Evaluating Competing Economic Models
You are a senior analyst reviewing the work of two junior economists, Alice and Ben. They were both tasked with modeling a single consumer's preferences for two goods, Pizza (P) and Soda (S), based on the same observational data. The quantities of both goods are always positive.
Alice's model uses the utility function: U_A(P, S) = P²S Ben's model uses the utility function: U_B(P, S) = 2*ln(P) + ln(S) - 10
Alice and Ben have reached different conclusions about how to price a new combo meal. Before proceeding, you must first evaluate their models. Will these two utility functions lead to the same predictions about how this consumer ranks different bundles of Pizza and Soda? Justify your conclusion by analyzing the mathematical relationship between the two functions.
0
1
Tags
CORE Econ
Economics
Social Science
Empirical Science
Science
Economy
Introduction to Microeconomics Course
The Economy 2.0 Microeconomics @ CORE Econ
Related
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