Question 1

Phil Rupp's sister Ethel 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

Accepted Answer

Ethel's utility function is based on the minimum of two expressions: $5x + y$ and $6y$. This creates indifference curves that are piecewise linear, consisting of segments where one part of the utility function dominates until the two expressions equal each other, leading to a kink. The kink occurs where $5x + y = 6y$, simplifying to $x = y$, indicating a negatively sloped line segment (since as x increases, y must decrease to maintain equality) and a horizontal line segment (representing the portion where an increase in x does not affect utility because the utility is determined by the other term, $6y$, which does not depend on x). This matches the description in choice A.

Question 2

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

The answer of Phil Rupp's sister Ethel has the utility...

Question 3

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

The answer of Joe Bob's cousin Peter consumes goods 1...

Question 4

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

Accepted Answer

Charlie's utility function is U(x_A, x_B) = x_A * x_B. The utility at 35 apples and 18 bananas is 35 * 18 = 630. To find the number of bananas when he consumes 5 apples, set 5 * x_B = 630, solving for x_B gives x_B = 126.

Question 5

Jim's utility function is U(x, y)= xy.Jerry's utility function is U(x, y)= 1,000xy + 0 2,000.Tammy's utility function is U(x, y)= xy(1 - xy).Oral's utility function is U(x, y)=-1/(10 + 2xy).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)= 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)= xy.Jerry's...

Question 6

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 7

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

To find the answer, we need to determine the marginal rate of substitution (MRS) between nuts and berries. MRS = MU of nuts / MU of berries Taking the partial derivatives of the utility function with respect to nuts and berries, we get: MU of nuts = 2x^1/2₁ F1F1F1S1F1F1F10 4x²₂ F1F1F1S1 MU of berries = 4x^1/2₂ F1F1F1S1F1F1F10 x₁ Plugging in the initial consumption bundle of (25,17), we get: MU of nuts = 9.8 MU of berries = 6.5 Therefore, MRS = 1.5. This means that Ambrose is willing to give up 1.5 units of berries for each additional unit of nuts. To get an additional 39 units of nuts, he would be willing to give up: 39 * 1.5 = 58.5 units of berries. He cannot give up 58.5 units of berries, so he would give up the largest integer value less than or equal to 58.5, which is 12. Therefore, the answer is (B).

Question 8

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

This utility function represents Leonard's preferences because it includes the minimum of 3x1 and 2x2, implying that he is willing to substitute 2 units of good 2 for every 3 units of good 1 to achieve the same level of utility. The other choices either do not have a minimum or do not have the same ratios between the two goods.

Question 9

Use separate graphs to draw indifference curves for each of the following utility functions:
a.U(x, y)= min{x + 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 10

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

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

Question 11

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 12

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

We need to find the marginal rate of substitution (MRS) between nuts and berries, which is given by the partial derivative of the utility function with respect to berries divided by the partial derivative of the utility function with respect to nuts. MRS = (∂U/∂x₂) / (∂U/∂x₁) = (1x1/2x(10-0)^(-1/2)) / (4x1/2x(64-0)^(-1/2)) = 1/8 This means that Ambrose is willing to give up 1 unit of berries in exchange for 8 additional units of nuts. In order to get 17 additional units of nuts, he would be willing to give up: = 17/8 ≈ 2 Therefore, the largest number of berries that he would be willing to give up is 2. The correct answer choice is C.

Question 13

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

Accepted Answer

Charlie's utility function is U(x_A, x_B) = x_A * x_B. At the point (32 apples, 8 bananas), his utility is 32 * 8 = 256. For the indifference curve to pass through (4 apples, x bananas), the utility must remain 256. Solving 4 * x = 256 gives x = 64 bananas.

Question 14

Charlie's utility function is U(A, B)= AB, where A and B are the numbers of apples and bananas, respectively, that he consumes.When Charlie is consuming 20 apples and 80 bananas, 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

Accepted Answer

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

Question 15

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 $4, then Harry will

Accepted Answer

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

Question 16

Charlie's utility function is U(A, B)= AB, where A and B are the numbers of apples and bananas, respectively, that he consumes.When Charlie is consuming 15 apples and 90 bananas, 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

Accepted Answer

The slope of an indifference curve is given by the marginal rate of substitution (MRS), which is the negative of the ratio of the marginal utilities of the two goods. For 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. Thus, MRS = -MU_A/MU_B = -B/A. At A = 15 apples and B = 90 bananas, MRS = -90/15 = -6.

Question 17

Victor Finick likes to have the same amount of x as he has of y.His utility function is U(x, y)= min{2x- y, 2y- x}.
a.Draw the indifference curve for Victor that passes through the bundle (0, 0)and the indifference curve that passes through (4, 4).(Hint: Each indifference curve is the intersection of two line segments.)
b.If Victor has a bundle that he likes better than (0, 0)and his consumption of both goods is doubled, is Victor better off?
c.Does Victor always prefer more of either good to less?

Accepted Answer

The answer of Victor Finick likes to have the same...

Quiz 3: Utility-Part A

Phil Rupp's sister Ethel 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

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

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

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

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?

Use separate graphs to draw indifference curves for each of the following utility functions: a.U(x, y)= min{x + 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?

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

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}.

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

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

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 $4, then Harry will

Quiz 3: Utility-Part A

Phil Rupp's sister Ethel 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

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

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(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

Ambrose has the utility function U(x1, x2) = 4x1/21 + x2.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?

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?

Use separate graphs to draw indifference curves for each of the following utility functions: a.U(x, y)= min{x + 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?

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

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}.

Ambrose has the utility function U(x1, x2) = 4x1/21 + x2.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?

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

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 $4, then Harry will

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

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

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

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

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

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 $4, then Harry will