Cobb-Douglas Utility Function
The Cobb-Douglas utility function is a specific mathematical form that can be used to represent an individual's preferences, for example as an alternative utility function for Karim. It is given by the formula , where the exponents and are positive constants. This function is noted for having convenient mathematical properties, making it common in economic analysis. It is named after the two people who introduced the function to the field of economics.
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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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Cobb-Douglas Utility Function
Utility Function of Karim's Friend
Utility Function of Angela's Friend (u(t, c) = c + 75 ln(t))
An economist is modeling the preferences of two consumers, Priya and Quinn, for two goods: digital music tracks (m) and physical books (b). Priya's preferences are represented by the utility function U_P(m, b) = 2m + b. Quinn's preferences are represented by the utility function U_Q(m, b) = m * b. What fundamental difference in their consumption preferences do these two functions reveal?
Modeling Consumer Preferences for Complementary Goods
An economist is modeling a consumer's preferences for two goods: weekly hours of a video streaming service (s) and cups of gourmet coffee (c). The consumer's description of their preferences indicates that each additional cup of coffee provides a consistent, fixed amount of satisfaction. In contrast, the first few hours of streaming provide a great deal of enjoyment, but each subsequent hour provides progressively less additional satisfaction. Which of the following utility functions would be the most appropriate model for this consumer's preferences?
Evaluating Utility Function Models
Modeling Preferences for Public Goods
An economist is modeling consumer preferences for two goods, Good X and Good Y. Match each of the following mathematical utility functions to the description of consumer preferences it best represents.
Interpreting a Utility Function for Complementary Goods
Formulating a Utility Function for Perfect Complements
Choosing a Utility Model for Urban Amenities
Evaluating a Utility Function for Urban Planning
Learn After
Simplifying the Marginal Utility of Free Time for a Cobb-Douglas Function
Positive Parameters in Cobb-Douglas Function and Positive Marginal Utility
Hypothetical Cobb-Douglas Utility Function for Karim ()
Yvonne's Hypothetical Utility Function
Consider two individuals, Priya and David, whose preferences for goods X and Y are represented by the following utility functions:
- Priya: U(X, Y) = X^0.3 * Y^0.7
- David: U(X, Y) = X^0.6 * Y^0.4
Based on these functions, which of the following statements accurately compares their preferences?
Consumer Preference Analysis
Calculating Utility with a Cobb-Douglas Function
Consider a utility function of the form u(x,y) = x^α * y^β, where x and y represent quantities of two different goods, and the exponents α and β are positive constants. If the exponent α is greater than the exponent β, this implies that the consumer has a stronger relative preference for good x compared to good y.
Interpreting the Parameters of a Cobb-Douglas Utility Function
For a utility function of the form u(x,y) = x^α * y^β, where x and y are quantities of two goods and α and β are positive constants, match each component or relationship with its correct economic interpretation.
A utility function of the form u(x,y) = x^α * y^β, where x and y are quantities of two goods and α and β are positive constants, is used to represent a consumer's preferences. This type of function provides an ordinal measure of utility, meaning it is used for the ________ of consumption bundles rather than measuring the absolute magnitude of satisfaction.
A consumer's preferences for two goods, Good A and Good B, are represented by a utility function of the form U(A, B) = A^α * B^β. To determine the rate at which this consumer is willing to trade Good B for one more unit of Good A while keeping their total satisfaction constant, a specific ratio must be calculated. Arrange the following steps in the correct logical order to derive this ratio.
A consumer's preferences for two goods, X and Y, are represented by the utility function U(X, Y) = X^0.2 * Y^0.8. Which of the following utility functions represents the exact same preferences?
Analyzing Preferences for Consumption Bundles
Consider a utility function of the form u(x,y) = x^α * y^β, where x and y represent quantities of two different goods, and the exponents α and β are positive constants. If the exponent α is greater than the exponent β, this implies that the consumer has a stronger relative preference for good x compared to good y.