Question 1

Joe Bob's cousin Leonard consumes goods 1 and 2. Leonard thinks that 2 units of good 1 is always a perfect substitute for 3 units of good 2. Which of the following utility functions is the only one that would not represent Leonard's preferences?

Accepted Answer

A)  U(x1, x2) = 3x1 + 2x2 + 1,000. 
B)  U(x1, x2) = 9x21 + 12x1x2 + 4x22. 
C)  U(x1, x2) = min{ 3x1, 2x2}. 
D)  U(x1, x2) = 30x1 + 20x2 - 10,000. 
E)  More than one of the above does not represent Leonard's preferences.

Question 2

Jeans utility function is U(x, y) = x + y 2 - y. If we draw her indifference curves with x on the horizontal axis and y on the vertical axis, then these indifference curves are everywhere downward sloping and get flatter as one moves from left to right.

Accepted Answer

A) True 
 B)False

Question 3

Henry's utility function is x2 + 16xw + 64w2, where x is his consumption of x and w is his consumption of w.

Accepted Answer

A)  Henry's preferences are nonconvex. 
B)  Henry's indifference curves are straight lines. 
C)  Henry has a bliss point. 
D)  Henry's indifference curves are hyperbolas. 
E)  None of the above.

Question 4

A consumer has a utility function of the form U(x, y) =x a + y b, where both a and b are nonnegative. What additional restrictions on the values of the parameters a and b are imposed by each of the following assumptions?
a. Preferences are quasilinear and convex, and x is a normal good.
b. Preferences are homothetic.
c. Preferences are homothetic and convex.
d. Goods x and y are perfect substitutes.

Accepted Answer

The answer of A consumer has a utility function of...

Question 5

Angela's utility function is U(x1, x2) = (x1 + x2)3. Her indifference curves are downward-sloping, parallel straight lines.

Accepted Answer

A) True 
 B)False

Question 6

Janet consumes x1 and x2 together in fixed proportions. She always consumes 2 units of x1 for every unit x2. One utility function that describes her preferences is

Accepted Answer

A)  U(x1, x2) = 2x1x2. 
B)  U(x1, x2) = 2x1 + x2. 
C)  U(x1, x2) = x1 + 2x2. 
D)  U(x1, x2) = min{ 2x1, x2}. 
E)  U(x1, x2) = min{x1, 2x2}.

Question 7

Henrietta's utility function is U(x1, x2) = x1x2. She has diminishing marginal rate of substitution between goods 1 and 2.

Accepted Answer

A) True 
 B)False

Question 8

Ike's utility function is U(x, y) = xy. Ike consumes 2 units of x and 8 units of y.

Accepted Answer

A)  Ike would be willing to make small exchanges of x for y in which he would give up 4 units of x for every unit of y he got. 
B)  Ike would be willing to trade away all of his x for y as long as he got more than 4 units of y for every unit of x he gave up. 
C)  Ike will always be willing to make trades at any price if he does not have equal amounts of the two goods. 
D)  Ike likes x and y equally well so he is always willing to exchange 1 unit of either good for more than 1 unit of the other. 
E)  None of the above.

Question 9

Harry Mazzola has the utility function U(x1, x2) = min{x1 + 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, then Harry will

Accepted Answer

A)  consume at least as many french fries as corn chips but might consume both. 
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)  definitely spend all of his income on french fries. 
E)  consume equal amounts of french fries and corn chips.

Question 10

Charles's utility function is U(x, y) = xy. Anne's utility function is U(x, y) = 1,000xy. Diana's utility function is -xy. Elizabeth's utility function is  . Fergie's utility function is xy - 10,000. Margaret's utility function is  . Philip's utility function is x(y + 1). (The goods x and y are two very expensive goods. We leave you to speculate about what they are.) Which of these persons have the same preferences as Charles?

Accepted Answer

A)  Everybody except Diana 
B)  Anne and Fergie 
C)  Anne, Fergie, and Elizabeth 
D)  None of them 
E)  All of them

Question 11

Tim has preferences represented by the utility function U(x, y) = min{ 6x + y, x + 2y}. If x is on the horizontal axis and y is on the vertical axis, what is the slope of his indifference curve at the point (8, 9)?

Accepted Answer

A)  -6 
B)  -2/6 
C)  -1/2 
D)  -1/6. 
E)  -8/9

Question 12

Quasilinear preferences are homothetic when the optimal amount of good 1 is not affordable.

Accepted Answer

A) True 
 B)False

Question 13

Ambrose has the utility function  . If Ambrose is initially consuming 25 units of nuts and 17 units of berries, then what is the largest number of berries that he would be willing to give up in return for an additional 39 units of nuts?

Accepted Answer

A)  8 
B)  12 
C)  25 
D)  6 
E)  3

Question 14

Jim's utility function is U(x, y) = xy. Jerry's utility function is U(x, y) = 1,000xy + 2,000. Tammy's utility function is U(x, y) = xy(1 - xy). Oral's utility function is  . Marjoe's utility function is U(x, y) = x(y + 1,000). Pat's utility function is U(x, y) = 0.5xy - 10,000. Billy's utility function is U(x, y) =  . Francis's utility function is U(x, y) = -xy. 
a. Who has the same preferences as Jim?
b. Who has the same indifference curves as Jim?
c. Explain why the answers to (a) and (b) differ.

Accepted Answer

The answer of Jim's utility function is U(x, y) =...

Question 15

If one utility function is a monotonic transformation of another, then the former must assign a higher utility number to every bundle than the latter.

Accepted Answer

A) True 
 B)False

Question 16

Oswald Odd consumes only goods 1 and 2. His utility function is U(x1, x2) = x1 + x2 + min{x1, x2}. Each of Oswald's indifference curves is

Accepted Answer

A)  L-shaped. 
B)  made up of three line segments with slopes -2, -1, and -. 
C)  made up of two line segments with slopes -2 and -. 
D)  is smooth and has no kinks. 
E)  is a diamond-shaped figure consisting of four line segments.

Question 17

Ambrose has the utility function  . If Ambrose is initially consuming 64 units of nuts and 10 units of berries, then what is the largest number of berries that he would be willing to give up in return for an additional 17 units of nuts?

Accepted Answer

A)  9 
B)  19 
C)  4 
D)  2 
E)  1

Question 18

Mac's utility function is U(x, y) = max{ 2x - y, 2y - x}.

Accepted Answer

A)  Mac's preferences are quasilinear. 
B)  If Mac has more x than y, any increase in his consumption of y would lower his utility. 
C)  If Mac has more x than y, a decrease in his consumption of y would raise his utility. 
D)  Mac always prefers more of each good to less. 
E)  Goods x and y are perfect substitutes.

Question 19

Alice's utility function is U(x, y) = x2y. Steve's utility function is U(x, y) = x2y + 2x. Alice and Steve have the same preferences since Steve's utility function is a monotonic transformation of Alice's.

Accepted Answer

A) True 
 B)False

Question 20

Maximilian consumes two goods, x and y. His utility function is U(x, y) = max{x, y}. Therefore x and y are perfect substitutes for Max.

Accepted Answer

A) True 
 B)False

Exam 3: Utility

Joe Bob's cousin Leonard consumes goods 1 and 2. Leonard thinks that 2 units of good 1 is always a perfect substitute for 3 units of good 2. Which of the following utility functions is the only one that would not represent Leonard's preferences?

Jeans utility function is U(x, y) = x + y 2 - y. If we draw her indifference curves with x on the horizontal axis and y on the vertical axis, then these indifference curves are everywhere downward sloping and get flatter as one moves from left to right.

Henry's utility function is x² + 16xw + 64w², where x is his consumption of x and w is his consumption of w.

Angela's utility function is U(x₁, x₂) = (x₁ + x₂)³. Her indifference curves are downward-sloping, parallel straight lines.

Janet consumes x₁and x₂together in fixed proportions. She always consumes 2 units of x₁ for every unit x₂. One utility function that describes her preferences is

Henrietta's utility function is U(x₁, x₂) = x₁x₂. She has diminishing marginal rate of substitution between goods 1 and 2.

Ike's utility function is U(x, y) = xy. Ike consumes 2 units of x and 8 units of y.

Harry Mazzola has the utility function U(x₁, x₂) = min{x₁ + 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, then Harry will

Tim has preferences represented by the utility function U(x, y) = min{ 6x + y, x + 2y}. If x is on the horizontal axis and y is on the vertical axis, what is the slope of his indifference curve at the point (8, 9) ?

Quasilinear preferences are homothetic when the optimal amount of good 1 is not affordable.

Ambrose has the utility function . If Ambrose is initially consuming 25 units of nuts and 17 units of berries, then what is the largest number of berries that he would be willing to give up in return for an additional 39 units of nuts?

If one utility function is a monotonic transformation of another, then the former must assign a higher utility number to every bundle than the latter.

Oswald Odd consumes only goods 1 and 2. His utility function is U(x₁, x₂) = x₁ + x₂ + min{x₁, x₂}. Each of Oswald's indifference curves is

Ambrose has the utility function . If Ambrose is initially consuming 64 units of nuts and 10 units of berries, then what is the largest number of berries that he would be willing to give up in return for an additional 17 units of nuts?

Mac's utility function is U(x, y) = max{ 2x - y, 2y - x}.

Alice's utility function is U(x, y) = x²y. Steve's utility function is U(x, y) = x²y + 2x. Alice and Steve have the same preferences since Steve's utility function is a monotonic transformation of Alice's.

Maximilian consumes two goods, x and y. His utility function is U(x, y) = max{x, y}. Therefore x and y are perfect substitutes for Max.