Microeconomics II Week 2 Quiz

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Questions and Answers

What does a weak preference relation represent in consumer preferences?

  • At least as preferred as another bundle (correct)
  • A strict preference for one bundle over another
  • Indifference between two bundles
  • Total avoidance of a particular bundle

If a consumer is indifferent between two bundles, they strictly prefer one over the other.

False (B)

Define strict preference in the context of consumer preferences.

Strict preference occurs when a consumer prefers one bundle over another and does not have a preference for the reverse.

A consumer is said to strictly prefer bundle x to bundle x0 if ____________.

<p>x % x0 and x0 %/ x</p> Signup and view all the answers

Match the following terms with their definitions:

<p>Weak Preference = At least as preferred as another bundle Strict Preference = Preferred without indifference Indifference = Both bundles are equally preferred Preference Relation = A way to rank consumption bundles</p> Signup and view all the answers

If a consumer weakly prefers bundle x to x0, then they also strictly prefer x to x0.

<p>False (B)</p> Signup and view all the answers

What does it mean when a consumer is indifferent between two bundles?

<p>The consumer considers both bundles to be at least equally preferred.</p> Signup and view all the answers

What does the consumption bundle typically denote?

<p>A vector of quantities of two goods (C)</p> Signup and view all the answers

The budget constraint is defined as p1x1 + p2x2 = m.

<p>False (B)</p> Signup and view all the answers

What happens to the budget constraint when a consumer spends all their income?

<p>It is satisfied with equality.</p> Signup and view all the answers

What is considered a leading example of a bad?

<p>Pollution. (D)</p> Signup and view all the answers

The consumer’s budget set contains all bundles where the inequality ______ is satisfied.

<p>p1x1 + p2x2 ≤ m</p> Signup and view all the answers

What does the slope of the budget line represent?

<p>The relative price of good 1 to good 2 (D)</p> Signup and view all the answers

More of a bad is always preferable to less of it.

<p>False (B)</p> Signup and view all the answers

What do indifference curves represent in relation to consumer preferences?

<p>Indifference curves represent the different combinations of goods that provide the same level of utility to the consumer.</p> Signup and view all the answers

How can the budget line be visually represented?

<p>As a straight line on a graph.</p> Signup and view all the answers

A typical example of a bad in economics is __________.

<p>labour</p> Signup and view all the answers

Match the following variables with their respective descriptions:

<p>x1 = Quantity of good 1 x2 = Quantity of good 2 p1 = Price of good 1 p2 = Price of good 2</p> Signup and view all the answers

A consumer can afford a bundle x = (x1, x2) if ______ is true.

<p>p1x1 + p2x2 ≤ m</p> Signup and view all the answers

Match the type of good with its related characteristic:

<p>Good = Typically preferred in greater amounts Bad = Not preferred, more consumption is undesirable Bliss point = Level of consumption beyond which goods behave as bads Indifference curve = Shows combinations providing equal utility</p> Signup and view all the answers

In which scenario do indifference curves have a positive slope?

<p>When one good is a good and the other is a bad. (A)</p> Signup and view all the answers

The consumer prefers more of both goods when both are classified as bads.

<p>False (B)</p> Signup and view all the answers

What happens to consumer preferences after reaching a bliss point?

<p>Goods behave as bads beyond the bliss point.</p> Signup and view all the answers

What does transitivity imply about consumer preferences?

<p>If a consumer prefers x to x0 and x0 to x00, they must prefer x to x00. (C)</p> Signup and view all the answers

A preference relation that is complete is always reflexive.

<p>True (A)</p> Signup and view all the answers

What does rationality imply for consumers in terms of their preferences?

<p>Consumers know what they like and can rank all alternatives.</p> Signup and view all the answers

A preference relation is said to be _________ if for every x X, x % x.

<p>reflexive</p> Signup and view all the answers

Which of the following statements is true regarding strict preference and indifference relations?

<p>Strict preference and indifference can be transitive but are not always complete. (A)</p> Signup and view all the answers

Explain why a preference relation can be reflexive but not complete.

<p>A preference relation can specify preferences only for individual items without comparing them to others.</p> Signup and view all the answers

Match the terms with their definitions:

<p>Transitivity = If x is preferred over x0 and x0 over x00, then x is preferred over x00 Reflexivity = An element x is always comparable to itself Completeness = For any two alternatives, one must be preferred, or they are indifferent Rationality = Consumers can consistently rank alternatives.</p> Signup and view all the answers

If a preference relation is complete, then for every pair of bundles x and x0, one of the following must hold: (a) x x0, (b) x0 x, or (c) x x0. This illustrates the concept of _______ in consumer theory.

<p>completeness</p> Signup and view all the answers

What does it mean for preferences to be strictly monotonic?

<p>More of one good is always preferred if the other good is unchanged. (B)</p> Signup and view all the answers

Local non-satiation is a stronger axiom than strict monotonicity.

<p>False (B)</p> Signup and view all the answers

What graphical effect does local non-satiation have on indifference curves?

<p>It removes the thick portions from the indifference sets.</p> Signup and view all the answers

Preferences that are _____ monotonic are weakly monotonic.

<p>strictly</p> Signup and view all the answers

Match the types of monotonicity with their definitions:

<p>Strictly monotonic = More of one good is strictly preferred Weakly monotonic = More of one good is preferred or indifferent Locally non-satiated = No thick portions in indifference curves Strictly convex = Combining bundles is strictly preferred</p> Signup and view all the answers

Which statement best describes strictly convex preferences?

<p>A consumer prefers combinations of bundles. (D)</p> Signup and view all the answers

Weak monotonicity is strictly stronger than local non-satiation.

<p>True (A)</p> Signup and view all the answers

What is the implication of weak monotonicity on indifference curves?

<p>Indifference curves cannot intersect.</p> Signup and view all the answers

Which set represents the bundles that are considered at least as good as a bundle x?

<p>At least as good set %(x) (A)</p> Signup and view all the answers

The preferred to set (x) and the indifference set (x) can contain the same bundles.

<p>False (B)</p> Signup and view all the answers

What is the relationship between the 'at least as good' set %(x) and the 'preferred to' set (x)?

<p>The at least as good set %(x) is equal to the union of the preferred to set (x) and the indifference set (x).</p> Signup and view all the answers

The set of bundles that are considered worse than a bundle x is called the ______ set.

<p>worse than</p> Signup and view all the answers

What is true about the set of bundles that can be included in both (x) and (x)?

<p>They are disjoint sets. (B)</p> Signup and view all the answers

If a bundle x0 belongs to the 'not better than' set -(x), it means x0 is better than x.

<p>False (B)</p> Signup and view all the answers

Explain in your own words what bundles are included in the 'indifference' set (x).

<p>Bundles in the indifference set (x) are those that are considered equal in preference to bundle x.</p> Signup and view all the answers

Flashcards

Consumption Bundle (x)

A collection of goods that a consumer considers buying.

Consumption Set (X)

A set of all possible consumption bundles that a consumer can choose from.

Price Vector (p)

A specific set of prices for each good available in the consumption set.

Consumer's Income (m)

The total amount of money a consumer has to spend on goods.

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Budget Set (B)

The set of all possible consumption bundles that a consumer can afford to buy given their income and prices.

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Budget Constraint (p1x1 + p2x2 ≤ m)

An equation that represents the maximum amount of money a consumer can spend to buy a given bundle while using their entire income.

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Budget Line

A straight line that shows all the consumption bundles that can be purchased when the consumer spends all their income.

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Slope of the Budget Line (-p1/p2)

The negative ratio of the prices of the two goods, representing the rate at which one good can be exchanged for the other.

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Transitivity of Preferences

Preferences are transitive when, if we prefer one option over another, and that second option over a third, we must also prefer the first option over the third.

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Rationality in Consumer Theory

Rationality in consumer theory means that consumers have consistent and non-contradictory preferences. They know what they like and can rank their choices.

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Reflexive Preference Relation

A preference relation is reflexive if a consumer is indifferent between choosing a good and choosing the same good again.

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Complete Preference Relation

A preference relation is complete if, for any two goods, the consumer either prefers one over the other or is indifferent between them.

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Completeness and Preference Pairs

If a preference relation is complete, for any two goods, either one is preferred over the other, the other is preferred, or the consumer is indifferent.

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Transitivity and Completeness of Strict and Indifference Preferences

Both the strict preference relation and the indifference relation are transitive if the overall preference relation is rational, but neither is complete.

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Transitive Strict and Indifference Preferences

For both the strict preference relation and the indifference relation to be transitive, the overall preference relation must be rational.

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Rationality and Best Choice

Rationality is a crucial assumption in consumer theory because it allows consumers to consistently rank all alternatives and identify the best choice.

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Preference Relation

A consumer's preference over bundles that specifies which bundles are considered at least as good as others.

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x % x0

Indicates that bundle x is at least as preferred as bundle x0.

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x % / x0

Means that bundle x is not at least as preferred as x0.

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x x0

Means that bundle x is strictly preferred to bundle x0 if x is at least as preferred as x0, and x0 is not at least as preferred as x.

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x ∼ x0

Means that the consumer is indifferent between bundles x and x0 if both are at least as preferred as the other.

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What is a preference relation in consumer choice?

A relation that defines which bundles are considered at least as good as others. It's a way to capture a consumer's preferences between different goods and services.

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Explain the different symbols used to represent preference relations.

A consumer's preference relation can be represented by different symbols depending on the type of preference. For example, x % x0 indicates that bundle x is at least as preferred as bundle x0. x % / x0 means that bundle x is not at least as preferred as x0. x x0 means that x is strictly preferred to x0. Finally, x ∼ x0 indicates that the consumer is indifferent between the two.

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Why is it important to understand the relationship between the bundles and the preference relation?

To determine a consumer's preferences, we need to consider the relationship between the bundles and their preference relation. For example, if a consumer has a preference relation % and they prefer bundle x at least as much as bundle x0 (x % x0), it signifies that they are indifferent between x and x0 or they prefer x.

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Strictly Monotonic Preferences

A preference relation where bundles with more of at least one good, and no less of the other, are strictly preferred. If you have more of one good, and at least as much of the other, you definitely like it better.

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Weakly Monotonic Preferences

A preference relation where bundles with more of at least one good, and no less of the other, are weakly preferred, or indifferent. If you have more of one good, and at least as much of the other, you either like it better or are indifferent.

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Locally Non-Satiated Preferences

A preference relation where for any chosen bundle, you can always find another bundle nearby which is strictly preferred. You can always get a little bit of that 'extra' you want.

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Convex Preferences

A preference relation where combinations of bundles are weakly preferred to the original bundles. If you combine two equally preferred bundles, you'll get a bundle that's at least as good.

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Strictly Convex Preferences

A preference relation where combinations of bundles are strictly preferred to the original bundles. If you combine two equally preferred bundles, you'll get a bundle that's definitely better.

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Strongly Monotonic Preferences

A preference relation that is both strictly monotonic and convex. This is the most common type of preference studied in microeconomics.

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Indifference Curve

The set of all bundles that are indifferent to a given bundle. All bundles on the indifference curve are equally preferred by the consumer.

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Indifference Map

The graphical representation of a preference relation. It shows the indifference curves for different levels of satisfaction.

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At least as good set (%(x))

A set containing all bundles in R2+ that are considered at least as good as a given bundle x. This includes bundles that are either preferred to x or are indifferent to x.

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Not better than set (-(x))

A set containing all bundles in R2+ that are not better than a given bundle x. This might include bundles that are strictly worse than x or indifferent to x.

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Preferred to set ((x))

A set containing all bundles in R2+ that are strictly preferred to a given bundle x.

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Worse than set (≺(x))

A set containing all bundles in R2+ that are strictly worse than a given bundle x.

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Indifference set (∼(x))

A set containing all bundles in R2+ that are indifferent to a given bundle x.

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Partitioning of R2+

The strict preference relation and the indifference relation partition all bundles in R2+ in a way that every bundle belongs to either the 'preferred to' set or the 'indifference' set, and never both. This ensures that every bundle's relationship to a given bundle is clearly defined either as 'preferred' or 'indifferent'.

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Relationship between 'at least as good' and other sets

The 'at least as good' set (%(x)) is equal to the union of the 'preferred to' set ((x)) and the 'indifference' set (∼(x)). This means that all bundles considered at least as good include both those preferred and those indifferent to a given bundle.

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Disjointness of 'preferred to' and 'indifference' sets

The 'preferred to' set ((x)) and the 'indifference' set (∼(x)) are disjoint, meaning they don't share any common bundles. This implies that no bundle can be both 'preferred' and 'indifferent' to a given bundle.

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Bad (in economics)

A good that a consumer would prefer to have less of, rather than more. This is seen as something undesirable, unlike typical goods.

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Non-Monotonic Preferences

Preferences are not monotonic when a consumer prefers less of a good rather than more, and the indifference curves slope upwards.

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Diminishing Marginal Utility (with bads)

This occurs when consuming more of a good results in a decrease in satisfaction, even if the consumer has more of it.

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Bliss Point

When a consumer has a maximum point of satisfaction for goods, beyond which consuming more of the good makes them worse off.

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Preferences with Two Bads

This describes the situation where a consumer prefers less of both goods, leading to indifference curves closer to the origin.

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Preferred To Set

The set of all possible consumption bundles that a consumer prefers over the current bundle (x)

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Saturation Point

The point where a consumer has reached their maximum satisfaction level, and consuming more leads to lower satisfaction.

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Non-Monotonic and Non-Satiated Preferences

Preferences that violate both monotonicity and local non-satiation, meaning a consumer may desire less of a good as they consume more.

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Study Notes

Course Information

  • Course title: Microeconomics II
  • Instructors: Shaun Grimshaw, Max Posch, and Alejandro Robinson-Cortés
  • Institution: University of Exeter
  • Term: Autumn 2024
  • Week: 2

Contents

  • Introduction (pages 5-7)
    • Models and mathematics
    • Desirable allocations (efficiency and fairness)
    • How to use the notes
  • Budget Sets (pages 10-16)
    • Consumption Sets, Bundles, and Budget Sets
    • Changes in Prices and Income
    • Policies Affecting Budget Sets
      • Per-unit and ad-valorem taxes and subsidies
      • Lump-sum taxes and rationing
      • Non-linear taxes and subsidies
      • Vouchers
  • Preferences (pages 18-30)
    • Preference Relations
    • Axioms of Consumer Theory
      • Rational Preferences (completeness and transitivity)
      • Visualizing Preferences
      • Local Non-satiation and Monotonicity
      • Convexity
      • Well-behaved Preferences
    • Goods, Bads, and Bliss Points
    • Marginal Rate of Substitution
  • References (page 34)
  • Glossary (page 35)

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