Rational Choice in Economics

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Questions and Answers

Which equation represents the indifference curve when the utility function is set to a utility level of 30 for U = 2x + 4y?

y = 15 - x

y = 30 - 4x

y = 30 - 2x

y = 7.5 - 0.5x (correct)

What does MRS stand for in the context of indifference curves?

Market Rate of Substitution

Maximum Rate of Substitution

Minimum Rate of Substitution

Marginal Rate of Substitution (correct)

In the equation U = x^(1/2)y^(1/2), which variable would be isolated to derive an indifference curve for various utility levels?

Both x and y

y (correct)

What shape does the indifference curve take when the utility function is linear, such as U = 2x + 4y?

Straight line Signup and view all the answers

If we set the utility level Ū to a higher value in the equation U = 2x + 4y, what can we expect about the position of the resulting indifference curve?

It will shift outward away from the origin. Signup and view all the answers

What is the correct interpretation of the utility values for ice cream cones and pizza?

Ice cream cones are preferred because they provide higher utility. Signup and view all the answers

Which utility function does NOT preserve the original preference ordering?

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

Which transformation preserves the preference ordering of the original utility function?

f(x) = ln(x) Signup and view all the answers

What is indicated by the utility function U(N, V) = -N V^2?

It requires a decreasing transformation to maintain preferences. Signup and view all the answers

Which of the following combinations corresponds to the preference ordering D ≽ C ≽ B ≽ A ∼ E?

(4, 0), (3, 1), (2, 2), (1, 3), (0, 4) Signup and view all the answers

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

Any monotonically increasing transformation. Signup and view all the answers

Which of the following utility functions is regarded as preserving the same preference order as the original function?

U(N, V) = N V^2 + 10 Signup and view all the answers

Which utility function shows a relationship that is likely to create confusion regarding preference?

U(N, V) = N(V - 1) Signup and view all the answers

What does the completeness axiom imply about consumer preferences?

Consumers must always be able to compare any two choices. Signup and view all the answers

What does the transitivity axiom imply in consumer choice?

If A is preferred to B and B is preferred to C, then A must be preferred to C. Signup and view all the answers

Which of the following statements about rationality in consumer choice is true?

Rationality ensures that a consumer's choices are internally consistent. Signup and view all the answers

In the notation used for consumer choice, what does A ∼ B signify?

A is indifferent to B. Signup and view all the answers

Which of the following best describes the concept of utility functions in the context of choice theory?

Utility functions assign a numerical value to consumer preferences. Signup and view all the answers

What is the purpose of indifference curves in consumer choice theory?

To show combinations of goods that provide the same level of satisfaction. Signup and view all the answers

How is the marginal rate of substitution defined in relation to consumer choice?

The rate at which a consumer can give up some quantity of one good in exchange for another good while maintaining the same level of utility. Signup and view all the answers

Which of the following is NOT a characteristic of rational consumer choice?

Consumers avoid making mistakes in their choices. Signup and view all the answers

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

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

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

4 Signup and view all the answers

If the MRS for goods x and y is 1/2, how much of good y would a consumer need to compensate for a loss of one unit of good x?

0.5 units of y Signup and view all the answers

What does a constant MRS indicate about a consumer's preferences?

The consumer values both goods equally. Signup and view all the answers

When given the utility function U(x, y) = x^(1/2) * y^(1/2), how is the MRS calculated?

MRS = (1/2)x^(-1/2)y^(1/2) / (1/2)x^(1/2)y^(-1/2) Signup and view all the answers

If a consumer increases x by 1 unit and decreases y by 0.5 units, what can be inferred about their MRS if their utility remains constant?

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

In the example given, if the consumer's basket (5, 5) provides a utility of 30, what new basket (x, y) can provide the same utility if x decreases by 1?

(4, 5.5) Signup and view all the answers

What key aspect is indicated by the marginal utility when considering consumer preferences?

The additional satisfaction gained from consuming one more unit of a good. Signup and view all the answers

What happens to the marginal rate of substitution (MRS) as the quantity of good x increases relative to good y?

The MRS decreases. Signup and view all the answers

Which statement best describes convexity in the context of the given utility function?

The marginal utility of good x falls relative to good y with increased consumption. Signup and view all the answers

If a consumer has an MRS of 1, what does this imply about their consumption of goods x and y?

They are indifferent between an additional unit of x or y. Signup and view all the answers

What does an increase and movement up and to the right on an indifference curve signify?

Increased utility from consuming more x and more y. Signup and view all the answers

In the context of indifference curves, what does the slope of the curve represent?

The marginal rate of substitution (MRS). Signup and view all the answers

What is indicated by convex indifference curves?

Diminishing marginal returns in consumption. Signup and view all the answers

When moving down and to the left on an indifference curve, what occurs?

Utility decreases with a decrease in both goods. Signup and view all the answers

What characteristic of the utility function is highlighted in the relationship between goods x and y?

The MRS is equal to the ratio of y to x. Signup and view all the answers

Study Notes

Rational Choice

The concept of rationality in economics is distinct from its everyday meaning.
For a choice to be considered rational, it must be consistent with the individual's preferences, even if the choice isn't "ideal".
Consumers are assumed to have preferences that are complete (able to compare any two choices) and transitive (if A is preferred to B and B is preferred to C, then A is preferred to C).

Utility Functions

Utility functions represent individual preferences over different choices.
A higher value in a utility function indicates a higher level of preference.
Utility functions are not unique. Multiple functions can represent the same preference ordering.
Valid transformations of utility functions must be monotonically increasing. This means the transformation must always preserve the order of preferences.

Marginal Rate of Substitution (MRS)

MRS represents the rate at which a consumer is willing to trade one good for another while maintaining the same level of utility.
It is calculated as the ratio of the marginal utilities of the two goods.
The MRS can be interpreted as the amount of one good required to compensate for a decrease in the other good.

Indifference Curves

Indifference curves plot all combinations of two goods that provide the same level of utility for a consumer.
The slope of an indifference curve at any point is equal to the negative of the MRS at that point.
Convex indifference curves show that as a consumer consumes more of one good, the marginal utility of that good decreases relative to the other good. The consumer is willing to trade less of the other good for an additional unit of the good they have more of.

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Description

This quiz explores the concept of rational choice in economics, focusing on how individual preferences are characterized. It covers utility functions, the marginal rate of substitution, and the principles guiding rational decision-making. Test your understanding of these fundamental concepts in economic theory.