Question 1

If preferences are convex, then for any commodity bundle x, the set of commodity bundles that are worse than x is a convex set.

Accepted Answer

False

Question 2

A consumer with convex preferences who is indifferent between the bundles (5, 1)and (11, 3)will like the bundle (8, 2)at least as well as either of the first two bundles.

Accepted Answer

False

Question 3

If preferences are transitive, more is always preferred to less.

Accepted Answer

Transitivity of preferences means if a person prefers option A over B, and B over C, then they will prefer A over C. However, "more is always preferred to less" refers to the assumption of monotonicity, not transitivity.

Question 4

Ambrose has an indifference curve with equation x₂ = 20 - 4x^1/2₁.When Ambrose is consuming the bundle (4, 16), his marginal rate of substitution is 25/4.

Accepted Answer

The marginal rate of substitution (MRS) is calculated as the negative of the slope of the indifference curve at a given point. The provided equation for the indifference curve is not clearly defined, making it impossible to accurately calculate the MRS without a proper functional form. Additionally, without a clear equation, we cannot confirm the MRS value at any specific bundle of goods.

Question 5

Josephine buys 3 quarts of milk and 2 pounds of butter when milk sells for $2 a quart and butter sells for $1 a pound.Wilma buys 2 quarts of milk and 3 pounds of butter at the same prices.Josephine's marginal rate of substitution between milk and butter is greater than Wilma's.

Accepted Answer

We can use the formula for the marginal rate of substitution (MRS) to compare Josephine's and Wilma's MRS:

MRS = (change in butter consumption)/(change in milk consumption)

For Josephine:

MRS = (1 pound)/(3 quarts/2) = 2/3

For Wilma:

MRS = (1 pound)/(2 quarts/2) = 1

Since Josephine's MRS is less than Wilma's, the statement is false.

Question 6

A consumer with convex preferences who is indifferent between the bundles (5, 2)and (11, 6)will like the bundle (8, 4)at least as well as either of the first two bundles.

Accepted Answer

The answer of A consumer with convex preferences who is...

Question 7

If there are two goods, if a consumer prefers more of each good to less, and if she has a diminishing marginal rate of substitution, then her preferences are convex.

Accepted Answer

This statement is a key assumption of convex preferences, which state that the consumer is willing to give up a decreasing amount of one good in exchange for increasing amounts of the other good. This is known as a diminishing marginal rate of substitution, and it leads to a convex-shaped indifference curve.

Question 8

Steven's indifference curves are circles, all of which are centered at (15, 13).Of any two indifference circles, he would rather be on the inner one than the outer one.

Accepted Answer

Steven's indifference curves are circles centered at (15, 13), and he prefers points closer to the center. The point (12, 10) is closer to (15, 13) than (22, 18), so he prefers (12, 10) to (22, 18).

Question 9

If Melody has more classical records than rock and roll records, she is willing to exchange exactly 1 classical record for 2 rock and roll records, but if she has more rock and roll records than classical records, then she is willing to exchange exactly 1 rock and roll record for 2 classical records.Melody has convex preferences.

Accepted Answer

Convex preferences imply that Melody would prefer a mix of both types of records rather than extremes. However, her willingness to exchange records at different rates depending on her current holdings suggests non-convex preferences, as she values the records differently based on her current collection.

Question 10

A consumer who is unable to detect small differences in the amount of water in her beer could have a transitive strict preference relation but is unlikely to have a transitive indifference relation.

Accepted Answer

A transitive strict preference relation implies that the consumer can rank different options in order of preference. However, a transitive indifference relation means that the consumer is unable to distinguish any differences between the options, which is not the case in the scenario given.

Question 11

Nancy's psychology teacher will give her a course grade that is the maximum of her scores on three midterm examinations.Nancy has convex preferences over the possible combinations of midterm scores.

Accepted Answer

Convex preferences imply that Nancy would prefer averages or mixtures of outcomes to extremes, but choosing the maximum score of three exams suggests a preference for maximizing one outcome, not averaging them.

Question 12

Nick's indifference curves are circles, all of which are centered at (12, 12).Of any two indifference circles, he would rather be on the inner one than the outer one.

Accepted Answer

The answer of Nick's indifference curves are circles, all of...

Question 13

Tim consumes only apples and bananas.He prefers more apples to fewer, but he gets tired of bananas.If he consumes fewer than 29 bananas per week, he thinks that 1 banana is a perfect substitute for 1 apple.But you would have to pay him 1 apple for each banana beyond 29 that he consumes.The indifference curve that passes through the consumption bundle with 30 apples and 39 bananas also passes through the bundle with A apples and 21 bananas, where A equals

Accepted Answer

To find the value of A, we need to establish the equation for the indifference curve passing through the given bundles. Let x represent the number of apples and y represent the number of bananas. The indifference curve passing through (30,39) and (A,21) can be represented by the equation: U(x,y) = k Where k is a constant representing the level of satisfaction Tim derives from consuming the bundles. We can set up a system of equations: U(30,39) = k U(A,21) = k Substituting in the conditions given in the problem: For Tim, 1 banana is a perfect substitute for 1 apple if he consumes fewer than 29 bananas per week. Beyond that, he requires 1 apple for each additional banana consumed. This means that the marginal rate of substitution (MRS) between bananas and apples changes at y = 29: MRS = -Δy / Δx = -1 for y < 29 (1 banana is a perfect substitute for 1 apple) MRS = -Δy / Δx = -1/29 for y > 29 (1 apple is required for each additional banana) Using the definition of MRS: MRS = MUx / MUy Where MUx is the marginal utility of apples and MUy is the marginal utility of bananas. Since Tim prefers more apples to fewer, we know that MUx > 0. However, he gets tired of bananas, so the marginal utility of bananas is diminishing. This means that MUy is decreasing as y increases. Let's assume for simplicity that the marginal utility of apples is constant. Then we can derive an equation for MUy as follows: For y < 29: MRS = MUx / MUy = -1 MUy = -MUx For y > 29: MRS = MUx / MUy = -1/29 MUy = -MUx / 29 Now we can set up the equations for the two indifference curves: U(30,39) = MUx(30) - MUy(39) = k U(A,21) = MUx(A) - MUy(21) = k Substituting in the expressions we derived for MUy: U(30,39) = MUx(30) + MUx(39) = k U(A,21) = MUx(A) + MUx(21) / 29 = k Now we can equate the two expressions for k: MUx(30) + MUx(39) = MUx(A) + MUx(21) / 29 Since we assumed that MUx is constant, we can simplify: 30MUx + 39MUx = AMUx + 21MUx / 29 Solving for A: 30MUx + 39MUx - 21MUx / 29 = AMUx A = (30MUx + 39MUx - 21MUx / 29) / MUx Simplifying: A = 28.6 Rounding up, we get: A = 29 Therefore, the indifference curve passing through the bundle with 30 apples and 39 bananas also passes through the bundle with 29 apples and 21 bananas.

Question 14

Bill Katz prefers more of good 1 to less and he prefers less of good 2 to more.Bill has convex preferences.If we draw his indifference curves with good 1 on the horizontal axis and good 2 on the vertical axis, then his indifference curves have positive slope but get steeper as they rise.

Accepted Answer

Given Bill's preferences, his indifference curves would actually have a negative slope because he prefers more of good 1 and less of good 2. Convex preferences imply that the curves are bowed inward towards the origin, but the slope of the indifference curves would still be negative due to the trade-off between the two goods where he prefers more of one and less of the other.

Question 15

A person with reflexive preferences is someone who does not shop carefully.

Accepted Answer

A person with reflexive preferences is someone who doesn't have a consistent preference and may make impulsive or inconsistent choices. It doesn't necessarily mean they don't shop carefully.

Question 16

Angela consumes goods x and y.Her indifference curves are described by the formula y = k/(x + 3).Higher values of k correspond to better indifference curves.

Accepted Answer

The indifference curve formula y = k/(x + 3) implies that Angela's utility increases with higher values of y and decreases with higher values of x. Therefore, Angela prefers bundles with more of good y and less of good x. In bundle (8, 9), she has more of good y compared to bundle (9, 8), so she prefers (8, 9).

Question 17

The marginal rate of substitution measures the distance between one indifference curve and the next one.

Accepted Answer

The marginal rate of substitution measures the rate at which a consumer is willing to substitute one good for another while maintaining the same level of utility, not the distance between indifference curves.

Question 18

If someone has the utility function U = 1,000 + 2min {x, y}, then x and y are perfect complements for that person.

Accepted Answer

The utility function U = 1,000 + 2min {x, y} indicates that the utility depends on the minimum of x and y, which is characteristic of perfect complements where goods are consumed in fixed proportions.

Question 19

Colette consumes goods x and y.Her indifference curves are described by the formula y = k/(x + 7).Higher values of k correspond to better indifference curves.

Accepted Answer

The answer of Colette consumes goods x and y.Her indifference...

Question 20

Leo consumes only apples and bananas.He prefers more apples to fewer, but he gets tired of bananas.If he consumes fewer than 24 bananas per week, he thinks that 1 banana is a perfect substitute for 1 apple.But you would have to pay him 1 apple for each banana beyond 24 that he consumes.The indifference curve that passes through the consumption bundle with 31 apples and 36 bananas also passes through the bundle with A apples and 18 bananas, where A equals

Accepted Answer

The answer of Leo consumes only apples and bananas.He prefers...

Quiz 2: Preferences-Part A

If preferences are convex, then for any commodity bundle x, the set of commodity bundles that are worse than x is a convex set.

A consumer with convex preferences who is indifferent between the bundles (5, 1)and (11, 3)will like the bundle (8, 2)at least as well as either of the first two bundles.

If preferences are transitive, more is always preferred to less.

Ambrose has an indifference curve with equation x₂ = 20 - 4x^1/2₁.When Ambrose is consuming the bundle (4, 16), his marginal rate of substitution is 25/4.

Josephine buys 3 quarts of milk and 2 pounds of butter when milk sells for $2 a quart and butter sells for $1 a pound.Wilma buys 2 quarts of milk and 3 pounds of butter at the same prices.Josephine's marginal rate of substitution between milk and butter is greater than Wilma's.

A consumer with convex preferences who is indifferent between the bundles (5, 2)and (11, 6)will like the bundle (8, 4)at least as well as either of the first two bundles.

If there are two goods, if a consumer prefers more of each good to less, and if she has a diminishing marginal rate of substitution, then her preferences are convex.

Steven's indifference curves are circles, all of which are centered at (15, 13) .Of any two indifference circles, he would rather be on the inner one than the outer one.

A consumer who is unable to detect small differences in the amount of water in her beer could have a transitive strict preference relation but is unlikely to have a transitive indifference relation.

Nancy's psychology teacher will give her a course grade that is the maximum of her scores on three midterm examinations.Nancy has convex preferences over the possible combinations of midterm scores.

Nick's indifference curves are circles, all of which are centered at (12, 12) .Of any two indifference circles, he would rather be on the inner one than the outer one.

Bill Katz prefers more of good 1 to less and he prefers less of good 2 to more.Bill has convex preferences.If we draw his indifference curves with good 1 on the horizontal axis and good 2 on the vertical axis, then his indifference curves have positive slope but get steeper as they rise.

A person with reflexive preferences is someone who does not shop carefully.

Angela consumes goods x and y.Her indifference curves are described by the formula y = k/(x + 3) .Higher values of k correspond to better indifference curves.

The marginal rate of substitution measures the distance between one indifference curve and the next one.

If someone has the utility function U = 1,000 + 2min {x, y}, then x and y are perfect complements for that person.

Colette consumes goods x and y.Her indifference curves are described by the formula y = k/(x + 7) .Higher values of k correspond to better indifference curves.

Quiz 2: Preferences-Part A

If preferences are convex, then for any commodity bundle x, the set of commodity bundles that are worse than x is a convex set.

A consumer with convex preferences who is indifferent between the bundles (5, 1)and (11, 3)will like the bundle (8, 2)at least as well as either of the first two bundles.

If preferences are transitive, more is always preferred to less.

Ambrose has an indifference curve with equation x2 = 20 - 4x1/21.When Ambrose is consuming the bundle (4, 16), his marginal rate of substitution is 25/4.

Josephine buys 3 quarts of milk and 2 pounds of butter when milk sells for $2 a quart and butter sells for $1 a pound.Wilma buys 2 quarts of milk and 3 pounds of butter at the same prices.Josephine's marginal rate of substitution between milk and butter is greater than Wilma's.

A consumer with convex preferences who is indifferent between the bundles (5, 2)and (11, 6)will like the bundle (8, 4)at least as well as either of the first two bundles.

If there are two goods, if a consumer prefers more of each good to less, and if she has a diminishing marginal rate of substitution, then her preferences are convex.

Steven's indifference curves are circles, all of which are centered at (15, 13) .Of any two indifference circles, he would rather be on the inner one than the outer one.

A consumer who is unable to detect small differences in the amount of water in her beer could have a transitive strict preference relation but is unlikely to have a transitive indifference relation.

Nancy's psychology teacher will give her a course grade that is the maximum of her scores on three midterm examinations.Nancy has convex preferences over the possible combinations of midterm scores.

Nick's indifference curves are circles, all of which are centered at (12, 12) .Of any two indifference circles, he would rather be on the inner one than the outer one.

Bill Katz prefers more of good 1 to less and he prefers less of good 2 to more.Bill has convex preferences.If we draw his indifference curves with good 1 on the horizontal axis and good 2 on the vertical axis, then his indifference curves have positive slope but get steeper as they rise.

A person with reflexive preferences is someone who does not shop carefully.

Angela consumes goods x and y.Her indifference curves are described by the formula y = k/(x + 3) .Higher values of k correspond to better indifference curves.

The marginal rate of substitution measures the distance between one indifference curve and the next one.

If someone has the utility function U = 1,000 + 2min {x, y}, then x and y are perfect complements for that person.

Colette consumes goods x and y.Her indifference curves are described by the formula y = k/(x + 7) .Higher values of k correspond to better indifference curves.

Ambrose has an indifference curve with equation x₂ = 20 - 4x^1/2₁.When Ambrose is consuming the bundle (4, 16), his marginal rate of substitution is 25/4.