Consumer Choice Theory Quiz

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Questions and Answers

What does the axiom of completeness imply about consumer preferences?

Consumers must be aware of their preferences for any two choices. (correct)

Consumers can only prefer one choice over another.

Consumers have no preference if they are indifferent.

Consumers must be indifferent between all choices.

What does the axiom of transitivity state regarding consumer choices?

Transitivity does not apply if A is a good and C is an abstract choice.

If a consumer prefers A to B and B to C, then they prefer A to C. (correct)

Preferences can be randomized, making transitivity irrelevant.

Consumers may switch preferences based on context.

In the context of rational choice theory, what is the most accurate definition of rationality?

Always preferring the more expensive option.

Never making mistakes in decision making.

Making the best possible choice every time.

Having preferences that are always consistent. (correct)

What does the notation A B indicate about the relationship between choices?

A is weakly preferred to B. Signup and view all the answers

Which statement about rational consumers is false?

They always make the right choice. Signup and view all the answers

What is meant by the term 'marginal rate of substitution' in the context of consumer choice?

The rate at which a consumer can trade off one good for another while maintaining the same level of utility. Signup and view all the answers

Which condition best illustrates the concept of indifference in consumer choice?

A B indicates that the consumer is indifferent between the two choices. Signup and view all the answers

What can be concluded about the utility values for eating an ice cream cone and a slice of pizza?

An ice cream cone is preferred over a slice of pizza. Signup and view all the answers

Which representation maintains the original preference ordering while transforming the utility function?

U(N, V) = ln(N) + 2 ln(V) Signup and view all the answers

Which of the following utility functions does not preserve the original preference ordering?

U(N, V) = - N V^2 Signup and view all the answers

What does an indifference curve represent for a consumer?

A plot of all values that give the consumer the same utility level Signup and view all the answers

What type of transformation can be applied to a utility function while preserving preference ordering?

Any monotonically increasing function Signup and view all the answers

What is the purpose of applying transformations to utility functions?

To simplify decision-making about preferences. Signup and view all the answers

In the utility function U = 2x + 4y, what value yields an indifference curve where the consumer has exactly 30 utility?

y = 7.5 - 0.5x Signup and view all the answers

Based on the consumer's utility function U(N, V) = NV^2, what is the preference order from highest to lowest utility for the combinations provided?

D ∼ C ∼ B ∼ A ∼ E Signup and view all the answers

What does the slope of the indifference curve represent?

The marginal rate of substitution (MRS) between the two goods Signup and view all the answers

Which of the following transformations would NOT retain the preference ordering given the original utility function U(N, V) = NV^2?

f(x) = x^3 Signup and view all the answers

For the utility function U(x, y) = x^{1/2} y^{1/2}, what is the derived equation for y when Ū is fixed?

y = Ū^2 / x Signup and view all the answers

How many indifference curves can be derived from a single utility function?

Infinitely many indifference curves can be plotted for different utility levels Signup and view all the answers

Which utility function would require a decreasing transformation to maintain the preference order?

U(N, V) = -N V^2 Signup and view all the answers

What does the axiom of transitivity imply about consumer preferences?

If a consumer prefers A over B and B over C, then they must prefer A over C. Signup and view all the answers

Which statement best describes the continuity axiom?

If A is preferred to B, then any choice close to A should also be preferred to B. Signup and view all the answers

What defines a utility function?

A mathematical representation that assigns values to choices based on preference. Signup and view all the answers

What is meant by the non-uniqueness of utility?

Multiple utility functions can represent the same preferences while preserving order. Signup and view all the answers

What distinguishes ordinal utility functions from cardinal utility functions?

Ordinal functions indicate only the order of preferences without showing magnitude. Signup and view all the answers

If a consumer prefers a 250 mL can of Coke to a 250 mL can of Sprite, what does the continuity axiom suggest about their preference for a 249.9 mL can of Coke?

The consumer will definitely prefer the 249.9 mL can of Coke to the Sprite. Signup and view all the answers

Which of the following best illustrates the concept of utility in consumer choice?

Utility quantifies how much happiness a choice brings to a consumer. Signup and view all the answers

Why is the transformation from preference relations to a utility function important?

It allows the use of mathematical tools to analyze consumer behavior. Signup and view all the answers

What happens to utility as the consumer moves up and to the right on the indifference curve?

Utility increases Signup and view all the answers

What does MRS represent in relation to indifference curves?

The marginal rate of substitution, or slope of the indifference curve Signup and view all the answers

When the consumer has more of good x, what happens to the MRS according to the given utility function?

MRS decreases Signup and view all the answers

What is indicated by convexity in the context of indifference curves?

The marginal utility of a good declines as consumption increases Signup and view all the answers

If a consumer currently possesses 10 units of both goods x and y, what is their MRS?

1 Signup and view all the answers

What effect does increasing the quantity of good y while holding good x constant have on utility?

Utility also increases Signup and view all the answers

What shape do indifference curves take when the utility function has decreasing marginal utility?

Convex Signup and view all the answers

What happens to the consumer's preference as the MRS falls while consuming more of good x?

The consumer starts to prefer more of good y relative to good x Signup and view all the answers

What does the marginal rate of substitution (MRS) represent?

The ratio of marginal utilities of two goods. Signup and view all the answers

In the utility function U(x, y) = 2x + 4y, what is the marginal utility of good y?

4 Signup and view all the answers

If a consumer has 5 units of x and 5 units of y, how much would y need to increase if x decreases by 1 unit to maintain the same utility?

0.5 units Signup and view all the answers

Which of the following expressions correctly describes the MRS in terms of marginal utility?

MRS = ∂U/∂x / ∂U/∂y Signup and view all the answers

In the utility function U(x, y) = x^(1/2) y^(1/2), what is the form of the MRS?

Dependent on the levels of x and y Signup and view all the answers

If the MRS between x and y is constant, what does this imply about the consumer's utility function?

The utility function is linear. Signup and view all the answers

Which situation best demonstrates a changing MRS?

A consumer increasingly willing to give up less y for each additional unit of x consumed. Signup and view all the answers

What characteristic do indifference curves exhibit?

They show combinations of goods yielding the same level of utility. Signup and view all the answers

What does the completeness axiom imply about consumer preferences?

Consumers can express indifference between any two choices. Signup and view all the answers

Which statement correctly describes transitivity in consumer preferences?

If a consumer prefers A over B and B over C, they will also prefer A over C. Signup and view all the answers

How is the notation A∼B interpreted in consumer choice?

A and B are considered equal in preference. Signup and view all the answers

What does the concept of a utility function primarily describe?

The consumer's preferences in a numerical form. Signup and view all the answers

In relation to indifference curves, what does the marginal rate of substitution (MRS) signify?

The maximum amount of one good a consumer is willing to give up for another. Signup and view all the answers

How does an increase in the quantity of one good typically affect the marginal rate of substitution (MRS)?

MRS generally decreases as one good increases. Signup and view all the answers

What is indicated by the assumption of rationality in consumer choice?

Consumers’ choices are consistent and based on their preferences. Signup and view all the answers

Which of the following best illustrates the completeness axiom in consumer choice?

A consumer states they prefer tea to coffee, and this preference is consistent. Signup and view all the answers

What principle ensures that if a consumer prefers one option over another, they will also prefer a choice that is only slightly different from the first option?

Continuity Signup and view all the answers

Which of the following statements best explains the significance of the non-uniqueness of utility?

A consumer's preferences can be represented in multiple ways while maintaining order. Signup and view all the answers

In the context of utility functions, what does 'ordinal' imply about the values assigned to consumer preferences?

They only indicate the order of preferences. Signup and view all the answers

What does the function U(A) ≥ U(B) signify in relation to consumer preferences?

A is preferred to B or equally preferred. Signup and view all the answers

If a consumer prefers a can of Coke to a can of Sprite, what does continuity imply about their preference for a slightly smaller can of Coke?

They will prefer it over a smaller Sprite. Signup and view all the answers

Which of the following best describes the concept of utility in relation to consumer choice?

It quantifies the happiness derived from choices. Signup and view all the answers

What does the continuity axiom suggest about consumer preferences between choices that are similar?

They should prefer similar options in a consistent manner. Signup and view all the answers

What characteristic differentiates cardinal utility from ordinal utility in consumer choice theory?

Cardinal utility represents exact magnitudes of preference. Signup and view all the answers

When given the utility function U = 2x + 4y, what is the correct linear equation for the indifference curve at a utility level of 30?

$y = 7.5 - 0.5x$ Signup and view all the answers

What does the slope of the indifference curve derived from the function U = 2x + 4y signify?

The marginal rate of substitution (MRS) between x and y Signup and view all the answers

For the utility function U(x, y) = $x^{1/2} y^{1/2}$, what is the relationship derived for y when Ū is fixed?

$y = Ū^2/x$ Signup and view all the answers

How do indifference curves behave when plotted for the utility function U(x, y) = $x^{1/2} y^{1/2}$ at varying levels of utility?

They are convex to the origin. Signup and view all the answers

What does the term 'MRS' represent in the context of indifference curves?

The rate at which one good can be substituted for another while maintaining utility Signup and view all the answers

Which of the following combinations of hours spent on Netflix and video games provides the highest utility according to the given function?

(4, 0) Signup and view all the answers

Which utility function would require a transformation that is not monotonically increasing to disrupt the original preference ordering?

U(N, V) = -N V^2 Signup and view all the answers

What is necessary for a new utility function to preserve the original preference ordering?

It must be monotonically increasing. Signup and view all the answers

Which of the following utility functions does not preserve the preference ordering given the initial function U(N, V) = N V^2?

U(N, V) = N + V^2 Signup and view all the answers

For what reason does the utility function U(N, V) = N V^2 rank the combination (1, 3) lower than (2, 2)?

It fails to utilize all available hours. Signup and view all the answers

In transforming utility functions, which of the following represents an increasing transformation for U(N, V) = N V^2?

f(x) = 3x + 1 Signup and view all the answers

Which of the following utility functions shows a preference similar to the original function yet increases complexity?

U(N, V) = N^{2} V Signup and view all the answers

Which function is confirmed to preserve preference ordering without complication by additional constants or transformations?

U(N, V) = N V^2 Signup and view all the answers

What does the marginal rate of substitution (MRS) indicate in consumer theory?

The quantity of one good that compensates for the loss of another good. Signup and view all the answers

If a consumer has 5 units of good x and 5 units of good y in the utility function U(x, y) = 2x + 4y, what is their total utility?

30 Signup and view all the answers

In the utility function U(x, y) = x^{1/2} y^{1/2}, how does the MRS depend on the amounts of x and y?

It decreases as the consumer has more of good x. Signup and view all the answers

Which of the following combinations preserves the same level of utility according to the MRS?

(4, 5.5) and (3, 6.5) Signup and view all the answers

What does a constant MRS suggest about the utility function?

It indicates linear preferences between the two goods. Signup and view all the answers

When considering the utility function U(x, y) = 2x + 4y, what will happen if the consumer decreases good x by one unit?

The amount of good y must increase by 1/2 unit to maintain utility. Signup and view all the answers

What defines an indifference curve in relation to a consumer's preferences?

It illustrates the trade-offs a consumer is willing to make between two goods. Signup and view all the answers

What happens to utility as one moves up and to the right on an indifference curve?

Utility increases. Signup and view all the answers

What does a decreasing marginal rate of substitution (MRS) imply about a consumer's preferences?

The consumer values one good less as they consume more of another. Signup and view all the answers

If the MRS is equal to $y/x$, what does this represent in terms of the slope of the indifference curve?

The slope is negative and varying. Signup and view all the answers

How does the convexity of indifference curves affect consumer preferences?

Consumers exhibit decreasing preference for additional units of a good. Signup and view all the answers

What is indicated by the property of convexity in utility functions?

Consumers derive decreasing additional utility from more units of a single good. Signup and view all the answers

What does it mean if a consumer is indifferent between receiving one more unit of good x versus one more unit of good y?

The consumer gains identical utility from both goods. Signup and view all the answers

Which scenario illustrates a consumer preferring good y over good x as their consumption of good x increases?

MRS is less than 1. Signup and view all the answers

What shape do indifference curves take when reflecting decreasing marginal utility?

Convex shapes. Signup and view all the answers

Study Notes

Choice Theory

People make choices for various reasons. Economics examines decision-making from a "rational" individual perspective.
Key concepts under study are axioms of rational choice, utility functions, marginal rate of substitution, and indifference curves—all used to analyze consumer choices.

Axioms of Rational Choice

Economic rationality has a specific definition, less broad than everyday use. It doesn't necessitate "right" choices or only correct decisions.
Rationality means internal consistency in an individual's choices.

Notation

A and B represent choices (can be concrete goods or abstract decisions).
A > B denotes A is strictly preferred to B.
A ~ B denotes the consumer is indifferent between A and B.
A ≥ B denotes A is weakly preferred to or indifferent to B.

Three Axioms

Completeness: Consumers must be able to state their preferences between any two choices (A > B or B > A). Indifference is permissible. This rules out cases where a consumer is unsure about their preferences.
Transitivity: If A > B and B > C, then A > C. This consistency avoids illogical preferences.
Continuity: If A > B, then anything sufficiently close to A will also be preferred.

Utility Functions

Utility functions map preferences onto numbers representing satisfaction.
If A > B, then the utility for A (U(A)) is greater than the utility for B (U(B)).
This transformation allows use of mathematical tools for exploring consumer choices. Utility functions are not unique; different functions can represent the same preference ordering if they are monotonic and increasing. Several examples (e.g., U(N, V) = NV^2) illustrate these functions in specific contexts.

Non-Uniqueness of Utility

One preference ordering can be represented by various utility functions.
The utility numbers represent preference order, not the magnitude of preference.
A cardinal utility function conveys magnitude, unlike an ordinal utility function that only relays order.

Example: Utility Function in Free Time Allocation

A consumer allocates free time between watching Netflix (N) and playing video games (V).
Utility function example U(N,V) = NV^2, with N representing Netflix hours and V representing Video Game hours.

Marginal Rate of Substitution (MRS)

MRS is a tool linking a consumer's preference over goods.
Mathematically: MRS = (Marginal Utility of X)/(Marginal Utility of Y).
MRS denotes how much of one good a consumer will give up for an additional unit of another good and maintain the same utility level. The slope of indifference curves is the negative of MRS.
As quantity of X increases, MRS for X decreases (and vice-versa).

Indifference Curves

Indifference curves plot all combinations of goods yielding a specific utility level.
Each point on the curve represents the same utility level for the consumer.
The slope of the indifference curve is the negative of the MRS.
Indifference curves are downward sloping, reflecting the trade-off between goods.

Convexity

If more of a good is consumed, the desire for more decreases relative to other goods.
This relative preference leads to convex indifference curves, reflecting diminishing marginal rate of substitution.

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Description

Test your understanding of key concepts in consumer choice theory, including the axioms of completeness and transitivity, as well as rationality and marginal rate of substitution. This quiz covers essential principles that define consumer preferences and decision-making processes.