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Questions and Answers
What does the axiom of completeness imply about consumer preferences?
What does the axiom of completeness imply about consumer preferences?
What does the axiom of transitivity state regarding consumer choices?
What does the axiom of transitivity state regarding consumer choices?
In the context of rational choice theory, what is the most accurate definition of rationality?
In the context of rational choice theory, what is the most accurate definition of rationality?
What does the notation A B indicate about the relationship between choices?
What does the notation A B indicate about the relationship between choices?
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Which statement about rational consumers is false?
Which statement about rational consumers is false?
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What is meant by the term 'marginal rate of substitution' in the context of consumer choice?
What is meant by the term 'marginal rate of substitution' in the context of consumer choice?
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Which condition best illustrates the concept of indifference in consumer choice?
Which condition best illustrates the concept of indifference in consumer choice?
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What can be concluded about the utility values for eating an ice cream cone and a slice of pizza?
What can be concluded about the utility values for eating an ice cream cone and a slice of pizza?
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Which representation maintains the original preference ordering while transforming the utility function?
Which representation maintains the original preference ordering while transforming the utility function?
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Which of the following utility functions does not preserve the original preference ordering?
Which of the following utility functions does not preserve the original preference ordering?
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What does an indifference curve represent for a consumer?
What does an indifference curve represent for a consumer?
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What type of transformation can be applied to a utility function while preserving preference ordering?
What type of transformation can be applied to a utility function while preserving preference ordering?
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What is the purpose of applying transformations to utility functions?
What is the purpose of applying transformations to utility functions?
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In the utility function U = 2x + 4y, what value yields an indifference curve where the consumer has exactly 30 utility?
In the utility function U = 2x + 4y, what value yields an indifference curve where the consumer has exactly 30 utility?
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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?
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?
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What does the slope of the indifference curve represent?
What does the slope of the indifference curve represent?
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Which of the following transformations would NOT retain the preference ordering given the original utility function U(N, V) = NV^2?
Which of the following transformations would NOT retain the preference ordering given the original utility function U(N, V) = NV^2?
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For the utility function U(x, y) = x^{1/2} y^{1/2}, what is the derived equation for y when Ū is fixed?
For the utility function U(x, y) = x^{1/2} y^{1/2}, what is the derived equation for y when Ū is fixed?
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How many indifference curves can be derived from a single utility function?
How many indifference curves can be derived from a single utility function?
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Which utility function would require a decreasing transformation to maintain the preference order?
Which utility function would require a decreasing transformation to maintain the preference order?
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What does the axiom of transitivity imply about consumer preferences?
What does the axiom of transitivity imply about consumer preferences?
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Which statement best describes the continuity axiom?
Which statement best describes the continuity axiom?
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What defines a utility function?
What defines a utility function?
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What is meant by the non-uniqueness of utility?
What is meant by the non-uniqueness of utility?
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What distinguishes ordinal utility functions from cardinal utility functions?
What distinguishes ordinal utility functions from cardinal utility functions?
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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?
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?
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Which of the following best illustrates the concept of utility in consumer choice?
Which of the following best illustrates the concept of utility in consumer choice?
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Why is the transformation from preference relations to a utility function important?
Why is the transformation from preference relations to a utility function important?
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What happens to utility as the consumer moves up and to the right on the indifference curve?
What happens to utility as the consumer moves up and to the right on the indifference curve?
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What does MRS represent in relation to indifference curves?
What does MRS represent in relation to indifference curves?
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When the consumer has more of good x, what happens to the MRS according to the given utility function?
When the consumer has more of good x, what happens to the MRS according to the given utility function?
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What is indicated by convexity in the context of indifference curves?
What is indicated by convexity in the context of indifference curves?
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If a consumer currently possesses 10 units of both goods x and y, what is their MRS?
If a consumer currently possesses 10 units of both goods x and y, what is their MRS?
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What effect does increasing the quantity of good y while holding good x constant have on utility?
What effect does increasing the quantity of good y while holding good x constant have on utility?
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What shape do indifference curves take when the utility function has decreasing marginal utility?
What shape do indifference curves take when the utility function has decreasing marginal utility?
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What happens to the consumer's preference as the MRS falls while consuming more of good x?
What happens to the consumer's preference as the MRS falls while consuming more of good x?
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What does the marginal rate of substitution (MRS) represent?
What does the marginal rate of substitution (MRS) represent?
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In the utility function U(x, y) = 2x + 4y, what is the marginal utility of good y?
In the utility function U(x, y) = 2x + 4y, what is the marginal utility of good y?
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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?
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?
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Which of the following expressions correctly describes the MRS in terms of marginal utility?
Which of the following expressions correctly describes the MRS in terms of marginal utility?
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In the utility function U(x, y) = x^(1/2) y^(1/2), what is the form of the MRS?
In the utility function U(x, y) = x^(1/2) y^(1/2), what is the form of the MRS?
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If the MRS between x and y is constant, what does this imply about the consumer's utility function?
If the MRS between x and y is constant, what does this imply about the consumer's utility function?
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Which situation best demonstrates a changing MRS?
Which situation best demonstrates a changing MRS?
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What characteristic do indifference curves exhibit?
What characteristic do indifference curves exhibit?
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What does the completeness axiom imply about consumer preferences?
What does the completeness axiom imply about consumer preferences?
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Which statement correctly describes transitivity in consumer preferences?
Which statement correctly describes transitivity in consumer preferences?
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How is the notation A∼B interpreted in consumer choice?
How is the notation A∼B interpreted in consumer choice?
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What does the concept of a utility function primarily describe?
What does the concept of a utility function primarily describe?
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In relation to indifference curves, what does the marginal rate of substitution (MRS) signify?
In relation to indifference curves, what does the marginal rate of substitution (MRS) signify?
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How does an increase in the quantity of one good typically affect the marginal rate of substitution (MRS)?
How does an increase in the quantity of one good typically affect the marginal rate of substitution (MRS)?
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What is indicated by the assumption of rationality in consumer choice?
What is indicated by the assumption of rationality in consumer choice?
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Which of the following best illustrates the completeness axiom in consumer choice?
Which of the following best illustrates the completeness axiom in consumer choice?
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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?
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?
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Which of the following statements best explains the significance of the non-uniqueness of utility?
Which of the following statements best explains the significance of the non-uniqueness of utility?
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In the context of utility functions, what does 'ordinal' imply about the values assigned to consumer preferences?
In the context of utility functions, what does 'ordinal' imply about the values assigned to consumer preferences?
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What does the function U(A) ≥ U(B) signify in relation to consumer preferences?
What does the function U(A) ≥ U(B) signify in relation to consumer preferences?
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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?
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?
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Which of the following best describes the concept of utility in relation to consumer choice?
Which of the following best describes the concept of utility in relation to consumer choice?
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What does the continuity axiom suggest about consumer preferences between choices that are similar?
What does the continuity axiom suggest about consumer preferences between choices that are similar?
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What characteristic differentiates cardinal utility from ordinal utility in consumer choice theory?
What characteristic differentiates cardinal utility from ordinal utility in consumer choice theory?
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When given the utility function U = 2x + 4y, what is the correct linear equation for the indifference curve at a utility level of 30?
When given the utility function U = 2x + 4y, what is the correct linear equation for the indifference curve at a utility level of 30?
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What does the slope of the indifference curve derived from the function U = 2x + 4y signify?
What does the slope of the indifference curve derived from the function U = 2x + 4y signify?
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For the utility function U(x, y) = $x^{1/2} y^{1/2}$, what is the relationship derived for y when Ū is fixed?
For the utility function U(x, y) = $x^{1/2} y^{1/2}$, what is the relationship derived for y when Ū is fixed?
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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?
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?
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What does the term 'MRS' represent in the context of indifference curves?
What does the term 'MRS' represent in the context of indifference curves?
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Which of the following combinations of hours spent on Netflix and video games provides the highest utility according to the given function?
Which of the following combinations of hours spent on Netflix and video games provides the highest utility according to the given function?
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Which utility function would require a transformation that is not monotonically increasing to disrupt the original preference ordering?
Which utility function would require a transformation that is not monotonically increasing to disrupt the original preference ordering?
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What is necessary for a new utility function to preserve the original preference ordering?
What is necessary for a new utility function to preserve the original preference ordering?
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Which of the following utility functions does not preserve the preference ordering given the initial function U(N, V) = N V^2?
Which of the following utility functions does not preserve the preference ordering given the initial function U(N, V) = N V^2?
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For what reason does the utility function U(N, V) = N V^2 rank the combination (1, 3) lower than (2, 2)?
For what reason does the utility function U(N, V) = N V^2 rank the combination (1, 3) lower than (2, 2)?
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In transforming utility functions, which of the following represents an increasing transformation for U(N, V) = N V^2?
In transforming utility functions, which of the following represents an increasing transformation for U(N, V) = N V^2?
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Which of the following utility functions shows a preference similar to the original function yet increases complexity?
Which of the following utility functions shows a preference similar to the original function yet increases complexity?
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Which function is confirmed to preserve preference ordering without complication by additional constants or transformations?
Which function is confirmed to preserve preference ordering without complication by additional constants or transformations?
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What does the marginal rate of substitution (MRS) indicate in consumer theory?
What does the marginal rate of substitution (MRS) indicate in consumer theory?
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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?
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?
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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?
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?
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Which of the following combinations preserves the same level of utility according to the MRS?
Which of the following combinations preserves the same level of utility according to the MRS?
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What does a constant MRS suggest about the utility function?
What does a constant MRS suggest about the utility function?
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When considering the utility function U(x, y) = 2x + 4y, what will happen if the consumer decreases good x by one unit?
When considering the utility function U(x, y) = 2x + 4y, what will happen if the consumer decreases good x by one unit?
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What defines an indifference curve in relation to a consumer's preferences?
What defines an indifference curve in relation to a consumer's preferences?
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What happens to utility as one moves up and to the right on an indifference curve?
What happens to utility as one moves up and to the right on an indifference curve?
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What does a decreasing marginal rate of substitution (MRS) imply about a consumer's preferences?
What does a decreasing marginal rate of substitution (MRS) imply about a consumer's preferences?
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If the MRS is equal to $y/x$, what does this represent in terms of the slope of the indifference curve?
If the MRS is equal to $y/x$, what does this represent in terms of the slope of the indifference curve?
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How does the convexity of indifference curves affect consumer preferences?
How does the convexity of indifference curves affect consumer preferences?
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What is indicated by the property of convexity in utility functions?
What is indicated by the property of convexity in utility functions?
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What does it mean if a consumer is indifferent between receiving one more unit of good x versus one more unit of good y?
What does it mean if a consumer is indifferent between receiving one more unit of good x versus one more unit of good y?
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Which scenario illustrates a consumer preferring good y over good x as their consumption of good x increases?
Which scenario illustrates a consumer preferring good y over good x as their consumption of good x increases?
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What shape do indifference curves take when reflecting decreasing marginal utility?
What shape do indifference curves take when reflecting decreasing marginal utility?
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Flashcards
Rationality in Economics
Rationality in Economics
A concept in economics where choices are internally consistent, not necessarily 'right' choices.
Completeness Axiom
Completeness Axiom
Consumers can always compare any two choices and state a preference (including indifference).
Transitivity Axiom
Transitivity Axiom
If a consumer prefers A to B, and B to C, then they must prefer A to C.
Notation A > B
Notation A > B
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Notation A ~ B
Notation A ~ B
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Notation A ≥ B
Notation A ≥ B
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What are the axioms of rational choice?
What are the axioms of rational choice?
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What does it mean for a consumer to be rational?
What does it mean for a consumer to be rational?
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Continuity Axiom
Continuity Axiom
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What does the Continuity Axiom imply?
What does the Continuity Axiom imply?
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Utility Function
Utility Function
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What does a higher utility value indicate?
What does a higher utility value indicate?
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What does the Utility Function theorem state?
What does the Utility Function theorem state?
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Is the Utility Function unique?
Is the Utility Function unique?
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Ordinal Utility
Ordinal Utility
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Cardinal Utility
Cardinal Utility
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Monotonically Increasing Transformation
Monotonically Increasing Transformation
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What does a utility function tell us?
What does a utility function tell us?
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Can we compare utility values across people?
Can we compare utility values across people?
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Why are monotonically increasing transformations useful?
Why are monotonically increasing transformations useful?
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What does it mean when two utility functions preserve the same preference ordering?
What does it mean when two utility functions preserve the same preference ordering?
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How do we know if a transformation preserves the original preference ordering?
How do we know if a transformation preserves the original preference ordering?
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What happens if a transformation is not monotonically increasing?
What happens if a transformation is not monotonically increasing?
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Indifference Curve
Indifference Curve
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What is Ū?
What is Ū?
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Why is the slope of an indifference curve negative?
Why is the slope of an indifference curve negative?
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How do we find indifference curves?
How do we find indifference curves?
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Marginal Rate of Substitution (MRS)
Marginal Rate of Substitution (MRS)
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What is the formula for MRS?
What is the formula for MRS?
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What does a constant MRS mean?
What does a constant MRS mean?
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What does a changing MRS mean?
What does a changing MRS mean?
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What does the slope of an indifference curve represent?
What does the slope of an indifference curve represent?
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What is the significance of indifference curves?
What is the significance of indifference curves?
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How is MRS related to the shape of an indifference curve?
How is MRS related to the shape of an indifference curve?
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MRS (Marginal Rate of Substitution)
MRS (Marginal Rate of Substitution)
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Convexity
Convexity
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Why do indifference curves have a diminishing MRS?
Why do indifference curves have a diminishing MRS?
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What does a higher utility value represent?
What does a higher utility value represent?
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How is the MRS related to the slope?
How is the MRS related to the slope?
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What happens to utility if you move up and to the right on the indifference curve?
What happens to utility if you move up and to the right on the indifference curve?
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What happens to utility if you move down and to the left on the indifference curve?
What happens to utility if you move down and to the left on the indifference curve?
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What is Rationality in Economics?
What is Rationality in Economics?
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What does a decreasing MRS mean?
What does a decreasing MRS mean?
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What is a Utility Function?
What is a Utility Function?
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What are indifference curves?
What are indifference curves?
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What is the purpose of using Utility Functions?
What is the purpose of using Utility Functions?
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What does MRS tell us?
What does MRS tell us?
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Constant MRS
Constant MRS
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Changing MRS
Changing MRS
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Convex Indifference Curve
Convex Indifference Curve
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Diminishing MRS
Diminishing MRS
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Utility Level (Ū)
Utility Level (Ū)
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Preference Ordering
Preference Ordering
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How can we transform a utility function without altering preferences?
How can we transform a utility function without altering preferences?
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What does a monotonically increasing transformation look like?
What does a monotonically increasing transformation look like?
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Why is a monotonically increasing transformation useful?
Why is a monotonically increasing transformation useful?
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What does it mean to preserve the same preference ordering?
What does it mean to preserve the same preference ordering?
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What is the relationship between MRS and slope?
What is the relationship between MRS and slope?
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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.