Karim's Specific Utility Function
Karim's preferences for free time () and consumption () are mathematically represented by the specific utility function . This function provides the basis for plotting the indifference curves illustrated in Figure E3.1. Beyond its use in graphical representation, this function also serves other analytical purposes, such as calculating the marginal utilities for both goods to determine his Marginal Rate of Substitution (MRS) and algebraically verifying the convexity of his indifference curves.
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An individual's preferences for consumption (represented by
c) and free time (represented byt) are captured by the utility functionU(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 functionU(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 functionU_A(t, c) = t + c, while Individual B's preferences are represented byU_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 byt) are captured by the utility functionU(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
tandcrepresent 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 + 5cto 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 functionU(t, c) = t + caccurately represents this individual's preferences.Karim's Specific Utility Function
Learn After
Subsistence Levels in Karim's Utility Function
Calculating Karim's Utility at Point E
Figure 3.7a - Diagram of Karim's Optimal Choice at a €30 Wage
An individual's preferences for hours of daily free time (t) and units of consumption (c) are described by the utility function u(t,c) = (t-6)²(c-45). The individual is currently at a point where they have 16 hours of free time and 55 units of consumption. Which of the following alternative bundles would this individual prefer to their current situation?
Interpreting Utility Function Parameters
An individual's preferences for daily hours of free time (t) and units of consumption (c) are represented by the utility function u(t, c) = (t - 6)²(c - 45). What does this specific functional form imply about the individual's underlying preferences?
An individual's preferences for daily free time (t) and consumption (c) are represented by the utility function u(t, c) = (t - a)² * (c - b), where 'a' and 'b' are positive constants representing minimum required levels of free time and consumption, respectively. For any combination where t > a and c > b, what happens to this individual's willingness to give up consumption for an additional hour of free time as their amount of free time increases (while keeping their overall satisfaction level constant)?
An individual's preferences for daily hours of free time (t) and units of consumption (c) are represented by the utility function u(t, c) = (t - 6)²(c - 45). Consider the consumption bundle where t=20 and c=40. Which of the following statements most accurately describes the individual's assessment of this bundle based on the given utility function?
To algebraically verify that the indifference curves for the utility function u(t, c) = (t - 6)²(c - 45) are convex (i.e., they bow inwards toward the origin), a specific sequence of mathematical steps is required. Arrange the following key steps of this procedure into the correct logical order.
Evaluating the Realism of a Utility Function
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Calculating the Marginal Rate of Substitution
An individual's preferences for daily hours of free time (t) and units of consumption (c) are represented by the utility function u(t, c) = (t - 6)²(c - 45). At the point where the individual has 16 hours of free time and 55 units of consumption, what is the value of their Marginal Rate of Substitution (the rate at which they are willing to trade consumption for an additional hour of free time)?
Figure E3.1: Mapping Karim's Preferences
Algebraic Verification of Convexity for Karim's Preferences
Formula for Karim's Marginal Rate of Substitution (MRS)