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Utility Function Transformations and Preference Invariance
Since utility is an ordinal measure used for ranking, the underlying preferences and corresponding indifference curves remain unchanged even if the utility function undergoes a monotonic transformation (a transformation that preserves the order of the values). For instance, multiplying a utility function by any positive constant will produce different utility values for the same bundles but will result in the exact same indifference map and represent the same consumer preferences.
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Introduction to Microeconomics Course
The Economy 2.0 Microeconomics @ CORE Econ
Ch.3 Doing the best you can: Scarcity, wellbeing, and working hours - The Economy 2.0 Microeconomics @ CORE Econ
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Utility Function Transformations and Preference Invariance
An economist models a consumer's preferences for two different bundles of goods, Bundle X and Bundle Y. The consumer's utility function assigns a value of 30 to Bundle X and a value of 60 to Bundle Y. Based solely on the principle that utility is an ordinal measure, what is the most accurate conclusion that can be drawn?
Evaluating a Business Decision Based on Utility Scores
A consumer reports that their utility for an apple is 10 and their utility for a banana is 20. Based on the ordinal interpretation of utility, this means the consumer desires the banana exactly twice as much as the apple.
An individual's preferences for goods A and B can be represented by the utility function U1 = A * B. A second utility function, U2 = 10 * (A * B) + 5, is also proposed to represent the same individual's preferences. Which of the following statements correctly analyzes the relationship between these two functions from an ordinal utility perspective?
Interpreting Utility Values
A consumer's preferences for three different market baskets, A, B, and C, are represented by a utility function. The function assigns the following values: Utility(A) = 100, Utility(B) = 200, and Utility(C) = 250. Based strictly on the ordinal nature of utility, what is the most accurate interpretation of these values?
Critiquing a Welfare Argument
Evaluating a Policy Argument on Utility
For each statement below regarding a consumer's utility from different bundles of goods, match it to the type of utility interpretation it represents.
Analyzing a Flawed Economic Conclusion
Learn After
Consider two different utility functions for a consumer who consumes two goods, x and y: U₁(x, y) = x²y and U₂(x, y) = 2ln(x) + ln(y). Assuming the quantities of both goods are positive, which of the following statements accurately describes the relationship between the preferences represented by these two functions?
Comparing Consumer Choices
Demonstrating Preference Equivalence
A consumer's preferences for two goods (x and y, where quantities are positive) can be represented by the utility function U₁(x, y) = xy. It follows that this consumer prefers the bundle (4, 3) over the bundle (2, 5).
True or False: If this same consumer's preferences were instead represented by the utility function U₂(x, y) = 10 - (1/xy), they would prefer the bundle (2, 5) over the bundle (4, 3).
A consumer's preferences for two goods, X and Y (where quantities are positive), are represented by a utility function in the left column. Match this original function to the function in the right column that represents the exact same set of preferences (i.e., would result in the same indifference map and the same ranking of any two consumption bundles).
Analyzing Preference Invariance
A consumer's preferences for goods X and Y (with quantities X>0, Y>0) are described by the utility function U(X, Y) = X²Y. For the consumption bundle (10, 5), the marginal rate of substitution (the rate at which the consumer is willing to trade Y for X) is 1.
Now, suppose the same consumer's preferences are instead represented by a different function, V(X, Y) = 0.5 * ln(X²Y) + 20. The marginal rate of substitution for this consumer at the same bundle (10, 5) must be _____.
Comparing Consumer Choice Models
A consumer's preferences for two goods, Apples (A) and Bananas (B), where quantities are always positive, are represented by the utility function U(A, B) = AB. An economist proposes several alternative functions to model this consumer's behavior. Which of the following functions would represent a different set of underlying preferences, meaning it would not result in the same ranking of all possible consumption bundles?
Evaluating Competing Economic Models