Property of Utility Functions: More is Better
A fundamental property of a utility function for goods is that it must reflect the 'more is better' principle. This means that if both free time () and consumption () are desirable, any increase in the quantity of or , while holding the other constant, will result in an increase in the total utility value ().
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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 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.
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Condition for an Increasing Utility Function
An individual's well-being is determined by two desirable things: hours of free time and units of consumption. A fundamental assumption is that their well-being increases if they get more of one of these things without having less of the other. If this individual currently has a combination of 20 hours of free time and 100 units of consumption, which of the following new combinations would unambiguously result in a higher level of well-being based only on the information provided?
Preference Consistency Analysis
Evaluating a Utility Scenario
Consider an individual whose satisfaction depends on two desirable goods: apples and oranges. According to the principle that 'more is better', this individual can be equally satisfied with a bundle of 15 apples and 10 oranges as they are with a bundle of 15 apples and 11 oranges.
An individual's satisfaction depends on two desirable goods: weekly consumption () and daily hours of free time (). Their current situation is represented by the bundle (c=500, t=10). Match each of the following new bundles of goods to the statement that correctly describes the change in the individual's satisfaction relative to their current situation, based only on the principle that 'more is better'.
An individual's satisfaction is determined by the quantities of two desirable goods they consume: concert tickets and restaurant meals. They currently have a bundle A, consisting of 5 tickets and 10 meals. They are then presented with a new bundle B, consisting of 5 tickets and 12 meals. The level of satisfaction from bundle B will be ______ than the level of satisfaction from bundle A.
The 'More is Better' Assumption in Economic Models
Evaluating a Proposed Satisfaction Model
An individual's satisfaction is determined by two desirable goods: weekly hours of leisure and weekly income. Their current situation is Bundle X: 15 hours of leisure and $400 of income. Consider three alternative bundles: Bundle A (15 hours, $450), Bundle B (14 hours, $400), and Bundle C (16 hours, $350). Based only on the principle that more of a desirable good is better, which statement correctly describes the relationship between these bundles?
An individual's satisfaction is derived from two desirable goods: digital music albums and streaming movie subscriptions. Based only on the principle that having more of a desirable good is always better, arrange the following bundles from the one that provides the least satisfaction to the one that provides the most satisfaction.