Question 1

Charlie has the utility function U(x_A, x_B)=x_Ax_B.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.

Accepted Answer

80 bananas.&#10;

Question 2

Ambrose has the utility function U(x₁, x₂)=4x^1/2₁ + 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

12

Accepted Answer

12&#10;

Question 3

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.

-2.

Accepted Answer

The slope of an indifference curve is given by the marginal rate of substitution (MRS), which in this case is the negative of the ratio of the marginal utilities of A and B. Given Charlie's utility function U(A, B) = AB, the marginal utility of A (MU_A) is B, and the marginal utility of B (MU_B) is A. Therefore, MRS = -MU_A/MU_B = -B/A. Plugging in A = 15 and B = 30, we get MRS = -30/15 = -2.

Question 4

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.

-2.

Accepted Answer

The slope of the indifference curve is given by the marginal rate of substitution (MRS), which is the ratio of the marginal utility of apples to the marginal utility of bananas. The marginal utility of apples (MU_A) is B, and the marginal utility of bananas (MU_B) is A. At the consumption point (A=40, B=160), MRS = MU_A / MU_B = 160 / 40 = 4. The slope of the indifference curve is the negative of the MRS, so it is -4.

Question 5

Ambrose has the utility function U(x₁, x₂)=4x^1/2₁ + 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

12

Accepted Answer

The answer of Ambrose has the utility function U(x₁, x₂)=4x^1/2₁...

Question 6

Joe Bob 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)= min{2x₁, 4x₂}.
D)U(x₁, x₂)=20x₁ + 40x₂ + 10,000.
E)More than one of the above does not represent Ike's preferences.

Accepted Answer

Option C is the only one that reflects the idea that 4 units of good 1 can be perfectly substituted for 2 units of good 2. The function takes the minimum of the two goods, which means that the marginal utility of each good is equal. Therefore, Ike is willing to substitute good 1 units for good 2 units at a constant rate of 2:1. The other options do not reflect this perfect substitutability.

Question 7

Charlie has the utility function U(x_A, x_B)=x_Ax_B.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.

Accepted Answer

The answer of Charlie has the utility function U(x_A, x_B)=x_Ax_B.His...

Question 8

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.

-2.

Accepted Answer

The slope of the indifference curve is given by the marginal rate of substitution (MRS), which is the ratio of the marginal utilities of the two goods. For the utility function U(A, B) = AB, the marginal utility of A is B and the marginal utility of B is A. Therefore, MRS = MU_A / MU_B = B / A = 175 / 35 = 5.

Question 9

Joe Bob 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 +0 3x₂ + 1000.
C)U(x₁, x₂)= min{4x₁, 3x₂}.
D)U(x₁, x₂)=16x²₁ + 24x₁x₂ + 9x²₂.
E)More than one of the above does not represent Pete's preferences.

Accepted Answer

Pete's preferences are such that he always thinks that 3 units of good 1 is a perfect substitute for 4 units of good 2. This means that his indifference curves must be straight lines with a slope of -3/4. Out of the given utility functions, only option C has a form that yields this property. In option C, the utility function takes the minimum value of either 4 units of good 1 or 3/4 units of good 2, which means that for any combination of goods, he would choose the combination that gives the same level of utility at the least cost. Thus, option C represents Pete's preferences.

Question 10

Ambrose has the utility function U(x₁, x₂)=4x^1/2₁ + 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

12

Accepted Answer

We need to find the Marginal Rate of Substitution (MRS) of nuts for berries, which is given by the partial derivative of the utility function with respect to berries (good 2) divided by the partial derivative of the utility function with respect to nuts (good 1). MRS = (∂U/∂x2)/(∂U/∂x1) Taking partial derivatives, we get: ∂U/∂x2 = 4x₂/F1F1F1S1 - F1F1F10 ∂U/∂x1 = 2x¹₁/F1F1F1S1 Therefore, MRS = (4x₂/F1F1F1S1 - F1F1F10)/(2x¹₁/F1F1F1S1) At Ambrose's initial consumption bundle, x1 = 49 and x2 = 12. Substituting these values, we get: MRS = (4(12)/F1F1F1 - F1F1F10)/(2(49)/F1F1F1) = 2/7 This means that Ambrose is willing to give up 2 units of berries for every 7 units of nuts he gains, while keeping his utility constant. To find the largest number of berries that he would be willing to give up in return for an additional 32 units of nuts, we need to solve the following equation: (12 - y)/(49 + 32) = 2/7 Solving for y, we get: y = 8 Therefore, Ambrose is willing to give up 8 units of berries for an additional 32 units of nuts while keeping his utility constant. So, the answer is option C.

Question 11

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.

-2.

Accepted Answer

The answer of Charlie's utility function is U(A, B)= AB,...

Question 12

Joe Bob 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)=min{2x₁, 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.

Accepted Answer

The answer of Joe Bob has a cousin Don who...

Question 13

Charlie has the utility function U(x_A, x_B)=x_Ax_B.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.

Accepted Answer

The answer of Charlie has the utility function U(x_A, x_B)=x_Ax_B.His...

Question 14

Ambrose has the utility function U(x₁, x₂)=4x^1/2₁ + 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

12

Accepted Answer

The answer of Ambrose has the utility function U(x₁,...

Question 15

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.

-2.

Accepted Answer

The answer of Charlie's utility function is U(A, B)= AB,...

Question 16

Ambrose has the utility function U(x₁, x₂)=4x^1/2₁ + 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

12

Accepted Answer

The answer of Ambrose has the utility function U(x₁,...

Question 17

Joe Bob 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)=min{4x₁, 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.

Accepted Answer

The answer of Joe Bob  has a cousin Sam...

Question 18

Charlie has the utility function U(x_A, x_B)=x_Ax_B.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.

Accepted Answer

The answer of Charlie has the utility function U(x_A, x_B)=x_Ax_B.His...

Question 19

Charlie has the utility function U(x_A, x_B)=x_Ax_B.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.

Accepted Answer

The answer of Charlie has the utility function U(x_A, x_B)=x_Ax_B.His...

Question 20

Joe Bob 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)= min{4x₁, 2x₂}.
D)U(x₁, x₂)=4x₁ + 2x₂ + 1000.
E)More than one of the above does not represent Martin's preferences.

Accepted Answer

The answer of Joe Bob has a cousin Martin who...

Question 21

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 $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.

Accepted Answer

The answer of Harry Mazzola has the utility function U(x₁,...

Question 22

Phil Rupp,has a sister Ethel who has the utility function U(x, y)=min{2x + y, 3y}.Where x is measured on the horizontal axis and y on the vertical axis, her indifference curves consist of a&#10;A)vertical line segment and a horizontal line segment that meet in a kink along the line x = 2y.&#10;B)positively sloped line segment and a negatively sloped line segment that meet along the line x = y.&#10;C)horizontal line segment and a negatively sloped line segment that meet in a kink along the line x = y.&#10;D)vertical line segment and a horizontal line segment that meet in a kink along the line y =2x.&#10;E)horizontal line segment and a positively sloped line segment that meet in a kink along the line x = 2y.

Accepted Answer

The answer of Phil Rupp,has a sister Ethel who has...

Question 23

Phil Rupp, has a sister Ethel who has the utility function U(x, y)=min{3x + y, 4y}.Where x is measured on the horizontal axis and y on the vertical axis, her indifference curves consist of a&#10;A)positively sloped line segment and a negatively sloped line segment that meet along the line x = y.&#10;B)vertical line segment and a horizontal line segment that meet in a kink along the line y =3x.&#10;C)horizontal line segment and a negatively sloped line segment that meet in a kink along the line x = y.&#10;D)vertical line segment and a horizontal line segment that meet in a kink along the line x =3y.&#10;E)horizontal line segment and a positively sloped line segment that meet in a kink along the line x = 3y.

Accepted Answer

The answer of Phil Rupp, has a sister Ethel who...

Question 24

Phil Rupp,has a sister Ethel who has the utility function U(x, y)=min{5x + y, 6y}.Where x is measured on the horizontal axis and y on the vertical axis, her indifference curves consist of a&#10;A)positively sloped line segment and a negatively sloped line segment that meet along the line x = y.&#10;B)vertical line segment and a horizontal line segment that meet in a kink along the line y = 5x.&#10;C)vertical line segment and a horizontal line segment that meet in a kink along the line x = 5y.&#10;D)horizontal line segment and a negatively sloped line segment that meet in a kink along the line x = y.&#10;E)horizontal line segment and a positively sloped line segment that meet in a kink along the line x = 5y.

Accepted Answer

The answer of Phil Rupp,has a sister Ethel who has...

Question 25

Phil Rupp, has a sister Ethel who 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&#10;A)vertical line segment and a horizontal line segment that meet in a kink along the line y = 4x.&#10;B)vertical line segment and a horizontal line segment that meet in a kink along the line x = 4y.&#10;C)horizontal line segment and a negatively sloped line segment that meet in a kink along the line x = y.&#10;D)positively sloped line segment and a negatively sloped line segment that meet along the line x = y.&#10;E)horizontal line segment and a positively sloped line segment that meet in a kink along the line x = 4y.

Accepted Answer

The answer of Phil Rupp, has a sister Ethel who...

Question 26

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 $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.

Accepted Answer

The answer of Harry Mazzola has the utility function U(x₁,...

Question 27

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 $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.

Accepted Answer

The answer of Harry Mazzola has the utility function U(x₁,...

Question 28

Phil Rupp, has a sister Ethel who has the utility function U(x, y)=min{x +y, 6y}.Where x is measured on the horizontal axis and y on the vertical axis, her indifference curves consist of a&#10;A)vertical line segment and a horizontal line segment that meet in a kink along the line y = 5x.&#10;B)positively sloped line segment and a negatively sloped line segment that meet along the line x = y.&#10;C)horizontal line segment and a negatively sloped line segment that meet in a kink along the line x = y.&#10;D)vertical line segment and a horizontal line segment that meet in a kink along the line x = 5y.&#10;E)horizontal line segment and a positively sloped line segment that meet in a kink along the line x = 5y.

Accepted Answer

The answer of Phil Rupp, has a sister Ethel who...

Question 29

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 $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.

Accepted Answer

The answer of Harry Mazzola has the utility function U(x₁,...

Question 30

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 $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.

Accepted Answer

The answer of Harry Mazzola has the utility function U(x₁,...

Deck 4: Extension: A: Utility