
both of them violate the weak axiom of revealed preferences.
c.
Jacques is better off than Bob.
d.
Bob is better off than Jacques.
e.
Bob and Jacques are equally well off.
11. Let us reconsider the case of Ronald in Problem 4. Let the prices and consumptions in the base year be
as in situation D, where p1 = $3, p2 = $1, x1 = 5, and x2 = 15. If in the current year, the price of good 1
is $1 and the price of good 2 is $2, and his current consumptions of good 1 and good 2 are 25 and 20
respectively, what is the Laspeyres price index of current prices relative to base year prices? (Pick the
most nearly correct answer.)
a.
1.17
b.
2.17
c.
0.75
d.
0.50
e.
1.75
12. Let us reconsider the case of Ronald in Problem 4. Let the prices and consumptions in the base year be
as in situation D, where p1 = $3, p2 = $1, x1 = 5, and x2 = 15. If in the current year, the price of good 1
is $1 and the price of good 2 is $1, and his current consumptions of good 1 and good 2 are 25 and 20
respectively, what is the Laspeyres price index of current prices relative to base year prices? (Pick the
most nearly correct answer.)
a.
0.25
b.
0.67
c.
0.50
d.
1.50
e.
1
13. Let us reconsider the case of Ronald in Problem 4. Let the prices and consumptions in the base year be
as in situation D, where p1 = $3, p2 = $1, x1 = 5, and x2 = 15. If in the current year, the price of good 1
is $1 and the price of good 2 is $3, and his current consumptions of good 1 and good 2 are 25 and 20
respectively, what is the Laspeyres price index of current prices relative to base year prices? (Pick the
most nearly correct answer.)
a.
1
b.
1.67
c.
0.75
d.
2.83
e.
2.50
14. Let us reconsider the case of Ronald in Problem 4. Let the prices and consumptions in the base year be
as in situation D, where p1 = $3, p2 = $1, x1 = 5, and x2 = 15. If in the current year, the price of good 1
is $1 and the price of good 2 is $1, and his current consumptions of good 1 and good 2 are 25 and 10
respectively, what is the Laspeyres price index of current prices relative to base year prices? (Pick the
most nearly correct answer.)
a.
0.50
b.
0.25
c.
1.17
d.
0.67
e.
1
15. Let us reconsider the case of Ronald in Problem 4. Let the prices and consumptions in the base year be
as in situation D, where p1 = $3, p2 = $1, x1 = 5, and x2 = 15. If in the current year, the price of good 1
is $1 and the price of good 2 is $1, and his current consumptions of good 1 and good 2 are 25 and 20
respectively, what is the Laspeyres price index of current prices relative to base year prices? (Pick the
most nearly correct answer.)
a.
0.67
b.
1.50
c.
0.25
d.
0.50
e.
1
16. On the planet Homogenia every consumer who has ever lived consumes only two goods, x and y, and
has the utility function U(x, y) = xy. The currency in Homogenia is the fragel. In this country in 1900,
the price of good 1 was 1 fragel and the price of good 2 was 2 fragels. Per capita income was 84
fragels. In 2000, the price of good 1 was 3 fragels and the price of good 2 was 4 fragels. The Laspeyres
price index for the price level in 2000 relative to the price level in 1900 is
a.
2.50.
b.
3.50.
c.
2.33.
d.
4.
e.
not possible to determine from this information.
17. On the planet Homogenia every consumer who has ever lived consumes only two goods, x and y, and
has the utility function U(x, y) = xy. The currency in Homogenia is the fragel. In this country in 1900,
the price of good 1 was 1 fragel and the price of good 2 was 2 fragels. Per capita income was 108
fragels. In 2000, the price of good 1 was 3 fragels and the price of good 2 was 4 fragels. The Laspeyres
price index for the price level in 2000 relative to the price level in 1900 is
a.
2.33.
b.
2.50.
c.
4.
d.
3.50.
e.
not possible to determine from this information.
18. On the planet Homogenia every consumer who has ever lived consumes only two goods, x and y, and
has the utility function U(x, y) = xy. The currency in Homogenia is the fragel. In this country in 1900,
the price of good 1 was 1 fragel and the price of good 2 was 2 fragels. Per capita income was 60
fragels. In 2000, the price of good 1 was 5 fragels and the price of good 2 was 3 fragels. The Laspeyres
price index for the price level in 2000 relative to the price level in 1900 is
a.
2.67.
b.
5.75.
c.
4.
d.
3.25.
e.
not possible to determine from this information.
19. On the planet Homogenia every consumer who has ever lived consumes only two goods, x and y, and
has the utility function U(x, y) = xy. The currency in Homogenia is the fragel. In this country in 1900,
the price of good 1 was 1 fragel and the price of good 2 was 2 fragels. Per capita income was 84
fragels. In 2000, the price of good 1 was 4 fragels and the price of good 2 was 2 fragels. The Laspeyres
price index for the price level in 2000 relative to the price level in 1900 is
a.
4.50.
b.
2.50.
c.
2.
d.
3.
e.
not possible to determine from this information.
20. On the planet Homogenia every consumer who has ever lived consumes only two goods, x and y, and
has the utility function U(x, y) = xy. The currency in Homogenia is the fragel. In this country in 1900,
the price of good 1 was 1 fragel and the price of good 2 was 2 fragels. Per capita income was 84
fragels. In 2000, the price of good 1 was 1 fragels and the price of good 2 was 5 fragels. The Laspeyres
price index for the price level in 2000 relative to the price level in 1900 is
a.
1.75.
b.
3.
c.
2.
d.
2.25.
e.
not possible to determine from this information.
21. On the planet Hyperion every consumer who has ever lived has a utility function U(x, y) = minx,
2y. The currency of Hyperion is the doggerel. In 1850 the price of x was 1 doggerel per unit and the
price of y was 2 doggerels per unit. In 2000, the price of x was 11 doggerels per unit and the price of y
was 4 doggerels per unit. The Paasche price index of prices in 2000 relative to prices in 1850 is
a.
6.50.
b.
5.
c.
2.75.
d.
3.75.
e.
not possible to determine without further information.
22. On the planet Hyperion every consumer who has ever lived has a utility function U(x, y) = minx,
2y. The currency of Hyperion is the doggerel. In 1850 the price of x was 1 doggerel per unit and the
price of y was 2 doggerels per unit. In 2000, the price of x was 4 doggerels per unit and the price of y
was 4 doggerels per unit. The Paasche price index of prices in 2000 relative to prices in 1850 is
a.
2.
b.
3.
c.
1.
d.
2.67.
e.
not possible to determine without further information.
23. On the planet Hyperion every consumer who has ever lived has a utility function U(x, y) = minx,
2y. The currency of Hyperion is the doggerel. In 1850 the price of x was 1 doggerel per unit and the
price of y was 2 doggerels per unit. In 2000, the price of x was 10 doggerels per unit and the price of y
was 4 doggerels per unit. The Paasche price index of prices in 2000 relative to prices in 1850 is
a.
6.
b.
4.67.
c.
2.50.
d.
3.50.
e.
not possible to determine without further information.
24. On the planet Hyperion every consumer who has ever lived has a utility function U(x, y) = minx,
2y. The currency of Hyperion is the doggerel. In 1850 the price of x was 1 doggerel per unit and the
price of y was 2 doggerels per unit. In 2000, the price of x was 4 doggerels per unit and the price of y
was 4 doggerels per unit. Paasche price index of prices in 2000 relative to prices in 1850 is
a.
1.
b.
2.67.
c.
2.
d.
3.
e.
not possible to determine without further information.
25. On the planet Hyperion every consumer who has ever lived has a utility function U(x, y) =
minx, 2y. The currency of Hyperion is the doggerel. In 1850 the price of x was 1 doggerel per unit
and the price of y was 2 doggerels per unit. In 2000, the price of x was 10 doggerels per unit and the
price of y was 4 doggerels per unit. Paasche price index of prices in 2000 relative to prices in 1850 is
a.
3.50.
b.
6.
c.
2.50.
d.
4.67.
e.
not possible to determine without further information.
26. In Problem 4, if situation D is p = (3, 1) and x = (5, 10),
a.
Ronald’s behavior is consistent with both the Weak and the Strong Axioms of Revealed
Preference.
b.
Ronald’s behavior is consistent with the Weak but not the Strong Axiom of Revealed
Preference.
c.
Ronald’s behavior violates both the Weak and the Strong Axioms of Revealed Preference.