Question 1

Jean-Pierre has preferences represented by the utility function U(x, y) = min{ 2x + y, x + 6y}. 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 (7, 7)?

Accepted Answer

A)   -1/2
B)   -6/2
C)   -1/6
D)   -2
E)   -7/7 D

Question 2

Joe Bob's cousin Peter consumes goods 1 and 2. Peter 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 Peter's preferences?

Accepted Answer

A)   U(x1, x2)  = min{ 2x1, 4x2}.
B)   U(x1, x2)  = 20x1 + 40x2 - 10,000.
C)   U(x1, x2)  = 2x1 + 4x2 + 1,000.
D)   U(x1, x2)  = 4x21 + 16x1x2 + 16x22.
E)   More than one of the above does not represent Peter's preferences. A

Question 3

Charlie has the utility function U(xA, xB) = xAxB. His indifference curve passing through 35 apples and 18 bananas will also pass through the point where he consumes 5 apples and

Accepted Answer

A)   131 bananas.
B)   137 bananas.
C)   21 bananas.
D)   42 bananas.
E)   126 bananas. E

Question 4

Ernie's utility function is U(x, y) = 32xy. He has 10 units of good x and 8 units of good y. Waldo's utility function for the same two goods is U(x, y) = 3x + 5y. Waldo has 9 units of x and 13 units of y.

Accepted Answer

A)   Waldo prefers Ernie's bundle to his own, but Ernie prefers his own bundle to Waldo's.
B)   Each prefers the other's bundle to his own.
C)   Neither prefers the other's bundle to his own.
D)   Ernie prefers Waldo's bundle to his own bundle, but Waldo prefers his own bundle to Ernie's.
E)   Since they have different preferences, there is not enough information to determine who envies whom.

Question 5

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 -  . Billy's utility function is  . Pat's utility function is U(x, y) = -xy.

Accepted Answer

A)   No two of these people have the same preferences.
B)   They all have the same preferences except for Billy.
C)   Jim, Jerry, and Pat all have the same indifference curves, but Jerry and Oral are the only ones with the same preferences as Jim.
D)   Jim, Tammy, and Oral all have the same preferences.
E)   None of the above.

Question 6

Wanda Lott has the utility function U(x, y) = max{x, y}. Wanda's preferences are convex.

Accepted Answer

A) True 
 B)False

Question 7

Raymond's preferences are represented by the utility function U(x, y) =  if y > 0 and U(x, y) = 0 if y = 0.

Accepted Answer

A)   Raymond has indifference curves that are rectangular hyperbolas.
B)   Raymond prefers more of each good to less.
C)   Raymond has quasilinear preferences.
D)   Raymond has a bliss point.
E)   Raymond has indifference curves that are upward-sloping straight lines if y > 0.

Question 8

Mr. Surly consumes only two goods and hates them both. His utility function is U(x, y) = 2max{x, y}. Mr. Surly has (weakly) convex preferences.

Accepted Answer

A) True 
 B)False

Question 9

Molly's utility function is U(x, y) = y + 4x.5. She has 25 units of x and 12 units of y. If her consumption of x is reduced to 0, how many units of y would she need in order to be exactly as well off as before?

Accepted Answer

A)   48
B)   37
C)   32
D)   112
E)   None of the above.

Question 10

Use separate graphs to draw indifference curves for each of the following utility functions:
a. U(x, y) = min{2x + y,2y + x}.
b. U(x, y) = max{2x + y,2y + x}.
c. U(x, y) = x + min{x, y}.
In which of these cases are preferences convex?

Accepted Answer

The answer of Use separate graphs to draw indifference curves...

Question 11

If someone has a utility function U = 2 min{x, y}, then x and y are perfect complements for that person.

Accepted Answer

A) True 
 B)False

Question 12

A person with the utility function U(x, y) = y + x2 has convex preferences.

Accepted Answer

A) True 
 B)False

Question 13

Harmon's utility function is U(x1, x2) = x1x2. His income is $100. The price of good 2 is p2 = 4. Good 1 is priced as follows. The first 15 units cost $4 per unit and any additional units cost $2 per unit. What consumption bundle does Harmon choose?

Accepted Answer

A)   (12.5, 12.5) 
B)   (25, 12.5) 
C)   (12.5, 25) 
D)   (15, 10) 
E)   None of the above.

Question 14

Use separate graphs to sketch two indifference curves for people with each of the following utility functions:
a. U(x, y) = x + 2y.
b. U(x, y) = min{x,2y}.
c. U(x, y) = max{x,2y}.

Accepted Answer

The answer of Use separate graphs to sketch two indifference...

Question 15

A person with the utility function U(x, y) = 10 + y2 + x has convex preferences.

Accepted Answer

A) True 
 B)False

Question 16

The absolute value of Mar's MRS at his current consumption bundle is greater than 3. (That is,  ). Mars has convex preferences and is currently consuming positive amounts of both goods.

Accepted Answer

A)   Taking away some of good 1 and giving Mars 3 units of good 2 for each unit of good 1 taken away will necessarily make him worse off.
B)   Taking away some of good 1 and giving Mars 3 units of good 2 for each unit of good 1 taken away will necessarily make him better off.
C)   Giving Mars some of good 1 and taking away 3 units of good 2 for each unit of good 1 he is given will necessarily make him worse off.
D)   Giving Mars some of good 1 and taking away 3 units of good 2 for each unit of good 1 he is given will necessarily make him better off.
E)   More than one of the above is true.

Question 17

Phil Rupp's sister Ethel has the utility function U(x, y) = min{ 4x + y, 5y}. Where x is measured on the horizontal axis and y on the vertical axis, her indifference curves consist of a

Accepted Answer

A)   vertical line segment and a horizontal line segment which meet in a kink along the line y = 4x.
B)   vertical line segment and a horizontal line segment which meet in a kink along the line x = 4y.
C)   horizontal line segment and a negatively sloped line segment which meet in a kink along the line x = y.
D)   positively sloped line segment and a negatively sloped line segment which meet along the line x = y.
E)   horizontal line segment and a positively sloped line segment which meet in a kink along the line x = 4y.

Question 18

With quasilinear preferences, the slope of indifference curves is constant along all rays through the origin.

Accepted Answer

A) True 
 B)False

Question 19

A consumer has preferences represented by the utility function U(x1, x2) = 10(x21 + 2x1x2 + x22) - 50. For this consumer, goods 1 and 2 are perfect substitutes.

Accepted Answer

A) True 
 B)False

Question 20

Charlie has the utility function U(xA, xB) = xAxB. His indifference curve passing through 32 apples and 8 bananas will also pass through the point where he consumes 4 apples and

Accepted Answer

A)   16 bananas.
B)   32 bananas.
C)   68 bananas.
D)   72 bananas.
E)   64 bananas.

Exam 3: Utility

Jean-Pierre has preferences represented by the utility function U(x, y) = min{ 2x + y, x + 6y}. 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 (7, 7) ?

Joe Bob's cousin Peter consumes goods 1 and 2. Peter 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 Peter's preferences?

Charlie has the utility function U(x_A, x_B) = x_Ax_B. His indifference curve passing through 35 apples and 18 bananas will also pass through the point where he consumes 5 apples and

Ernie's utility function is U(x, y) = 32xy. He has 10 units of good x and 8 units of good y. Waldo's utility function for the same two goods is U(x, y) = 3x + 5y. Waldo has 9 units of x and 13 units of y.

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 - . Billy's utility function is . Pat's utility function is U(x, y) = -xy.

Wanda Lott has the utility function U(x, y) = max{x, y}. Wanda's preferences are convex.

Raymond's preferences are represented by the utility function U(x, y) = if y > 0 and U(x, y) = 0 if y = 0.

Mr. Surly consumes only two goods and hates them both. His utility function is U(x, y) = 2max{x, y}. Mr. Surly has (weakly) convex preferences.

Molly's utility function is U(x, y) = y + 4x^.5. She has 25 units of x and 12 units of y. If her consumption of x is reduced to 0, how many units of y would she need in order to be exactly as well off as before?

Use separate graphs to draw indifference curves for each of the following utility functions: a. U(x, y) = min{2x + y,2y + x}. b. U(x, y) = max{2x + y,2y + x}. c. U(x, y) = x + min{x, y}. In which of these cases are preferences convex?

If someone has a utility function U = 2 min{x, y}, then x and y are perfect complements for that person.

A person with the utility function U(x, y) = y + x²has convex preferences.

Harmon's utility function is U(x₁, x₂) = x₁x₂. His income is $100. The price of good 2 is p₂= 4. Good 1 is priced as follows. The first 15 units cost $4 per unit and any additional units cost $2 per unit. What consumption bundle does Harmon choose?

Use separate graphs to sketch two indifference curves for people with each of the following utility functions: a. U(x, y) = x + 2y. b. U(x, y) = min{x,2y}. c. U(x, y) = max{x,2y}.

A person with the utility function U(x, y) = 10 + y² + x has convex preferences.

The absolute value of Mar's MRS at his current consumption bundle is greater than 3. (That is, ) . Mars has convex preferences and is currently consuming positive amounts of both goods.

Phil Rupp's sister Ethel has the utility function U(x, y) = min{ 4x + y, 5y}. Where x is measured on the horizontal axis and y on the vertical axis, her indifference curves consist of a

With quasilinear preferences, the slope of indifference curves is constant along all rays through the origin.

A consumer has preferences represented by the utility function U(x₁, x₂) = 10(x²₁+ 2x₁x₂ + x²₂) - 50. For this consumer, goods 1 and 2 are perfect substitutes.

Charlie has the utility function U(x_A, x_B) = x_Ax_B. His indifference curve passing through 32 apples and 8 bananas will also pass through the point where he consumes 4 apples and