Marginal Utility of Free Time
The marginal utility of free time measures the rate of change in a person's utility from an incremental increase in free time (), while holding consumption () constant. In calculus terms, this is given by the partial derivative of the utility function with respect to free time, denoted as .
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Introduction to Microeconomics Course
The Economy 2.0 Microeconomics @ CORE Econ
Ch.3 Doing the best you can: Scarcity, wellbeing, and working hours - The Economy 2.0 Microeconomics @ CORE Econ
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Marginal Utility of Free Time
Marginal Utility of Consumption
Calculus-Based Methods for Analyzing Indifference Curves
Specificity of Partial Derivative Expressions to the Utility Function
An individual's satisfaction from consuming a quantity 'c' of goods and enjoying 't' hours of free time is represented by the utility function U(c, t) = c^2 * t^3. What is the expression for the marginal utility of consumption (c)?
Calculating Marginal Utility of Free Time
Consumer Choice Analysis
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.
Match each utility function, which describes an individual's satisfaction from consuming a quantity 'c' of goods and enjoying 't' hours of free time, with its corresponding expression for the marginal utility of free time.
Evaluating Claims about Marginal Utility
Analyzing Diminishing Marginal Utility
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.
Learn After
An individual's satisfaction from consumption (c) and free time (t, measured in hours) is represented by the utility function U(c, t) = c * t². If this individual currently has 10 units of consumption and 5 hours of free time, what is the approximate change in their utility from one additional hour of free time?
An individual's satisfaction is described by the utility function U(c, t) = 5c + √t, where 'c' represents units of consumption and 't' represents hours of free time. According to this function, the additional satisfaction gained from one extra hour of free time is the same whether the individual currently has 4 hours or 9 hours of free time.
Interpreting Marginal Utility of Free Time
Comparing Preferences for Free Time
Match each utility function, which depends on consumption (c) and free time (t), with its corresponding mathematical expression for the marginal utility of free time.
Analyzing Preferences for Free Time
An individual's preferences for consumption (c) and free time (t) are represented by the utility function U(c, t) = √c * √t. If the individual currently has 100 units of consumption and 25 hours of free time, the marginal utility of an additional hour of free time is ____.
An individual's satisfaction is represented by the utility function U(c, t) = 10c + t³, where 'c' is consumption and 't' is hours of free time. The individual currently has 4 hours of free time. Arrange the following steps in the correct logical order to find and interpret the marginal utility of an additional hour of free time.
An economist models a person's satisfaction with consumption (c) and free time (t) using the utility function U(c, t) = 10c * (40t - t²), where 't' is hours of free time per week. This model suggests that beyond a certain point, having too much unstructured free time can lead to boredom and decreased satisfaction. At what point does an additional hour of free time start to decrease this person's total utility, assuming consumption is held constant?
An individual's preferences are such that each additional hour of free time adds to their overall satisfaction, but each successive hour provides less additional satisfaction than the previous one. For example, the fifth hour of free time is less valuable to them than the fourth. Which of the following utility functions, where 'c' is consumption and 't' is hours of free time, best represents this individual's preferences?