Calculating Marginal Utilities Using Partial Differentiation
Partial differentiation is the mathematical method used to find the marginal utility of a specific good. The process involves calculating the partial derivative of the overall utility function with respect to the variable representing a single good, while treating all other variables as constants.
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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.
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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
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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).
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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 (
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An individual is consuming slices of pizza, and their total satisfaction from consumption is measured in 'utils' as shown in the table below. What is the additional satisfaction gained from consuming the fourth slice of pizza?
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As a person consumes more and more units of a specific good, the total satisfaction they receive generally increases, but the additional satisfaction gained from each new unit tends to decrease. The economic term for this additional satisfaction from consuming one more unit is known as __________.
A hiker is consuming energy bars on a long trail. The table below shows the total satisfaction (utility) they receive from eating a certain number of bars. Arrange the following consumption choices in order, from the one that provides the most additional satisfaction to the one that provides the least.
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An individual's satisfaction from consuming a quantity 'c' of goods and enjoying 't' hours of free time is described by the utility function U(c, t) = 5c + 2√t. Based on this function, which of the following statements is true?
An individual's preferences for consumption (c) and free time (t) are described by the utility function U(c, t) = 10 * ln(c) + 5t. What is the marginal utility of free time (t)?
Consider an individual whose preferences for consumption (c) and free time (t) are represented by the utility function U(c, t) = 2c + 10√t. For this individual, the additional satisfaction gained from one more hour of free time is always greater than the additional satisfaction gained from one more unit of consumption, regardless of their current amounts of consumption and free time.
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Consider an individual's preferences for consumption (c) and free time (t) represented by the utility function U(c, t) = 4c^0.5 * t^0.5. A student calculates the marginal utility of consumption and claims it is equal to 2c^-0.5. This claim is correct.