Question 1

Ike's utility function is U(x, y)= 25xy.He has 12 units of good x and 8 units of good y.Ben's utility function for the same two goods is U(x, y)=0 4x + 4y.Ben has 9 units of x and 13 units of y.

Accepted Answer

Ike prefers Ben's bundle because U(9,13)=468>U(12,8)=240. Ben prefers his own bundle because U(9,13)=468>U(12,8)=288.

Question 2

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

Accepted Answer

Diminishing marginal rate of substitution means that as an individual consumes more of one good, they are willing to give up less and less of the other good in order to maintain the same level of utility. This concept indicates that the individual has a concave utility function, which is a characteristic of Henrietta's utility function in this scenario.

Question 3

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

Accepted Answer

The utility function provided is not clearly defined and seems to contain formatting errors, making it impossible to accurately determine the nature of the preferences (convex or otherwise) it represents.

Question 4

A person with the utility function U(x₁, x₂)= min+x₁ + 2x₂, 2x₁ + x₂} has convex but not strictly convex preferences.

Accepted Answer

The provided utility function is not clearly defined due to the presence of garbled text, making it impossible to accurately determine the nature of the preferences (convex, strictly convex, or otherwise) without a clear, coherent utility function.

Question 5

A consumer has preferences represented by the utility function U(x₁, x₂)=10(x²₁ + 2x₁x₂ - x²₂)-0 50.For this consumer, goods 1 and 2 are perfect substitutes.

Accepted Answer

The utility function is of the form U(x1,x2) = ax1 + bx2, which is the utility function for perfect substitutes.

Question 6

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

Accepted Answer

Quasilinear preferences are not necessarily homothetic because homothetic preferences imply that the shape of indifference curves is consistent across all levels of utility, which is not a requirement for quasilinear preferences. Quasilinear preferences focus on the linear utility of one good, which does not ensure that the optimal bundle scales proportionally with income, a key characteristic of homothetic preferences.

Question 7

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

Accepted Answer

Wanda's utility function U(x, y) = max{x, y} represents perfect substitutes, which are not convex preferences. Convex preferences require a preference for mixtures or averages, which is not the case here.

Question 8

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

Steve's utility function includes an additional term (2x), which alters the marginal rate of substitution between x and y compared to Alice's utility function, indicating different preferences.

Question 9

The utility function U(x₁, x₂)= 2lnx₁ + 3lnx₂ represents Cobb-Douglas preferences.

Accepted Answer

The given utility function represents Cobb-Douglas preferences as it follows the form U(x1, x2) = x1^α1 * x2^α2, where α1 = 2ln(_1/) and α2 = 3ln(_2/).

Question 10

Mark strictly prefers consumption bundle A to consumption bundle B and weakly prefers bundle B to bundle A.These preferences can be represented by a utility function.

Accepted Answer

This situation violates the transitivity property of preferences, so it cannot be represented by a utility function.

Question 11

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

Accepted Answer

With quasilinear preferences, the slope of the indifference curves (marginal rate of substitution) changes as one moves along a ray from the origin, because the marginal utility of one good remains constant while the marginal utility of the other good changes.

Question 12

Fiery Demon is a rotgut whisky made in Kentucky.Smoothy is an unblended malt whisky imported from Scotland.Ed regards these brands as perfect substitutes.When he goes into a bar, he sometimes buys only Fiery Demon.Other times he buys only Smoothy.This shows that Ed has unstable preferences.

Accepted Answer

Ed's preference for Fiery Demon or Smoothy is dependent on his mood or situation. This does not necessarily mean that he has unstable preferences. It could simply mean that he has a preference for variety or a willingness to try different things.

Question 13

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

Accepted Answer

A utility function represents an individual's preferences for certain combinations of goods. In this case, the utility function shows that the individual's utility depends only on the minimum of the two goods, F1 and S1. This implies that the individual values both goods equally and they are "perfect substitutes" for each other. In addition, the specific functional form of the utility function, which depends on the minimum of a linear function of x and a linear function of y, indicates that x and y are "perfect complements". Therefore, the answer is A.

Question 14

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

Mr. Surly's utility function is weakly convex because it is the maximum of two linear functions, which are both convex.

Question 15

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

Accepted Answer

The utility function has constant absolute risk aversion, which implies convex preferences.

Question 16

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

Jean's utility function is not clearly defined in the question, making it impossible to accurately determine the shape or slope of her indifference curves without a proper mathematical expression of her utility function.

Question 17

A person with utility function U(x, y)= 5 + y² + 2x has nonconvex preferences.

Accepted Answer

The utility function is nonconvex because the indifference curves are not convex.

Question 18

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

Maximilian's utility function, U(x, y) = max{x, y}, suggests that his utility is determined by the larger of the two quantities of goods x and y, which is characteristic of perfect complements, not perfect substitutes. In the case of perfect substitutes, the utility function would typically be linear, such as U(x, y) = ax + by.

Question 19

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 monotonic transformation of a utility function preserves the order of preferences but does not necessarily assign a higher utility number to every bundle. It means if one bundle is preferred over another in the original utility function, it will also be preferred in the transformed utility function, but the actual utility numbers can be higher, lower, or the same, as long as the order of preference is maintained.

Question 20

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

Accepted Answer

The fact that Angela's indifference curves are downward-sloping, parallel straight lines implies that her utility function exhibits perfect substitutes between x₁ and x₂.

Quiz 3: Utility-Part A

Ike's utility function is U(x, y) = 25xy.He has 12 units of good x and 8 units of good y.Ben's utility function for the same two goods is U(x, y) =0 4x + 4y.Ben has 9 units of x and 13 units of y.

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

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

A person with the utility function U(x₁, x₂)= min+x₁ + 2x₂, 2x₁ + x₂} has convex but not strictly convex preferences.

A consumer has preferences represented by the utility function U(x₁, x₂)=10(x²₁ + 2x₁x₂ - x²₂)-0 50.For this consumer, goods 1 and 2 are perfect substitutes.

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

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

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.

The utility function U(x₁, x₂)= 2lnx₁ + 3lnx₂ represents Cobb-Douglas preferences.

Mark strictly prefers consumption bundle A to consumption bundle B and weakly prefers bundle B to bundle A.These preferences can be represented by a utility function.

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

Fiery Demon is a rotgut whisky made in Kentucky.Smoothy is an unblended malt whisky imported from Scotland.Ed regards these brands as perfect substitutes.When he goes into a bar, he sometimes buys only Fiery Demon.Other times he buys only Smoothy.This shows that Ed has unstable preferences.

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

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.

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

A person with utility function U(x, y)= 5 + y² + 2x has nonconvex preferences.

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.

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.

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

Quiz 3: Utility-Part A

Ike's utility function is U(x, y) = 25xy.He has 12 units of good x and 8 units of good y.Ben's utility function for the same two goods is U(x, y) =0 4x + 4y.Ben has 9 units of x and 13 units of y.

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

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

A person with the utility function U(x1, x2)= min+x1 + 2x2, 2x1 + x2} has convex but not strictly convex preferences.

A consumer has preferences represented by the utility function U(x1, x2)=10(x21 + 2x1x2 - x22)-0 50.For this consumer, goods 1 and 2 are perfect substitutes.

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

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

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.

The utility function U(x1, x2)= 2lnx1 + 3lnx2 represents Cobb-Douglas preferences.

Mark strictly prefers consumption bundle A to consumption bundle B and weakly prefers bundle B to bundle A.These preferences can be represented by a utility function.

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

Fiery Demon is a rotgut whisky made in Kentucky.Smoothy is an unblended malt whisky imported from Scotland.Ed regards these brands as perfect substitutes.When he goes into a bar, he sometimes buys only Fiery Demon.Other times he buys only Smoothy.This shows that Ed has unstable preferences.

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

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.

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

A person with utility function U(x, y)= 5 + y2 + 2x has nonconvex preferences.

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.

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.

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

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

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

A person with the utility function U(x₁, x₂)= min+x₁ + 2x₂, 2x₁ + x₂} has convex but not strictly convex preferences.

A consumer has preferences represented by the utility function U(x₁, x₂)=10(x²₁ + 2x₁x₂ - x²₂)-0 50.For this consumer, goods 1 and 2 are perfect substitutes.

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.

The utility function U(x₁, x₂)= 2lnx₁ + 3lnx₂ represents Cobb-Douglas preferences.

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

A person with utility function U(x, y)= 5 + y² + 2x has nonconvex preferences.

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