Property of Utility Functions: More is Better

Utility Function as a 3D Surface

Calculating Marginal Utilities Using Partial Differentiation

An individual's preferences for consumption (represented by c) and free time (represented by t) are captured by the utility function U(t, c) = t * c. Which of the following combinations of free time and consumption provides the individual with the highest level of utility?

Interpreting a Utility Function

An individual's preferences are modeled using the general utility function U(t, c), where preferences depend on free time (t) and consumption (c). Match each component of this model to its correct description.

In a model where an individual's preferences are described by the function U(t, c), where 't' is free time and 'c' is consumption, the value of U represents the combined monetary cost of the consumption and the free time.

Modeling Preferences with Utility Functions

In a model of preferences for consumption (c) and free time (t), the function U(t, c) assigns a numerical value to each combination of these two goods. This numerical value represents the individual's level of __________.

The Role of the Utility Function in Economic Modeling

An individual uses a utility function, U(t, c), to model their preferences between different combinations of free time (t) and consumption (c). Arrange the following steps in the logical order required to use this function to compare two different combinations.

An economist is modeling the preferences of two individuals for consumption (c) and free time (t). Individual A's preferences are represented by the function U_A(t, c) = t + c, while Individual B's preferences are represented by U_B(t, c) = t * c. What key difference in their underlying preferences do these two functional forms reveal?

An individual describes their preferences for free time (t, measured in hours) and consumption (c, measured in dollars) as follows: 'I only derive satisfaction when I have them in a specific combination. For every 1 hour of free time I enjoy, I must have $20 worth of consumption. Having more of one without a proportional amount of the other adds no extra utility to me.' Which of the following utility functions, U(t, c), best captures this individual's preferences?

An individual's preferences for consumption (represented by c) and free time (represented by t) are captured by the utility function U(t, c) = t * c. Which of the following combinations of free time and consumption provides the individual with the highest level of utility?

Interpreting a Utility Function

In a model of individual choice, the function U(t, c) is used to calculate the exact monetary value an individual places on their combined satisfaction from free time (t) and consumption (c).

In a model of individual choice, preferences are represented by the function U(t, c). Match each component of this model to its correct description.

Analyzing the Structure of a Utility Function

In a model where an individual's preferences are described by the function U(t, c), the variables t and c represent the quantities of free time and consumption, respectively. The output of this function, U, represents the individual's level of ________.

Modeling Preferences with a Utility Function

A microeconomic model is built to represent an individual's preferences for two desirable items: consumption and free time. Arrange the following statements into the logical order that describes how these preferences are formally represented as a mathematical relationship.

An economist proposes the function U(t, c) = 2t + 5c to model an individual's preferences for free time (t) and consumption (c). A critic argues this function is a poor representation of how most people value these two items. Which of the following statements best supports the critic's argument?

Consider an individual whose satisfaction depends solely on their level of consumption (c) and is completely unaffected by the amount of free time (t) they have. The function U(t, c) = t + c accurately represents this individual's preferences.