CHAPTER 4: Utility
MULTIPLE CHOICE
1. In Problem 1, Charlie has the utility function U(xA, xB) = xAxB. His indifference curve passing through 6
apples and 16 bananas will also pass through the point where he consumes 2 apples and
a.
12 bananas.
b.
24 bananas.
c.
50 bananas.
d.
54 bananas.
e.
48 bananas.
2. In Problem 1, Charlie has the utility function U(xA, xB) = xAxB. His indifference curve passing through
24 apples and 6 bananas will also pass through the point where he consumes 4 apples and
a.
12 bananas.
b.
40 bananas.
c.
24 bananas.
d.
43 bananas.
e.
36 bananas.
3. In Problem 1, Charlie has the utility function U(xA, xB) = xAxB. His indifference curve passing through
15 apples and 16 bananas will also pass through the point where he consumes 3 apples and
a.
40 bananas.
b.
83 bananas.
c.
20 bananas.
d.
87 bananas.
e.
80 bananas.
4. In Problem 1, Charlie has the utility function U(xA, xB) = xAxB. His indifference curve passing through
12 apples and 64 bananas will also pass through the point where he consumes 2 apples and
a.
386 bananas.
b.
48 bananas.
c.
96 bananas.
d.
394 bananas.
e.
384 bananas.
5. In Problem 1, Charlie has the utility function U(xA, xB) = xAxB. His indifference curve passing through
40 apples and 9 bananas will also pass through the point where he consumes 5 apples and
a.
48 bananas.
b.
77 bananas.
c.
80 bananas.
d.
24 bananas.
e.
72 bananas.
6. In Problem 1, Charlie’s utility function is U(A, B) = AB, where A and B are the numbers of apples and
bananas, respectively, that he consumes. If Charlie is consuming 15 apples and 30 bananas, then if we
put apples on the horizontal axis and bananas on the vertical axis, the slope of his indifference curve at
his current consumption is
a.
−16.
b.
−2.
c.
−4.
d.
−1/2.
e.
−1/4.
7. In Problem 1, Charlie’s utility function is U(A, B) = AB, where A and B are the numbers of apples and
bananas, respectively, that he consumes. If Charlie is consuming 35 apples and 175 bananas, then if
we put apples on the horizontal axis and bananas on the vertical axis, the slope of his indifference
curve at his current consumption is
a.
−36.
b.
−10.
c.
−1/5.
d.
−5.
e.
−1/10.
8. In Problem 1, Charlie’s utility function is U(A, B) = AB, where A and B are the numbers of apples and
bananas, respectively, that he consumes. If Charlie is consuming 40 apples and 240 bananas, then if
we put apples on the horizontal axis and bananas on the vertical axis, the slope of his indifference
curve at his current consumption is
a.
−1/6.
b.
−12.
c.
−41.
d.
−6.
e.
−1/12.
9. In Problem 1, Charlie’s utility function is U(A, B) = AB, where A and B are the numbers of apples and
bananas, respectively, that he consumes. If Charlie is consuming 40 apples and 160 bananas, then if
we put apples on the horizontal axis and bananas on the vertical axis, the slope of his indifference
curve at his current consumption is
a.
−4.
b.
−8.
c.
−41.
d.
−1/4.
e.
−1/8.
10. In Problem 1, Charlie’s utility function is U(A, B) = AB, where A and B are the numbers of apples and
bananas, respectively, that he consumes. If Charlie is consuming 30 apples and 120 bananas, then if
we put apples on the horizontal axis and bananas on the vertical axis, the slope of his indifference
curve at his current consumption is
a.
−31.
b.
−8.
c.
−1/4.
d.
−4.
e.
−1/8.
11. In Problem 2, Ambrose has the utility function U(x1, x2) = 4x1/21 + x2. If Ambrose were initially
consuming 49 units of nuts (good 1) and 12 units of berries (good 2), then what is the largest number
of berries that he would be willing to give up in return for an additional 32 units of nuts?
a.
9
b.
21
c.
8
d.
4
e.
2
12. In Problem 2, Ambrose has the utility function U(x1, x2) = 4x1/21 + x2. If Ambrose were initially
consuming 9 units of nuts (good 1) and 21 units of berries (good 2), then what is the largest number of
berries that he would be willing to give up in return for an additional 16 units of nuts?
a.
26
b.
5
c.
8
d.
4
e.
2
13. In Problem 2, Ambrose has the utility function U(x1, x2) = 4x1/21 + x2. If Ambrose were initially
consuming 81 units of nuts (good 1) and 22 units of berries (good 2), then what is the largest number
of berries that he would be willing to give up in return for an additional 40 units of nuts?
a.
4
b.
8
c.
11
d.
33
e.
2
14. In Problem 2, Ambrose has the utility function U(x1, x2) = 4x1/21 + x2. If Ambrose were initially
consuming 4 units of nuts (good 1) and 27 units of berries (good 2), then what is the largest number of
berries that he would be willing to give up in return for an additional 21 units of nuts?
a.
5
b.
12
c.
6
d.
32
e.
3
15. In Problem 2, Ambrose has the utility function U(x1, x2) = 4x1/21 + x2. If Ambrose were initially
consuming 4 units of nuts (good 1) and 23 units of berries (good 2), then what is the largest number of
berries that he would be willing to give up in return for an additional 45 units of nuts?
a.
30
b.
7
c.
10
d.
20
e.
5
16. Joe Bob from Problem 12 has a cousin Ike who consumes goods 1 and 2. Ike thinks that 4 units of
good 1 is always a perfect substitute for 2 units of good 2. Which of the following utility functions is
the only one that would not represent Ike’s preferences?
a.
U(x1, x2) = 2x1 + 4x2 + 1000.
b.
U(x1, x2) = 4x21 + 16x1x2 + 16x22.
c.
U(x1, x2) = min2x1, 4x2.
d.
U(x1, x2) = 20x1 + 40x2 − 10,000.
e.
More than one of the above does not represent Ike’s preferences.
17. Joe Bob from Problem 12 has a cousin Don who consumes goods 1 and 2. Don thinks that 3 units of
good 1 is always a perfect substitute for 2 units of good 2. Which of the following utility functions is
the only one that would not represent Don’s preferences?
a.
U(x1, x2) = min2x1, 3x2.
b.
U(x1, x2) = 20x1 + 30x2 − 10,000.
c.
U(x1, x2) = 2x1 + 3x2 + 1000.
d.
U(x1, x2) = 4x21 + 12x1x2 + 9x22.
e.
More than one of the above does not represent Don’s preferences.
18. Joe Bob from Problem 12 has a cousin Pete who consumes goods 1 and 2. Pete thinks that 3 units of
good 1 is always a perfect substitute for 4 units of good 2. Which of the following utility functions is
the only one that would not represent Pete’s preferences?
a.
U(x1, x2) = 40x1 + 30x2 − 10,000.
b.
U(x1, x2) = 4x1 + 3x2 + 1000.
c.
U(x1, x2) = min4x1, 3x2.
d.
U(x1, x2) = 16x21 + 24x1x2 + 9x22.
e.
More than one of the above does not represent Pete’s preferences.
19. Joe Bob from Problem 12 has a cousin Sam who consumes goods 1 and 2. Sam thinks that 2 units of
good 1 is always a perfect substitute for 4 units of good 2. Which of the following utility functions is
the only one that would not represent Sam’s preferences?
a.
U(x1, x2) = 16x21 + 16x1x2 + 4x22.
b.
U(x1, x2) = min4x1, 2x2.
c.
U(x1, x2) = 40x1 + 20x2 − 10,000.
d.
U(x1, x2) = 4x1 + 2x2 + 1000.
e.
More than one of the above does not represent Sam’s preferences.
20. Joe Bob from Problem 12 has a cousin Martin who consumes goods 1 and 2. Martin thinks that 2 units
of good 1 is always a perfect substitute for 4 units of good 2. Which of the following utility functions
is the only one that would not represent Martin’s preferences?
a.
U(x1, x2) = 40x1 + 20x2 − 10,000.
b.
U(x1, x2) = 16x21 + 16x1x2 + 4x22.
c.
U(x1, x2) = min4x1, 2x2.
d.
U(x1, x2) = 4x1 + 2x2 + 1000.
e.
More than one of the above does not represent Martin’s preferences.
21. In Problem 7, Harry Mazzola has the utility function U(x1, x2) = minx1 + 2x2, 2x1 + x2. He has $40 to
spend on corn chips and french fries. If the price of corn chips is $4 per unit and the price of french
fries is $2 per unit, then Harry will
a.
definitely spend all of his income on corn chips.
b.
definitely spend all of his income on french fries.
c.
consume at least as many corn chips as french fries but might consume both.
d.
consume at least as many french fries as corn chips but might consume both.
e.
consume equal amounts of french fries and corn chips.
22. In Problem 7, Harry Mazzola has the utility function U(x1, x2) = minx1 + 2x2, 2x1 + x2. He has $40 to
spend on corn chips and french fries. If the price of corn chips is $3 per unit and the price of french
fries is $5 per unit, then Harry will
a.
definitely spend all of his income on french fries.
b.
consume at least as many corn chips as french fries but might consume both.
c.
definitely spend all of his income on corn chips.
d.
consume at least as many french fries as corn chips but might consume both.
e.
consume equal amounts of french fries and corn chips.
23. In Problem 7, Harry Mazzola has the utility function U(x1, x2) = minx1 + 2x2, 2x1 + x2. He has $40 to
spend on corn chips and french fries. If the price of corn chips is $2 per unit and the price of french
fries is $2 per unit, then Harry will
a.
definitely spend all of his income on corn chips.
b.
consume at least as many french fries as corn chips but might consume both.
c.
consume at least as many corn chips as french fries but might consume both.
d.
definitely spend all of his income on french fries.
e.
consume equal amounts of french fries and corn chips.
24. In Problem 7, Harry Mazzola has the utility function U(x1, x2) = minx1 + 2x2, 2x1 + x2. He has $40 to
spend on corn chips and french fries. If the price of corn chips is $1 per unit and the price of french
fries is $4 per unit, then Harry will
a.
consume at least as many corn chips as french fries but might consume both.
b.
consume at least as many french fries as corn chips but might consume both.
c.
definitely spend all of his income on french fries.
d.
definitely spend all of his income on corn chips.
e.
consume equal amounts of french fries and corn chips.
25. In Problem 7, Harry Mazzola has the utility function U(x1, x2) = minx1 + 2x2, 2x1 + x2. He has $40 to
spend on corn chips and french fries. If the price of corn chips is $2 per unit and the price of french
fries is $2 per unit, then Harry will
a.
consume at least as many corn chips as french fries but might consume both.
b.
definitely spend all of his income on corn chips.
c.
consume at least as many french fries as corn chips but might consume both.
d.
definitely spend all of his income on french fries.
e.
consume equal amounts of french fries and corn chips.
26. Phil Rupp, from Problem 4, has a sister Ethel who has the utility function U(x, y) = min4x + y, 5y.
Where x is measured on the horizontal axis and y on the vertical axis, her indifference curves consist
of a
a.
vertical line segment and a horizontal line segment that meet in a kink along the line
y = 4x.
b.
vertical line segment and a horizontal line segment that meet in a kink along the line
x = 4y.
c.
horizontal line segment and a negatively sloped line segment that meet in a kink along the
line x = y.
d.
positively sloped line segment and a negatively sloped line segment that meet along the
line x = y.
e.
horizontal line segment and a positively sloped line segment that meet in a kink along the
line x = 4y.
27. Phil Rupp, from Problem 4, has a sister Ethel who has the utility function U(x, y) = min2x + y, 3y.
Where x is measured on the horizontal axis and y on the vertical axis, her indifference curves consist of
a
a.
vertical line segment and a horizontal line segment that meet in a kink along the line
x = 2y.
b.
positively sloped line segment and a negatively sloped line segment that meet along the
line x = y.
c.
horizontal line segment and a negatively sloped line segment that meet in a kink along the
line x = y.
d.
vertical line segment and a horizontal line segment that meet in a kink along the line
y = 2x.
e.
horizontal line segment and a positively sloped line segment that meet in a kink along the
line x = 2y.
28. Phil Rupp, from Problem 4, has a sister Ethel who has the utility function U(x, y) = min5x + y, 6y.
Where x is measured on the horizontal axis and y on the vertical axis, her indifference curves consist of
a
a.
vertical line segment and a horizontal line segment that meet in a kink along the line
y = 5x.
b.
positively sloped line segment and a negatively sloped line segment that meet along the
line x = y.
c.
horizontal line segment and a negatively sloped line segment that meet in a kink along the
line x = y.
d.
vertical line segment and a horizontal line segment that meet in a kink along the line
x = 5y.
e.
horizontal line segment and a positively sloped line segment that meet in a kink along the
line x = 5y.
29. Phil Rupp, from Problem 4, has a sister Ethel who has the utility function U(x, y) = min3x + y, 4y.
Where x is measured on the horizontal axis and y on the vertical axis, her indifference curves consist of
a
a.
positively sloped line segment and a negatively sloped line segment that meet along the
line x = y.
b.
vertical line segment and a horizontal line segment that meet in a kink along the line
y = 3x.
c.
horizontal line segment and a negatively sloped line segment that meet in a kink along the
line x = y.
d.
vertical line segment and a horizontal line segment that meet in a kink along the line
x = 3y.
e.
horizontal line segment and a positively sloped line segment that meet in a kink along the
line x = 3y.
30. Phil Rupp, from Problem 4, has a sister Ethel who has the utility function U(x, y) = min5x + y, 6y.
Where x is measured on the horizontal axis and y on the vertical axis, her indifference curves consist of
a
a.
positively sloped line segment and a negatively sloped line segment that meet along the
line x = y.
b.
vertical line segment and a horizontal line segment that meet in a kink along the line
y = 5x.
c.
vertical line segment and a horizontal line segment that meet in a kink along the line
x = 5y.
d.
horizontal line segment and a negatively sloped line segment that meet in a kink along the
line x = y.
e.
horizontal line segment and a positively sloped line segment that meet in a kink along the
line x = 5y.