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 ($u(t,c) = t^2 c^3$)

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.